quantitative research about learning strategies

ORIGINAL RESEARCH article

How and why do students use learning strategies a mixed methods study on learning strategies and desirable difficulties with effective strategy users.

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Corrigendum: How and Why Do Students Use Learning Strategies? A Mixed Methods Study on Learning Strategies and Desirable Difficulties With Effective Strategy Users

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$\r\nSanne F. E. Rovers*$

School of Health Professions Education, Maastricht University, Maastricht, Netherlands

In order to ensure long-term retention of information students must move from relying on surface-level approaches that are seemingly effective in the short-term to “building in” so called “desirable difficulties,” with the aim of achieving understanding and long-term retention of the subject matter. But how can this level of self-regulation be achieved by students when learning? Traditionally, research on learning strategy use is performed using self-report questionnaires. As this method is accompanied by several drawbacks, we chose a qualitative, in-depth approach to inquire about students' strategies and to investigate how students successfully self-regulate their learning. In order to paint a picture of effective learning strategy use, focus groups were organized in which previously identified, effectively self-regulating students ( N = 26) were asked to explain how they approach their learning. Using a constructivist grounded theory methodology, a model was constructed describing how effective strategy users manage their learning. In this model, students are driven by a personal learning goal, adopting a predominantly qualitative, or quantitative approach to learning. While learning, students are continually engaged in active processing and self-monitoring. This process is guided by a constant balancing between adhering to established study habits, while maintaining a sufficient degree of flexibility to adapt to changes in the learning environment, assessment demands, and time limitations. Indeed, students reported using several strategies, some of which are traditionally regarded as “ineffective” (highlighting, rereading etc.). However, they used them in a way that fit their learning situation. Implications are discussed for the incorporation of desirable difficulties in higher education.

Introduction

Self-regulated learning (SRL) refers to the “process whereby students activate and sustain cognitions, behaviors and affects, which are systematically oriented toward the attainment of their goals” [( Schunk and Zimmerman, 1994 ), p. 309]. With the enormous increase in available information since the emergence of the Internet ( Arbesman, 2013 ), SRL is becoming increasingly important in modern education. This can be especially daunting for students in a problem-based curriculum, as this approach places high demands on students' independent self-study and individual search for information (e.g., Kirschner et al., 2006 ). Students will need effective self-regulatory strategies in order to successfully navigate this educational landscape. As students often rely on ineffective, surface-level study strategies ( Kornell and Bjork, 2007 ), it is important to understand what constitutes effective strategy use in a problem-based curriculum, and how to improve SRL in students not skilled in self-regulation.

An important concept in this regard is that of “desirable difficulties.” What constitutes as “desirable” when introducing difficulties into the learning process, at least from the students' perspective, will likely depend on the goals they set for learning. Learning goals can include long-term understanding and transfer, or simply a desire to pass an exam. When the aim is simply to pass the test, different learning strategies apply than when the focus is on long-term understanding and transfer. In fact, strategies which have a positive effect on long-term understanding and transfer, may even have a negative effect on learning in the short term and vice versa ( Van Merriënboer et al., 1997 ; Helsdingen et al., 2011 ; Van Merriënboer and Kirschner, 2018 ). However, this short-term achievement will not prepare students for long-term, professional practice ( Boud and Falchikov, 2006 ). From an educational perspective, the focus should therefore be on long-term retention and transfer. Indeed, as defined by Bjork (1994) , creating desirable difficulties when learning refers to the process in which students use effortful learning strategies, with the aim of achieving long-term learning benefits, rather than surface-level strategies which are only effective in the short-term.

The traditional way of measuring students' strategy use is through self-report surveys ( Panadero et al., 2016 ). These studies often reveal that students rely on ineffective strategies when studying. For example, Blasiman et al. (2017) found that over the course of a semester, students often relied on ineffective strategies such as reading notes and rereading text. Similarly, Karpicke et al. (2009) found that while students often rely on rereading strategies, few students use more effective strategies like retrieval practice. One of the drawbacks of this form of measurement is that students are usually confronted with a set of predefined strategy categories to choose from. Authors have raised questions about whether self-report questionnaires are able to gauge students' use of different learning strategies across different contexts and tasks ( Winne and Hadwin, 1998 ; Perry and Winne, 2006 ; Schellings, 2011 ; McCardle and Hadwin, 2015 ), students' ability to recover the required information from their memory ( Perry and Winne, 2006 ), the possibility of socially desirable answers ( Bråten and Samuelstuen, 2007 ), and a potential tendency for students to rate the value they attach to a certain strategy rather than their actual use ( Bråten and Samuelstuen, 2007 ; Bernacki et al., 2012 ). Another possibility is that students use certain strategies to regulate their learning which they do not recognize as belonging to a particular category ( Veenman, 2011 ). Furthermore, it is possible that strategies which are traditionally treated as ineffective by these self-report questionnaires are in fact adapted by students to fit their learning situation and goals in an effective way. These expectations were the basis for exploration in the current study.

In order to overcome these difficulties, a more qualitative, in-depth approach to inquiring about students' use of learning strategies can be worthwhile in order to investigate how students successfully self-regulate their learning. Specifically, this rich form of data collection allows for the description of different contexts and learning tasks, allowing students to distinguish between different learning strategies used in different situations and for different goals, as well as how they potentially use seemingly “ineffective” strategies to adapt to a learning situation or goal. A qualitative approach to inquiry enables students to give more elaborate explanations for as to how and why they use particular strategies, as well as potential variations with regard to varying circumstances. By carefully constructing the questions, it should also be possible to distinguish between the value students attach to different strategies vs. their actual use. Furthermore, students' rich descriptions of their approaches to learning allow the researcher to identify strategies that students would be unable to correctly label in a questionnaire.

As a qualitative approach to data collection, the focus group method can have several advantages over traditional interviews. When using focus groups, participants' interactions with each other can yield insights that would not be possible to obtain with individual interviews ( Kitzinger, 1995 ). In addition to being able to complement each other, participants have the opportunity to respond to each other's answers, making it easier to identify differences between their views. These differences can further be used to clarify the reasons behind participants' views ( Kitzinger, 1994 ). Finally, with regard to social desirability, research has also found that focus groups, when compared to individual interviews, can actually induce participants to take a more critical stance ( Watts and Ebbutt, 1987 ; Kitzinger, 1995 ). What matters here is to create a safe atmosphere for participants in which to express their views ( Kitzinger, 1995 ).

For this study, we chose to focus on effective self-regulators, rather than making a comparison between effective vs. less effective students. Rather than focusing on the factors that influence effective self-regulation and the incorporation of desirable difficulties, the aim of this study was to take a step back and come to a comprehensive picture of what this effectiveness actually looks like.

In summary, in order to acquire more in-depth insight into the variation of students' strategy use and the reasons behind it, these considerations led us to choose a focus group approach to study students' self-regulation and incorporation of desirable difficulties into their learning. We complemented the focus group approach with a traditional learning strategy survey (cf., Hartwig and Dunlosky, 2012 ) to compare and contrast results between approaches and analyze the value of each. The research questions guiding this study were: How do highly effective self-regulating students in a PBL higher-education curriculum approach their learning? How do they incorporate desirable difficulties into this process?

This study took place in the context of the first and second year of the 6-year undergraduate medical program at Maastricht University. This university uses a problem-based learning (PBL) format, in which learning takes place starting from authentic, real-world cases ( Schmidt, 1983 ). Students work on these problems in small tutorial groups, typically consisting of approximately 10–12 students. These tutorial sessions are moderated by a tutor, who is expected to act as a facilitator, rather than as a knowledge transmitter. To structure the PBL process, Maastricht University uses a seven-step model called the Seven-Jump ( Moust et al., 2005 ), consisting of clarification of terms, problem definition, brainstorming about possible explanations to the problem, structuring and analysis of the identified explanations, identification of learning questions, self-study, and post-discussion aimed at integrating individual students' findings. The first five steps take place in one tutorial group session, after which students individually study the literature to answer the learning questions outside the tutorial group. A few days later, the tutorial group gets together again to discuss their findings in the post-discussion, after which the cycle repeats for a new problem. In this curriculum, the academic year is divided into six courses, ranging between four to 8 weeks, each focusing on a specific multidisciplinary topic. At the end of a course, students are tested with an exam focused on the contents of this course (mostly multiple-choice).

Given its emphasis on students' independent literature search and self-study, the PBL format provides a fruitful context for the study of students' use of learning strategies and incorporation of desirable difficulties. Specifically, as students are required to find their own literature and use it to independently answer their learning questions they will need a range of strategies to manage this process and monitor their understanding, leading to a large pool of potential strategies for students to report on. This situation offers a unique potential to gain insight into what constitutes an effective approach.

Participants

In order to come to a picture of effective strategy use and the incorporation of desirable difficulties for students in a PBL curriculum, we used a purposive sampling strategy ( Ritchie et al., 2013 ). At the end of the first year (academic year 2013–2014), mentors of first-year undergraduate medical students were asked to identify students who they perceived to use effective learning strategies (the instructions for the mentors can be found in Appendix A in the Supplementary Material). Sixteen mentors identified 42 students for the study. These students were approached by e-mail to invite them for our study, to be held at the beginning of their second year (academic year 2014–2015). Thirty students (71%) indicated willingness to participate. Two students indicated it would not be possible to be present at the times the focus groups were held. Two students filled out the learning strategy questionnaire (see below) but did not attend the focus groups, and were therefore excluded from further analysis. The final number of students participating in the focus groups was therefore N = 26, of which 20 students were female, ages ranging between 18 and 23 years old (one student did not provide an age). The total number of students enrolled for the tutorial groups at the beginning of Year 2 was 298. Written informed consent was obtained from all participants prior to the start of the study. The study was approved by the ethical review board of the Netherlands Association for Medical Education (file number 402). Students were offered a small monetary gift voucher as a reward for their participation in the study.

Learning Strategy Questionnaire

At least one week prior to the focus groups, students were asked to fill out a learning strategy questionnaire. We adapted the questionnaire used by Hartwig and Dunlosky (2012) to fit our PBL learning situation. Specifically, we adapted the wording of the questionnaire to refer to the tutorial group meetings that students encounter in the PBL setting. Furthermore, rather than asking students whether they do or do not use a specific strategy regularly (using a binary yes/no format), we used a Likert scale asking students how often they use these strategies while studying, ranging from 1 (never) to 5 (every study session). This was also applied to the question of whether students go back to course material after a course has ended, and whether students read study sources more than once. For the questions asking students on what parts of the day they study most and on what parts of the day they study most effectively, “evening” and “late night” were combined into one category (“evening”). Furthermore, the strategy questions were adapted to reflect the ones most relevant for the current educational context.

We dropped the question asking students whether they study more for open questions or multiple-choice questions, as the tests that medical students encounter in the program are mostly multiple-choice. The question of how students decide what to study next was posed as an open question. Finally, in order to reflect the focus of our study, we added four questions: (1) How did you develop the study strategies you are using now (open question, replacing the question if whether students' study strategies were taught to them by a teacher), (2) If you had the time and somebody would explain it to you, would you want to change your study strategies (yes/no), (3) What and why would you then want to change (open question), and (4) What kind of education would you most appreciate to change your study strategies? Think about: lectures, videos, practice with a trainer, etc. (open question). Finally, we added a question asking students for any further comments they may have. All questions not rated on a Likert scale (open questions and study times) were thematically coded by two raters. Inconsistencies were discussed until consensus was reached.

With this questionnaire we attempted to obtain a baseline measure of students' strategy use ( what are the strategies that are used), to later complement this with the in-depth focus groups ( how are the strategies used). In summary, the adapted questionnaire consisted of 10 questions assessing students' strategy use, using a Likert scale ranging from 1 (never) to 5 (every study session), as well as one question allowing students to list other strategies they use during studying. Furthermore, there were 12 questions inquiring about additional aspects of students' study behavior, for example, preferred study time (with five questions being open ended). Appendix B in the Supplementary Material provides an overview of the questionnaire.

Focus Groups

Students were divided into four separate focus groups. Each focus group lasted ~1 to 1.5 h. Each focus group was moderated by the second author and observed by the last author and a student assistant. The second author is an educational scientist by background and specializes in qualitative methodology. The last author specializes in effective study strategies. She served as an observer, in order to avoid influencing the results or “leading” the participants. The student assistant observed as well and organized the focus groups. Based on a vignette approach, students were asked how they prepare for different educational activities in the PBL medical curriculum. A total of six vignettes was used (see Appendix C in the Supplementary Material for the interview protocol, including the vignettes used). These vignettes concerned the post-discussion, exam, progress test, skills lab, Pscribe (written assignments assessing students' pharmacotherapeutic reasoning) and extracurricular activities. To answer our research question related to students' learning strategies during self-study, we focused our analysis on the first two vignettes (post-discussion and exam). After 4 months, students were invited back for a second focus group meeting, in which we discussed preliminary results, in order to check our interpretation of the findings (member checking), and to see whether students were consistent in their reports. Two students did not attend the second meeting because the interview dates did not fit their schedule.

The interview protocol used for the focus groups can be found in Appendix C in the Supplementary Material.

All focus groups were audio recorded and transcribed verbatim. A constructivist grounded theory methodology ( Charmaz, 2014 ) was taken when analyzing the data. In grounded theory, the aim is to generate a theory or understanding of a certain process ( Creswell, 2007 ). In a process of iterative data analysis, the researchers go through the different steps of open coding (generating initial codes for data categories), axial coding (identifying a core phenomenon and its surrounding categories), and selective coding (connecting categories and developing the theory). We chose this approach due to our focus on understanding the process of effective strategy use and incorporation of desirable difficulties, with a strong interest in the conditions that support or hinder this process ( Creswell, 2007 ).

Initial, open coding was done by the first author. This was done in a line-by-line fashion, in which representative codes were assigned to the participants' utterances. During this process, several meetings were held with the second and last author to discuss the codes. After arriving at an initial codebook, codes were related to each other in a process of axial coding. During this process, codes were compared and contrasted with each other, looking for connections in order to create themes from overlapping codes. This step was initially done by the first author, with the second and last author each coding a non-overlapping 25% of the codebook to ensure rigor. Findings from this step were discussed until consensus was reached. Results from the analysis were discussed with the third and fourth author. Finally, in a process of selective coding by the first, second and last author, themes were related to each other in order to come to an overarching model of the data.

Tables 1 , 2 show the results from the survey on students' strategy use and the additional aspects of students' study behavior, respectively.

Table 1 . Means and standard deviations for students' responses on the learning strategy questions, from highest to lowest mean.

Table 2 . Summary of students' responses to questions about additional aspects of their study behavior.

Interestingly, the students in our sample indicate a frequent use of the strategies regarded in the literature as effective, such as self-testing, questioning and self-explanation ( Hartwig and Dunlosky, 2012 ; Dunlosky et al., 2013 ), indicating that our purposeful sampling strategy was effective. Furthermore, as indicated in Table 2 , students report spacing their tutorial preparations over multiple sessions, indicating use of distributed practice ( Dunlosky et al., 2013 ). However, as indicated by Table 2 , students also report using some of the strategies that are typically viewed as ineffective for reaching long-term retention and transfer, particularly summarizing, mental imagery and underlining/marking ( Dunlosky et al., 2013 ).

When responding to the question about which other strategies they use, strategies students reported (restricted to the ones not covered by the questionnaire) were: preparing their case on their laptop and shortly summarizing it before the tutorial group, writing out practical activities and going over this information during the exam week, drawing or writing out difficult things, making practice tests and correcting incorrectly answered items, watching videos, making diagrams after studying a case to summarize as much as possible, making concrete and compact cases, working in a disciplined manner, creating mind maps and drawings, drawing figures or pictures, rereading summaries, writing down and rereading difficult parts, printing out all cases and information from practicals and putting them together in one-folder to create an overview of the entire course, rehearsing lectures, and attentively working out learning materials in the case.

When responding to the question asking students whether they had any further comments, students emphasized the importance of lectures, active processing of learning materials through the creation of summaries, the added value of PBL and discussions during tutorial groups, and the importance of keeping order in the learning materials to avoid missing information.

In the focus groups, students were asked about their study approaches, in order to gain more insight into the ways in which they use their learning strategies.

Using the constructivist grounded theory methodology, a model was constructed describing how highly effective strategy users approach their learning. The results of this process are depicted in Figure 1 . In this model, students are driven by a personal learning goal, adopting either a qualitative or quantitative approach to learning. When learning, these highly effective strategy users are continually engaged in active processing of subject matter, while monitoring their understanding of the content and adjusting their approach when necessary. This process is guided by a constant balance between adhering to established study habits, while maintaining a sufficient degree of flexibility to adapt to changes in the learning environment, assessment demands and time limitations. Although students demonstrated metacognitive knowledge of the effectiveness of their strategies and the reasons for using them, this was not the case for all aspects of their strategy use. Indeed, students reported using several strategies which are traditionally regarded as “ineffective” (highlighting, rereading etc.), but used them in a way that helped them adjust to their learning situation and goal.

Figure 1 . Model describing highly effective strategy users' approach to learning.

In the following, we will describe the different components of this model, the implications for students' self-regulation, and the incorporation of desirable difficulties into their learning.

Quantity and Quality

During the focus groups, many of the students described being driven by a personal learning goal, adopting a quantitative or qualitative approach to learning. Specifically, quantitatively oriented students used numerical indicators as the basis for their learning. For example, when referring to collecting information for the post-discussion, one student stated:

“ And then, yeah, just translate it a little bit and write it down in my own words. And uh, yeah, then I just have about fifteen pages usually. And when I have three pages I really feel like I, yeah, have too little .”

Focus group 1, session 1, participant A

On the other hand, students adopting a qualitative approach emphasized the quality of their materials and of their understanding. Rather than focusing on how much material they had produced, these students would focus on how well they understood and remembered what they had studied. As one student explained:

“ Well, if you have 7 pages and you don't understand any of it, you haven't achieved anything in the end. You'll have a lot of material to study and when you study you can brag about having a 50-page case .”

Focus group 1, session 1, participant B

Active Processing and Monitoring

During focus group discussions it became clear that students were continually engaged in active processing of the subject matter, while monitoring their understanding of the content and adjusting their approach when necessary. In this sense, students are incorporating desirable difficulties into their learning, as they are not content with passively reading the subject matter, but try to find ways to be actively engaged.

“ You should never literally copy an entire text. Or [you should do it] in the way he [other participant] does it, explain it or write it in your own words, but do something that makes it your own.”

Focus group 4, session 1, participant A

In some cases, the PBL system at Maastricht University was indicated as a contributing factor to this active approach, as students are required to be able to discuss their findings in the post-discussions. This became clear in the words used to describe it:

“ I think that is really the key, treat the subject matter in an active way. You're in Maastricht, this is what they ask from you and it also just works.”

Focus group 1, session 1, participant C

“ Well I had, yes in [a different city] I really had to learn from books. (…), so I think that that is just, that's not possible here, in Maastricht you also have to be able to tell everything coherently. So then I made a mix from that, that I, because I was good at studying from books, but that I could also reproduce it in the tutorial group.”

Focus group 2, session 1, participant A

In addition to this active processing, students reported a continuous monitoring of understanding, and adjusting their learning when necessary. In many cases, this monitoring was achieved by various forms of self-testing. A commonly reported tactic for this was explaining the subject matter to another person, either physically or hypothetically:

“ (…) sometimes it is nice when people are like asking questions. Then I hear myself explaining it and then I hear whether I understand it, so to speak.”

Focus group 3, session 1, participant A

“ And, uhm, when I look through my case at the end I should actually be able to explain each component that I discuss to someone else. I don't actually do that, but I should be able to.”

Also, students often used externally provided resources such as practice tests to test their knowledge and understanding. Interestingly, the strategies students reported using to correct learning when this monitoring revealed knowledge deficits, were mostly surface-level strategies such as rereading. However, self-testing is an important strategy to improve learning ( Roediger and Karpicke, 2006 ) and has to be actively built into the learning process. The fact that students reported using practice tests and testing themselves indicated again students' willingness to incorporate desirable difficulties into their learning.

Habits and Flexibility

Students' learning process, as guided by their learning goal and characterized by active processing of subject matter and continuous monitoring of understanding, is further guided by a constant balance between adhering to established study habits, while maintaining a sufficient degree of flexibility to adapt to changes in the learning environment, assessment demands and time limitations. For example, students often indicated they had fixed times or places for studying, or a fixed order in which to process the materials for studying. At the same time, students also found themselves in situations where they had to adapt to changes in their learning situation and reported several strategies to maintain this flexibility. For example, one student indicated photocopying book sections in advance to be able to study when going home to parents during the weekends, thereby maintaining flexibility in time and location on which to study. This flexibility was also evident in students' strategy use. Students reported that they had experimented with strategies over the years, finding out “what works for them.” While some students indicated that they had not experienced the need to change their strategies, because they felt comfortable with their strategies and were happy with the results they produced, others indicated that they had used criteria such as their performance as benchmarks for whether or not they should adjust their strategies. As one student indicated:

“ I think this is something in which you are supposed to grow and if you keep telling yourself that your own strategy works and you score 6's [points out of 10, 10 being the highest] then you're actually doing something wrong. But then you're just, I would almost say lazy, you just don't feel like changing it .”

Furthermore, several students indicated adapting their strategies according to the demands of the test. Although some students reported using the same studying methods regardless of the way of questioning on the test, others indicated adapting their strategies depending on whether they would have to answer multiple choice questions (focusing on retention and recognition) or open questions (studying more, with a stronger focus on understanding).

Metacognitive Knowledge

Although students demonstrated metacognitive knowledge of the effectiveness of their strategies and the reasons for using them, this was not the case for all aspects of their strategy use. Students indicated in the second session that, when given a list of all strategies mentioned in the first session and asked to indicate which strategies they used most often, it was difficult to label these strategies properly. As one student indicated:

“ (…) with me mostly with visualizing, that I didn't realize that I was doing it or how I was doing it, until I wrote down that I was doing it. Then I thought, oh yes, I do this quite a lot.”

Focus group 1, session 2, participant B

It was especially difficult for students to indicate how they monitored their understanding, or how they distinguished between important and less important topics and how deep to process the information. Many students indicated this was a “feeling,” or something they had learned from experience.

Furthermore, students reported using several strategies which are traditionally regarded as “ineffective,” such as highlighting and rereading of text ( Dunlosky et al., 2013 ). However, students used them in a way that helped them adjust to their learning situation, by using the strategies in an active way. Although there were some exceptions (e.g., highlighting text in order to reread it afterwards), examples include repeating subject matter using different sources and media, making handwritten summaries to be actively engaged with the subject matter, paraphrasing in order to monitor understanding, or rereading text to check whether it still makes sense in the context of clinical practice.

In fact, in one of the focus groups students indicated the need to incorporate desirable difficulties into their learning process, emphasizing the wish to attain long-term retention, rather than short-term storage, in order to become a competent doctor after graduation. Students often recognized the need to invest effort in learning, as opposed to relying on low-effort surface-level strategies (for example, purposefully using English rather than Dutch books, as the additional effort required prevents a shallow reading of the text). An overarching theme in this regard was a focus on creating understanding, finding the logic in the educational material and making connections between different topics and educational activities, as opposed to for example rote learning or memorizing symptoms. One student explained:

“ I always do that [check if you can apply the case to medical practice] , I always try to make the case explainable. Just because I like that, then I know that I understand and when it is written down on sheets everywhere then I think oh, why is this value high or that value low. Or, because that lab test, oh yes, that makes sense too. It is not that I will think about what it is [come up with a diagnosis], but I do check to see if it makes sense or not”

Focus group 2, session 1, participant B

In summary, the participants in our study use a variety of strategies to regulate their learning and to incorporate desirable difficulties into this process. In addition to active processing of subject matter and a continuous monitoring of understanding, participants understand the need to obtain long-term storage and understanding, rather than short-term results, in some cases prompted by the perspective of having to become a capable doctor.

This paper outlines the results of a study investigating highly effective strategy users' approaches to learning. As a starting point, a survey was administered to students asking about how their study strategies and how they approach their learning. Results from this survey indicated students' adherence to some highly effective strategies (e.g., self-testing), but also the use of some of the less effective strategies (e.g., highlighting). Afterwards, focus groups were organized in order to gain insight into how students use these learning strategies. Specifically, as survey data can provide insight into which strategies students use and how often they use them, the qualitative approach can clarify why students use these strategies, under which circumstances, and how flexible they are regarding their use.

Based on the focus groups, a model was constructed which describes how these students prepare for different learning activities. The first element in our model, as emanating from the focus groups was the distinction between quantitatively vs. qualitatively oriented students. The students who mentioned having a learning goal, expressed this in a way that suggests a sharp distinction between these two opposites: students are either quantitatively or qualitatively oriented. However, from a motivational or self-regulatory perspective, one would expect this variable to fall along a continuum ( Ryan and Deci, 2000 ), with students leaning more toward either side of the spectrum depending on varying contexts and conditions. For example, it is conceivable that students who have a predominantly qualitative orientation might become more quantitatively oriented in the face of insecurities or time constraints. Conversely, generally quantitatively oriented students might adopt a more qualitative orientation when studying topics they are highly interested in. Possibly, students who did not express a learning goal might fall somewhere along this spectrum (a point we have tried to emphasize by adding the dotted line connecting the two opposites). Validating the polarized vs. continuous nature of this distinction, as well as determining the factors that influence students' respective orientations, could be an interesting avenue for future research.

The second theme concerned students maintaining a continuous balance between established habits vs. a flexibility to meet changing demands. Indeed, this would make sense from a desirable difficulties perspective, as these students do not “give up” in the face of changing demands, but rather persist and adapt to the situation in order to reach their goals. Earlier research also correlated flexibility (termed adaptive control) with self-regulated learning, deep processing, and a propensity to undertake effortful cognitive activities ( Evans et al., 2003 ). In terms of implications, several follow-up questions can be asked. First, what is the optimal combination between habits and flexibility? Will this balance be different in less effective students? What are students' core habits? What should be flexible, and what should be stable? What can be taught? Interventions should focus on optimizing this balance. Monitoring of understanding could be at the core of these interventions. When students have an accurate insight into which aspects they do and do not understand, and which strategies lead to a better understanding, it can be easier to make decisions about which strategies need to remain stable, and which should be adapted.

The third theme arising from the data, which characterized students' learning process, was students' continuous engagement in active processing of the learning material and monitoring of understanding. In addition to being aspects of effective (self-regulated) strategy use ( Zimmerman, 1990 ; Dunlosky et al., 2013 ), it is also possible that this result can (at least partly) be attributed to the PBL curriculum in which this study took place, as these learning methods are hallmarks of this instructional approach ( Hmelo-Silver, 2004 ; Loyens et al., 2008 ). Indeed, one of the students in the focus group even indicated the problem-based curriculum as a reason for adopting an active approach to learning. Given the fact that this study has only been carried out in a PBL context, it is difficult to disentangle these influences. Future studies could seek to unravel these factors further.

The final theme emerging from the focus groups concerned students' metacognitive knowledge. Interestingly, students reported using several strategies which traditional self-report questionnaires tend to treat as “ineffective,” but used them in an active way to help cope with the demands of their specific learning situation. This indicates that what matters most is not which strategies students use, but rather how they use them. In other words, students adapted strategies to fit their particular learning situation. Indeed, students' adaptability in their strategy use has been identified by other authors as an important feature of effective self-regulation in students ( Broekkamp and Van Hout-Wolters, 2007 ). This sense of flexibility was also evident in other parts of the model, where students maintained a continuous balance between established study habits on the one hand, and a sense of flexibility to deal with changes on the other.

Another reason for students' use of surface-level learning strategies could be the form of assessment. Students are often assessed with multiple-choice question tests or open question tests focused solely on short-term retention of information. Several studies have found that students will adapt their strategies based on what they perceive will be expected of them on the examination ( Thomas and Rohwer, 1986 ; Broekkamp and Van Hout-Wolters, 2007 ). Indeed, students in our study indicated changing their strategies according to whether questions would be asked in a multiple choice vs. an open question format. In this sense, rather than being “ineffective,” these surface-level strategies could be interpreted as being highly efficient in terms of the (short-term) goal students are aiming to achieve, if this goal is to obtain a good grade on the retention-based exam ( Morris et al., 1977 ). If the goal of the curriculum is for students to strive for deep-level processing and understanding, the test demands need to be aligned with this objective ( Broekkamp and Van Hout-Wolters, 2007 ), asking questions that will require this approach from students.

On the other hand, several students indicated an understanding of the need to obtain long-term retention and understanding, an inclination that seemed to be promoted by a desire to become a capable doctor. This can have important implications for interventions aimed at improving self-regulation for students who are less skilled self-regulators. Specifically, if interventions would focus on aiding students in attaining a clear perspective of their goals and long-term profession, this could improve their self-regulatory behavior and intention to build in desirable difficulties into their learning. Although we did not originally set out to investigate the link between students' learning behavior and their future time perspective, previous work has been done to establish this link, with research indicating that students' long-term time perspectives are associated with adaptive self-regulatory strategies and deep cognitive processing ( Bembenutty and Karabenick, 2004 ; de Bilde et al., 2011 ). As these studies are mostly correlational, the direction of these effects is not entirely clear. Future research could try to establish the direction of causality by employing a longitudinal ( de Bilde et al., 2011 ) or experimental approach.

The model identified can elaborate on existing theoretical models of metacognition by explicating the criteria students use to monitor and control their learning and how they adapt their strategies to fit their learning needs. For example, Nelson and Narens (1990) outline a theoretical framework in which students' allocation of study time is determined by their judgments about the difficulty it takes them to master certain information (ease of learning; EOL), their judgments about how well they have mastered certain recallable information (judgments of learning; JOL), and the degree to which they believe they have previously known currently unrecalled information (feeling of knowing; FOK). Their research found that students will allocate extra study time based on their EOL, JOL, and FOK judgments, with students studying general information items generally allocating extra study time to information with a lower EOL (meaning they are judged to be harder), higher FOK, and lower JOL. Also when it comes to the allocation of restudy , students will allocate this restudy time to information they judge as poorly learned ( Nelson et al., 1994 ). The current study adds to this literature by shedding light on some of the criteria students may use to make these judgments. Specifically, students seem to focus on qualitative or quantitative criteria for making these judgments. Furthermore, for FOK, Nelson and Narens (1990) indicate that these judgments monitor the recallable aspects of the information a student has in memory (such as whether they have used it to correctly answer a question before). This could potentially explain the differences between the qualitative and quantitative orientations found in our study. For some students, the qualitative aspects related to the studied information may be hard to recall. For example, some of the information may never have been tested yet, making it difficult for students to derive these judgments. This may lead them to focus on more easily recallable, quantitative information instead.

Following this line of reasoning, this focus on easily recallable, quantitative aspects of learning may lead students to adopt more surface-level strategies, as these might be sufficient to satisfy the quantitative criteria. Indeed, Koriat (1997) found that extrinsic cues are less informative for students' JOLs than intrinsic cues, and these inaccurate JOLs could in turn lead to inadequate study strategies. Although students in our study seemed to follow the same general path of self-regulation, the qualitative approach might lead to more elaborative learning strategies and incorporation of desirable difficulties. However, a focus on quantitative criteria is apparently sufficient for students to pass their exams and be successful in university (a point which was already elaborated upon above). However, we do not have any information about their long-term retention. Future studies should focus on more elaborative learning outcomes and longer retention intervals, to further unravel the potentially differential effects of the different approaches to learning.

This study has several limitations. First, our focus groups were limited to second-year undergraduate medical students who were effectively self-regulating their learning. Given the PBL context in which these students are learning, this provided a fruitful basis to start from when investigating effective students' approaches to learning, but we cannot be sure about how these findings relate to other student populations. Furthermore, our study was limited to students from the undergraduate medical program. It is possible that there are characteristics in this program, which are not easily transferable to programs focusing on other domains. A specific example of this can be found in the long-term perspective that several students indicated as the basis for their desire to understand the subject matter, as hinted at above. In a study program like Medicine, the end goal of becoming a doctor is quite clear. In many other undergraduate programs, this long-term perspective may be less evident. Future research could look into what constitutes effective self-regulation in other study programs and other, non-PBL oriented universities. Furthermore, although the purpose of this study was to illustrate effective self-regulation rather than to contrast different groups of students, it would be interesting to see what picture will emerge when asking the same questions to low self-regulating students. We have tried to ensure replicability by providing rich descriptions of context, methods, and results, in an attempt to increase opportunities for judgments of transferability.

Related to the distinction between effective vs. ineffective strategy users is the questions of whether we were able to correctly identify which students were effective strategy users. We used students' mentors as informants for our purposeful sampling strategy. We have confidence in this strategy, as mentors are among the few key persons who have a bird's eye view of students' overall performance, for both the entire duration of the program, as well as in comparison to other students. They also discuss students' learning strategies at least two times during the first year in an individual mentor meeting. However, their judgments are inherently subjective, and although they were given instructions on what is meant by effective strategy users, we have no insight into their decision making when they selected these students. Although it was a conscious decision not to include grades as a measure of self-regulation (as students using shallow strategies may very well obtain good test results in the short term), it could be worthwhile to think about other ways to triangulate students' strategy effectiveness.

Finally, we chose to use learning questionnaire used by Hartwig and Dunlosky (2012) as a starting point for our study, in order to build further on this work and demonstrate the added value of the focus groups in this context. However, as this survey measures each strategy by only one item, it was not possible to compute reliability or internal consistency estimates. This problem is mitigated by the fact that we used the survey as a starting point for our focus groups, rather than conducting analyses analyzing differences between groups or as a result of some intervention. However, the research design could be strengthened by adding more items per strategy, in order to be able to make inferences about the reliability and internal consistency of students' responses.

Overall, this study contributes to the literature by providing an in-depth, qualitative description of how highly self-regulated medical students in a PBL curriculum approach their learning and build in desirable difficulties in their learning process. This model can serve as a framework for further study into the various factors that influence (effective) self-regulation, and as a starting point for designing interventions focused on improving strategy use in less effective students.

Author Contributions

AdB and RS were responsible for the design and data collection of the study. SR performed analysis of the data, in close collaboration with AdB and RS. SR drafted the article, incorporating edits, and feedback from all other authors (AdB, RS, JvM, and HS). All authors made a substantial contribution to the interpretation of the data for this work.

This research was funded by the Netherlands Organization for Scientific Research (Veni grant number 451-10-035).

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyg.2018.02501/full#supplementary-material

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Keywords: problem–based learning, desirable difficulties, self-regulated learning, learning strategies, mixed methods&lt, research methodology, grounded theory analysis

Citation: Rovers SFE, Stalmeijer RE, van Merriënboer JJG, Savelberg HHCM and de Bruin ABH (2018) How and Why Do Students Use Learning Strategies? A Mixed Methods Study on Learning Strategies and Desirable Difficulties With Effective Strategy Users. Front. Psychol . 9:2501. doi: 10.3389/fpsyg.2018.02501

Received: 18 June 2018; Accepted: 23 November 2018; Published: 14 December 2018.

Reviewed by:

Copyright © 2018 Rovers, Stalmeijer, van Merriënboer, Savelberg and de Bruin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Sanne F. E. Rovers, [email protected]

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Relationship between learning strategies and academic performance: a comparison between accreditation of prior experiential learning (APEL) and regular entry undergraduates

Asian Association of Open Universities Journal

ISSN : 2414-6994

Article publication date: 19 October 2021

Issue publication date: 4 November 2021

The purpose of this study aims to compare the academic performance and types of learning strategies used by APEL and regular entry undergraduates. It also explored the relationship between the academic performance and the types of learning strategies utilised by these two groups of undergraduate.

Design/methodology/approach

This quantitative study involved 400 undergraduates from an open distance learning (ODL) institution. A correlational research design was used in this study. Data were collected through archival data and questionnaire. Independent t -test and Pearson’s correlation analyses were performed using SPSS.

Regular entrants were found to perform slightly better than APEL entrants. There is no significant difference between the types of learning strategies used by APEL and regular entrants. For both groups, the higher performers adopted time and study environment management as well as effort regulation strategies. Besides this, there was no correlation between cognitive skills and peer learning with their academic performance. Meta-cognitive self-regulation and help-seeking which were found to affect the regular entrants’ academic performance did not correlate with those of APEL entrants.

Research limitations/implications

This study was conducted within only one institution. The generalisation of findings may therefore be limited. Future studies could be conducted to include students from several institutions.

Practical implications

Time management training could be provided to students. Additional support, like foundation courses and supplementary readings, could be provided to APEL entrants to support their learning.

Originality/value

The findings would be beneficial to ODL institutions who offer APEL entry to understand the academic performance and learning strategies used by APEL entrants relative to regular entrants.

APEL (accreditation of prior experiential learning)
Academic performance
Learning strategy
Undergraduate

Tan, S.F. , Din Eak, A. , Ooi, L.H. and Abdullah, A.C. (2021), "Relationship between learning strategies and academic performance: a comparison between accreditation of prior experiential learning (APEL) and regular entry undergraduates", Asian Association of Open Universities Journal , Vol. 16 No. 2, pp. 226-238. https://doi.org/10.1108/AAOUJ-08-2021-0081

Emerald Publishing Limited

Published in Asian Association of Open Universities Journal . Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode

Introduction

The open distance learning (ODL) mode of study was introduced to allow Malaysians to develop themselves professionally while still working to contribute to the economy. It was created with the aim of upgrading and expanding the pool of Malaysia’s human resources which was part of the 11th Malaysia Plan to develop its human capital through lifelong learning ( Economic Planning Unit, 2015 ). The access to higher education via Accreditation of Prior Experiential Learning (APEL) was created through the collaboration between the Malaysian Ministry of Education and the Malaysian Qualification Agency (MQA). By leveraging on working experience or prior working experience, APEL allows learners to enrol into tertiary education, giving access to learners from diverse backgrounds to conventional higher education institutions or ODL institutions. There are three categories of APEL, namely, APEL-A (Admission), APEL-C (Credits) and the newly introduced APEL-Q (Qualifications) in 2020. All three categories and their assessment methods stem from Adult Learning Theory, Experiential Learning Theory and the Johari Window Concept ( Kaprawi, 2011 ). For this study, we will be focusing on APEL-A only.

APEL-A offers an alternative route for admission into the university using a different approach to entry requirements as compared to the regular entry criteria. In this article, APEL entry students refer to students who enter the university through the APEL-A route. These students leverage on their prior learning acquired through formal/informal training, life and/or work experience to compensate for the lack in their academic qualifications. As outlined by MQA (2014) , candidates who wish to pursue an undergraduate programme through APEL must be at least 21 years of age in the year of application and possess a minimum PMR/SRP/LCE (these refer to the lower secondary certification of completion) qualification or its equivalent. Candidates must also possess prior learning experience in the programme of interest as well as pass the APEL-A assessment conducted by the university. As a result, APEL entry students have a lower academic background as compared to their peers who are admitted into the university through the regular entry. Yet, both groups of students will receive the same learning services, inputs and assessment upon commencement of studies and up to completion.

Some researchers (e.g. Awang et al. , 2014 ; Latifah et al. , 2009 ) have reported that APEL entrants do not perform as well as their regular peers. Hence, there is a need to explore the differences in personal traits, abilities or behaviours between these two groups of students to predict their academic performance so that the institutions of higher learning can provide them with the appropriate support. Learning strategies were studied instead of other learner variables (e.g. language skills, problem-solving skills and logical skills) in this study because: firstly, this study is carried out in the ODL context. Students are physically apart from their lecturers, tutors and peers. Thus, they need to be independent learners and have to be largely responsible for themselves about their own studies and outcomes in order to succeed in their studies ( Das, 2010 ). So, learning strategies have become an important factor that affect their performance. Learning strategies are specific actions, behaviours or techniques that students consciously use to improve their own learning ( Zamora Menéndez et al. , 2020 ). Several studies (e.g. Lam and Hassan, 2015 ; Lee and Mao, 2016 ; Neroni et al. , 2019 ) have reported that academic performance and learning strategies are interrelated. Secondly, learning studies are not a fixed trait; it is a skill that can be developed via experience and practice ( Zimmerman, 2015 ). By knowing the relationship between learning strategies and academic performance of these two groups of students, the institutions would be able to provide relevant training to assist the students to develop the skills they need to perform well academically.

Although there are many studies (e.g. Lam and Hassan, 2015 ; Lee and Mao, 2016 ; Neroni et al. , 2019 ) that relate academic performance to learning strategies, they were conducted overseas. Research in this area, specifically among APEL learners in Malaysia, remains under-researched. Therefore, this study can contribute to the field of knowledge by identifying and comparing the learning strategies used by both regular entry and APEL entry undergraduates and determine if there is a relationship between academic performance and learning strategies between these two groups of students. This study would be greatly beneficial to higher education providers, as they can better prepare to meet the demands of this growing group of APEL learners as the number of APEL learners will inadvertently increase in the future. Besides knowing which form of learning strategies is helpful for academic success for students, higher education providers should also be aware of them so that they may implement effective scaffolds in their curriculum to help their students achieve academic success.

Literature review

Students use various learning strategies to improve their learning. According to Stumm and Furnham (2012) , learning strategies are a collection of cognitive and behavioural processes and abilities that influence how information is acquired, maintained and retrieved. They further stated that students could use strategies such as the rehearsal, organisation, elaboration, critical thinking, effort learning, time and environment management, help-seeking and peer learning ( Stumm and Furnham, 2012 ). Learning strategies are skills that can be taught ( Zeidner and Stoeger, 2019 ). Educators or instructors must understand students’ learning strategies so that they use suitable teaching approaches to promote successful teaching and learning in the classroom. Students’ learning processes and responses in different circumstances are affected by their learning strategies ( Duff et al. , 2004 ; Stumm and Furnham, 2012 ).

With regard to academic performance, Narad and Abdullah (2016) define it as the knowledge acquired that is assessed by a teacher via grades or educational objectives set by students and instructors to be fulfilled over a defined period. Additionally, they said that these objectives are assessed regularly or via examinations. Similarly, Ward et al. (1996) claimed that academic performance measures educational outcomes. They emphasised that it shows and measures the degree to which an educational institution, its faculty and students achieve their educational goals. Narad and Abdullah (2016) further emphasised that the “academic performance of an individual is influenced by various factors such as personality, intellectual ability, environment, learning strategies and etc” (p. 2). To summarise, learning strategies play a crucial role in determining students’ academic success.

There is extensive literature on investigations into the relationship between learning strategies and academic performance among on-campus students. However, not many studies have been done on this relationship among distance education (DE) students. According to Valle et al. (2008) , students at a public university in Northern Spain used the organisational approach the most, with a mean score of 3.74 out of a potential maximum score of 5.00. Mean scores for metacognitive self-regulation, time and study environment management, effort regulation and elaboration were 3.45, 3.45, 3.41 and 3.37, respectively. Puzziferro (2008) , in his research titled “Online Technologies Self-Efficacy and Self-Regulated Learning as Predictors of Final Grade and Satisfaction in College-Level Online Courses” found that self-efficacy scores for online technologies were not correlated with student performance. However, it was found that time, study environment and effort control were all substantially linked to performance. Students who scored better on these subscales got higher overall scores. In contrast to Valle et al. (2008) , Al-Alwan (2008) obtained the opposite result in his study. His study showed that students utilised the metacognitive self-regulation technique the most (mean score = 4.21). The average scores for time and study environment management, peer learning, effort control and assistance seeking were 3.96, 3.60, 2.50 and 2.36, respectively. Credé and Phillips (2011) conducted similar research with on-campus students. They investigated the relationship between the use of learning strategies and grades in individual courses. The findings revealed that the strongest relationships between reported strategy use and individual grades (i.e. sample size weighted mean correlation, r +) were effort regulation ( r + = 0.27), time and study environment management ( r + = 0.22) and metacognitive self-regulation ( r + = 0.18). When it comes to the relationship between learning strategies and grade point average (GPA), they found comparable findings, albeit the impact sizes were generally lower. The strongest were effort control ( r + = 0.16), time and study environment management ( r + = 0.17) and metacognitive segregation ( r + = 0.18). The remaining learning strategies were found to have no relationship with academic achievement. In addition, Richardson et al. (2012) conducted a systematic examination and meta-analysis of the relationship between learning strategies and GPA for students at a campus-based college. They investigated the correlations between learning strategies and GPA and a model with learning strategies as predictors of GPA. They discovered that effort regulation is the most important academic learning strategy, followed by time and study environment, management and metacognitive self-regulation. In another study conducted by Yip (2021) , which involved Japanese students, learning strategies and academic performances were found to be related closely, and that those strategies were good predictors of academic performance. From the previously mixed findings, there seems to be uncertainty in the relationship between both variables. Lee and Mao (2016) used various learning strategies to examine the relationship between self-efficacy, preferred learning strategies and academic performance in a unique hospitality course environment. The findings showed that hospitality management students prefer a “learn by doing” approach to that of computer-based learning and lecturing. The findings suggested that self-efficacy has an impact on academic performance.

Within the DE sector, Radovan (2011) , in his research, explored potential correlations between self-regulated learning characteristics and students’ success in a distance-learning program. He found that effort regulation had a positive impact on course grades among university undergraduates. In the following year, Agricola et al. (2012) discovered significant differences in learning regulation and efficiency between traditional (under the age of 24) and non-traditional (24 years of age and above) students in a distance institution; traditional students performed significantly better on the rehearsal scale than non-traditional students. In cognition, motivation, behaviour and context, non-traditional students’ capacity to control their learning was shown to be superior to traditional students. In addition, Neroni et al. (2019) conducted their research on learning strategies and academic performance at a DE institution in The Netherlands. Their results showed that time and effort management was the most significant factor and a good predictor of academic success. In a recent study by Zhou and Wang (2019) , which involved Chinese adult students in an ODL setting, there was a significant and positive indirect relationship between mastery goal orientation and academic performance through self-regulated learning strategies. They also further emphasised that the performance-approach goal orientation had a positive indirect influence on academic performance, with the effort-regulation strategy fully mediating this relationship. There have not been many studies that compare the relationship between learning strategies and academic performance between regular and non-regular entry students. This research aims to examine the relationship between both variables among regular and APEL students in DE.

Comparable studies in the Malaysian context include that of Kosnin (2007) which used the Motivated Strategies for Learning Questionnaires (MSLQ) to study the ability of self-regulated learning (SRL) to predict academic performance among Malaysian students. A total of 460 second-year engineering students from Universiti Teknologi Malaysia participated in the research. Self-regulated learning accounted for 35.2% of the variation in cumulative grade point aAverage (CGPA) among Electrical Engineering students. Furthermore, resource management and meta-cognitive learning strategies were shown to be significant predictors of academic performance (=0.40; = 0.28, p. 01).

For studies that compared the relationship between regular and APEL entry students, Latifah et al. (2009) found that regular entrance students outscored APEL entry students. Awang et al. (2014) performed similar research that supported the results of Latifah et al. (2009) . On the other hand, Cheng and Siow (2018) found no statistically significant difference in academic performance between regular and APEL-routed entrants. Lam and Hassan (2015) suggested that future educators in Malaysia should use more cognitive and meta-cognitive strategies than resource management strategies. To sum up, even though a few studies have been carried out in Malaysia to examine the relationship between learning strategies and academic performance, research on the learning strategies used by regular and APEL entrance students is still limited. Previous studies conducted in Malaysian distance learning institutions yielded inconsistent results regarding the differences in academic performance of APEL and regular entrants. Therefore, there is a research gap that has to be addressed.

Research questions

Is there a significant difference in academic performance between APEL and regular entry students?

Is there a significant difference in learning strategies used between APEL and regular entry students?

What is the relationship between the learning strategies used and the academic performance of APEL entry students?

What is the relationship between the learning strategies used and the academic performance of regular entry students?

Methodology

This study used the quantitative methodology approach. The comparative design was used to examine the difference in academic performance and learning strategies used by APEL and regular entry undergraduates. Then, a correlational design was used to explore the relationship between the learning strategies used and the academic performance of these students. The data was collected from archival data and a questionnaire. The archival data included the intake of students, the type of entry and CGPA, which were obtained from the Registry of the university. The instrument, as appended in this article, was adapted from the MSLQ. MSLQ is a self-report instrument developed by Pintrich et al. (1991) . It is comprised of motivational scales and learning strategies scales. This study only focused on the learning strategies scales. Two of these learning strategies scales are cognitive and metacognitive strategies and resource management strategies. Cognitive and metacognitive strategies refer to the strategies used by the students to process information from learning resources and classroom activities while resource management refers to the students’ regulatory strategies in controlling other resources besides their own cognitive strategies. Table 1 lists the nine subscales of learning strategies.

Some changes were made in the questionnaire to suit the context of the university. Two stages of preliminary studies were conducted on the questionnaire to confirm that the modified version of MSLQ was a reliable instrument. Firstly, a debriefing interview was conducted with four students. The questionnaire was revised based on the feedback collected from the interview. Then, the questionnaire was administered to 40 students as the pilot study. The alpha coefficient obtained was 0.857. The results of the pilot study revealed that the questionnaire was reliable as the alpha value was within the acceptable range. The university started APEL entry in the January 2016 semester. The list of students from January 2016 to January 2019 was obtained from the Registry. There were 4,452 undergraduates, 2,706 regular entrants and 1,746 APEL entrants, enrolled during this period. The questionnaire was administered to 4,452 undergraduates using SurveyMonkey. Informed consent was obtained through the questionnaire. Seven hundred students, 410 regular entrants and 290 APEL entrants, completed the questionnaire. The CGPA of these students was then obtained from the Registry of the university. The data were imported into SPSS for data analysis. Independent t -tests were conducted to compare the difference in academic performance and learning strategies used between APEL and regular entry undergraduates. Then, Pearson correlation was carried out to explore the relationship between academic performance and learning strategies used for both groups of students.

An independent sample t -test was conducted to compare the academic performance of APEL and regular entry students. There was a significant difference in the scores for regular [ M :2.38, SD: 1.23] and APEL entry students [ M :2.12, SD:1.35; t (700) = 4.587, p = 0.000]. The magnitude of the differences in the means was small (eta squared = 0.03). An independent sample t -test was also conducted to compare the learning strategies used by the APEL and regular entry students. Table 2 shows the results of the independent sample t -test. It was found that there is no significant difference in the types of learning strategies used by these two groups of students.

Pearson correlation was conducted to explore the relationship between the learning strategies and academic performance of regular entrants. As shown in Table 3 , meta-cognitive self-regulation, time and study environment management, effort regulation and help-seeking are positively correlated with academic performance. The magnitude of the relationship is small ( Cohen, 1988 ).

Pearson correlation was also conducted to explore the relationship between the learning strategies and academic performance of APEL entrants. As shown in Table 4 , only time and study environment management and effort regulation are positively correlated with academic performance. The magnitude of the relationship is also small ( Cohen, 1988 ).

The findings of this study showed that there is a significant difference in academic performance between the regular and APEL undergraduates. It is aligned with the findings reported by Awang et al. (2014) and Latifah et al. (2009) . However, Cheng and Siow (2018) reported that there was no significant difference in performance between these two groups of students. The inconsistency in the findings from the above studies and the current study could be caused by institutional factors, such as support provided by the university, quality of the programme, competence of teaching staff, relationship between students and lecturers/tutors amongst others. All these studies including the current study only focused on students from one ODL institution. Some institutions may have a better support system that enables their APEL entry students to perform equally well as regular entry students. Future studies can be conducted by comparing the academic performance of these two groups of students from several ODL institutions.

When a t -test was conducted to compare the learning strategies used by these two groups of undergraduates, it was found that there was no significant difference between these two groups of students. For both regular and APEL entry students, time and study environment management and effort regulation were positively correlated with academic performance. Time and study environment management includes scheduling, planning, allocation of study time as well as regulating the general study environment. Effort regulation is the management of academic tasks. It reflects the level of commitment the students maintained when they faced difficulties or obstacles ( Pintrich et al. , 1991 ). In this study, students who scored high in these two sub-scales had higher CGPA scores. Similar results were reported by Agricola et al. (2012) , who studied non-traditional learners (students who are 24 years old and above); as well as Neroni et al. (2019) , Radovan (2011) and Puzziferro (2008) , who studied distance learners. The adult ODL learners faced many challenges in their studies like studying off-campus and having both work and family obligations ( Ronning, 2009 ). Therefore, it is crucial for them to acquire a high level of self-regulated behaviour. Students who can regulate and influence their study environment are more capable of resisting distraction ( Pintrich, 2004 ) as well as of maintaining concentration and ultimately being able to perform well in their studies.

For both regular and APEL entrants, there was no significant relationship found between peer learning and academic performance. Similar to the findings reported by Puzziferro (2008) , the mean score of peer learning in this study was the lowest compared with the mean score of all the learning strategies. Like Puzziferro (2008) , it is recommended that more research can be conducted to better understand the lack of peer learning amongst ODL learners, regardless of regular or APEL entrants, as this phenomenon can be influenced by various factors which were not addressed in this study. Meta-cognitive self-regulation involves planning, monitoring their own learning and regulating ( Duncan and McKeachie, 2005 ). Some researchers ( Agricola et al. , 2012 ; Neroni et al. , 2019 ) have also reported that meta-cognitive self-regulation is a positive predictor of academic performance for distance learners. Neroni et al. (2019) further explained that meta-cognitive self-regulation is important for ODL learners because they are busy with work and family. In this study, only the meta-cognitive self-regulation scores of regular entrants were positively correlated with their academic performance while there is no significant relationship between the APEL entrants’ meta-cognitive self-regulation scores and their academic performance. Further study is needed to study why meta-cognitive self-regulation is not correlated with the academic performance of APEL entrants.

The same goes for help-seeking where it is positively correlated with regular entrants’ academic performance but not correlated with APEL entrants. Inconsistent findings can be found in the literature. Neroni et al. (2019) reported that help-seeking is a negative predictor of academic performance, whereas Credé and Phillips (2011) reported that these two variables are not interrelated. In this study, regular entrants who have experienced conventional studies did not shy away to seek help from others when they faced difficulties as they were taught to always seek assistance and clarification when they do not understand the subject matter. Comparatively, APEL entrants may not be used to seeking help from others, as they may have experiences that view help-seeking as a sign of weakness and, therefore, were more inclined to help themselves.

It was surprising to find that there is no significant relationship between cognitive strategies (which included rehearsal, elaboration, organization and critical thinking) and academic performance. These findings contradict the findings reported by Neroni et al. (2019) , where some of the cognitive skills were positive predictors of academic performance. They reported that complex cognitive skills were positive predictors of academic performance, whereas simple cognitive skills and academic thinking were not related to academic performance. The inconsistency in findings could be caused by the difference in the participants selected. The participants of the study conducted by Neroni et al. (2019) were students who were 14 months after they first joined the university whereas the participants in the current study were all undergraduates in a university, regardless of whether they were in the first year, mid-way through their studies or in the final year. When the students are still new to their study in the university, some students might not equip themselves with the cognitive strategies yet. As a result, students who were able to apply the cognitive strategies outperformed their peers who were yet to acquire the cognitive strategies. In the current study, the participants comprised of all the undergraduates who were at different stages of their studies. Some students might have acquired the learning strategies as they progress through their studies. This might be the reason causing that no significant correlation was found between the cognitive skills and academic performance. Therefore, further research is needed to explore the relationship between the learning strategies and academic performance of students who are at different stages of their studies.

From the discussion above, we can come to a few conclusions. Firstly, although regular entrants performed slightly better than the APEL entry students, there was no significant difference between the types of learning strategies used by both of them. For both regular and APEL entry students, both time and study environment management, as well as effort regulation, were positively correlated with their academic performance. Help-seeking and meta-cognitive self-regulation were positively correlated with regular entrants’ academic performance but have no significant relationship with APEL entrants’ academic performance. The cognitive skills (rehearsal, elaboration, organisation and critical thinking) and peer learning were not correlated with the academic performance for both regular and APEL entry students.

Recommendations

Based on the results of this study, the following recommendations are made to support the students learning.

Learning strategies are skills that can be developed. These skills can be improved when instructional methods and environmental conditions support the students to use these skills. Being able to manage time well is crucial for both regular and APEL entry students for them to perform well in their studies. The institution may provide the students with guidelines on time management skills when they commence their studies to prepare them to manage their time judiciously. In doing so, students will be able to allocate more time for their studies.

Identify the requirement of the task given;

Self-assess their current knowledge related to the requirement of the task;

Determine any discrepancies between their current knowledge and the task requirement;

Plan how to acquire the additional knowledge needed to complete the task;

Implement strategies to complete the task and monitor their progress from time to time.

The institution could organise social events or in-person sessions for the students to meet up with their peers, tutors and lecturers from time to time throughout the semester. During the sessions, the students can share their challenges and how they cope with their study life with each other. They would be able to learn from their peers how to manage their time and effort in order to learn well. Besides, the sessions would create an opportunity for the APEL entrants to develop closer relationships with others and ultimately be more comfortable seeking help from others whenever they are in need.

Suggestion for future studies

Like studies conducted by Awang et al. (2014) , Cheng and Siow (2018) and Latifah et al. (2009) , this study involved students from only one institution. The sample size is not big enough to be generalised to a larger population. The results may have been affected by the institutional factors. Hence, future studies can be conducted by including more students from several distance learning institutions. Larger and multi-institutional samples would provide a broader and clearer picture of how well APEL students perform as compared with their regular entry peers. Furthermore, the current study only explored the learning strategies used by the students. Future studies could investigate other personal traits of these students, for example, self-efficacy, motivation and so forth.

In this study, the APEL entrants performed slightly lower than the regular entrants and there was no significant difference in terms of the learning strategies they used. The analysis was done at a general level regardless of the context, for example, the stages of study and the programme enrolled by the students were discounted. It could be that there was no significant difference in learning strategies used between these two groups of students because the students have picked up the learning strategies as they progress in their study path. The difference in terms of academic performance between these two groups of students might vary at different stages of their study path. Therefore, future studies could compare the academic performance and learning strategies of these two groups of students who are in the first year, mid-way through their studies and in their final year. The findings of such a study would be able to identify the needs of students at different stages, especially first year students as the dropout rate is highest in the first year. Consequently, institutions would be able to provide appropriate support at different stages of a student’s studies.

The comparison of learning strategies and academic performance between these two groups of students can also be done on students enrolled in different programmes. The learning strategies used might be different in a different programme. Besides, the foundation knowledge needed in different disciplines is not the same. Some programmes might need a formal and highly structured educational background for the students to study well at a higher level, while for some programmes, additional independent readings might be enough for the APEL entry students to study as well as the regular entrants. The findings of such a study would enable educational institutions to provide specific support for APEL students enrolled in a different programme.

As argued by Meijs et al. (2018) , the modified questionnaire adapted from MSLQ ( Pintch et al. , 1993 ) is more applicable to DE learners as the educational system and living and study circumstances they experience are different from those of campus-based college students. MSLQ which was designed for on-campus college students in traditional education settings might not be able to measure the learning strategies used by DE learners accurately. To date, not many researchers have used this questionnaire to study the DE learners’ learning strategies. Future studies should be conducted using the modified questionnaire to explore the learning strategies of DE learners to enhance the validity and reliability of the questionnaire so that we have a better instrument to study the DE learners’ learning strategies.

Learning strategies scales in MSLQ

Scale	Subscale
Learning strategies

Independent sample t -test of the learning strategies for regular and APEL entrants

Learning strategies	Regular entrants		APEL entrants			Sig
Learning strategies	Mean	Standard deviation	Mean	Standard deviation		Sig

Rehearsal	2.95	0.40	2.94	0.40	0.516	0.606
Elaboration	3.05	0.45	3.00	0.44	1.134	0.257
Organization	3.01	0.53	2.98	0.53	0.837	0.403
Critical thinking	2.93	0.49	2.91	0.48	0.487	0.627
Meta-cognitive self-regulation	2.82	0.40	2.85	0.44	−0.868	0.386

Time and study environment management	2.65	0.41	2.67	0.45	−0.498	0.625
Effort regulation	2.97	0.43	2.99	0.46	−0.655	0.513
Peer learning	2.39	0.61	2.34	0.61	1.009	0.313
Help seeking	2.69	0.63	2.67	0.59	0.331	0.741

Coefficients of the relationship between learning strategies and academic achievement of Regular entrants

Learning strategies		Academic achievement ( )
Rehearsal	Pearson correlation		0.030
Rehearsal	Sig. (2-tailed)	0.550
Elaboration	Pearson correlation		0.056
Elaboration	Sig. (2-tailed)	0.259
Organization	Pearson correlation		0.008
Organization	Sig. (2-tailed)	0.866
Critical thinking	Pearson correlation		-0.023
Critical thinking	Sig. (2-tailed)	0.645
Meta-cognitive self-regulation	Pearson correlation		0.072
Meta-cognitive self-regulation	Sig. (2-tailed)	0.043
Time and study environment management	Pearson correlation		0.152**
Time and study environment management	Sig. (2-tailed)	0.002
Effort regulation	Pearson correlation		0.174**
Effort regulation	Sig. (2-tailed)	0.000
Peer learning	Pearson correlation		0.087
Peer learning	Sig. (2-tailed)	0.080
Help-seeking	Pearson correlation		0.161
Help-seeking	Sig. (2-tailed)	0.001

**. Correlation is significant at the 0.01 level (2-tailed)

Learning strategies		Academic achievement ( )
Rehearsal	Pearson correlation		−0.079
Rehearsal	Sig. (2-tailed)	0.177
Elaboration	Pearson correlation		−0.067
Elaboration	Sig. (2-tailed)	0.255
Organization	Pearson correlation		−0.046
Organization	Sig. (2-tailed)	0.437
Critical thinking	Pearson correlation		−0.0.98
Critical thinking	Sig. (2-tailed)	0.096
Meta-cognitive self-regulation	Pearson correlation		−0.060
Meta-cognitive self-regulation	Sig. (2-tailed)	0.306
Time and study environment management	Pearson correlation		0.197**
Time and study environment management	Sig. (2-tailed)	0.001
Effort regulation	Pearson correlation		0.172**
Effort regulation	Sig. (2-tailed)	0.003
Peer learning	Pearson correlation		−0.076
Peer learning	Sig. (2-tailed)	0.198
Help-seeking	Pearson correlation		0.023
Help-seeking	Sig. (2-tailed)	0.694

Note(s): **. Correlation is significant at the 0.01 level (2-tailed)

*. Correlation is significant at the 0.05 level (2-tailed)

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Acknowledgements

This research was funded by the Centre for Research and Innovation (CeRI), Wawasan Open University, Malaysia.

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Research Article
Open access
Published: 09 February 2016

Learning strategies and styles as a basis for building personal learning environments

Blanca J. Parra 1

International Journal of Educational Technology in Higher Education volume 13 , Article number: 4 ( 2016 ) Cite this article

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This paper presents the results and reflections from a study conducted on students using the e-learning mode from the Panamerican University Foundation. The aim of the study was to identify learning strategies and styles as a basis for building personal learning environments (PLEs). This study was conducted under the parameters of a mixed research approach, which uses quantitative and qualitative techniques, as well as an interpretative approach. The main learning styles found were active, visual and global. In relation to learning strategies, a tendency towards web searching as well as schemes and summary preparation was found. Although these are the prevailing trends, the study allowed us to recognize that each person learns differently; their style and learning strategies are influenced by the environment and the resources at their disposal. This enables educational institutions to identify and make a available the techno-pedagogical tools and strategies required to strengthen and build PLEs that are more assertive and better adapted to the needs and interests of students.

Introduction

Education, over time and through the challenges of society, has undergone several transformations in educational communities, giving rise to the need to propose new strategies and resources that promote, encourage and strengthen learning, making it a meaningful and enriching experience for the various stakeholders in the process (Carrillo et al. 2012 ). When asked about new educational proposals, we are faced with a number of possibilities, ranging from traditional teacher-centered approaches to student-centered approaches; in the case of the latter, the student plays a fully participatory role and control stance, not only in the process but also in the selection of content and activities, as suggested by Coomey and Stephenson (cited by Casamayor et al., 2008 ) on the grid of e-learning educational models.

Segmentation and classification of data from the interview

Among the different concepts that have gained strength in recent years is the personal learning environment (PLE), which refers to innovative spaces that encourage the generation of knowledge through the integration of different elements, both pedagogical and technological, and allow students to take control of their learning process so that they can set their own goals, manage their work and communicate with others.

Cabero et al. ( 2011 ) suggest, with regard to the origins of PLE, that there are two approaches, a pedagogical one and a technological one. The pedagogical one is understood as a change in educational methodology that promotes self-learning through the use of resources available on the network. It is a system that focuses on the student and allows him/her to take control of his/her learning process to set his/her own goals, manage his/her activity process and communicate with others.

The technological approach refers to the PLE as a software application comprising a repository of content and different management and communication tools.

Meanwhile, Adell and Castañeda ( 2010 ) do not directly relate PLEs to technological resources, and indicate that all types of variables are involved in them (home, school and friends, among others), because the processes of learning achieved in groups and in interaction with others. Ron Lubenskyv says that PLEs have a facility for individuals to access, add, configure and manipulate digital artifacts or tools for continuous learning experiences (cited by Santamaría 2010 ).

However, PLE implementation is not always achieved successfully by culture and traditional methods of teaching and learning in the formative stage: institutions provide resources and implement, in some cases, innovative teaching strategies for learning, but to what extent do they respond to the needs and learning styles of the students?

This study has been designed to answer this question; it takes into account the different learning styles and strategies for effective PLE construction.

Problem statement

A constant concern of tutors, consultants and, in general, educational institutions offering education in e-learning mode is related to how students acquire, analyze and share knowledge. Many of the resources provided in virtual learning platforms are not adjusted to the needs and learning styles of each person, and the potential of resources is not taken advantage of to build PLEs.

On the other hand, students are unaware of their learning styles and the effectiveness of the strategies used in the education process.

Hence the need arises to implement strategies and resources aimed at strengthening the teaching-learning process, enabling students to enhance their skills and abilities by identifying their learning strategies and styles. This is the key focus of this research, based on the following question:

How can students’ learning strategies and styles, in e-learning mode, be identified so that they can contribute to the assertive construction of their PLEs?

Justification

One of the challenges of education in Colombia, listed in the Ten-Year Education Plan 2006–2016, is to ensure access to, and use and critical appropriation of information and communication technologies (ICTs) as tools for learning, creativity, and scientific, technological and cultural progress, such that it allows for human development and active participation in the knowledge society. There is also a need to promote curricular renovation of school levels and the basic functions of education and research and innovation, and to establish content and assessment practices that encourage learning and the social construction of knowledge according to the stages of development, expectations and individual and collective needs of students within their context and the world today (Ministerio de Educación Nacional de Colombia 2006 ).

At this stage and in order to contribute to the education plan, it is important for educational institutions to have the resources and didactic tools required to enable students to identify and enhance their learning styles and strategies, providing educational materials that respond to their needs and encourage their active participation. In this way, we can contribute to a genuine process of personalized and student-centered learning, under the premise that every individual learns and constructs knowledge differently based on their cognitive abilities, interests and preconceptions, hence the importance of promoting active, dynamic and collaborative learning, sharing experiences and generating new knowledge, supported by the use of ICTs. This will be possible if educational institutions have techno-pedagogical resources and strategies adapted to the learning styles of each student, and through the identification of these, more assertive PLEs can be built that are tailored to their needs and interests.

The outcomes of this research are instruments that can be applied to students using the e-learning mode in order to perform continuous monitoring to identify students’ learning styles and develop strategies ranging from the very process of mentoring to the development and availability of resources on the platform.

The aim of this study is to identify the learning strategies and styles of students using the e-learning mode as a basis for building PLEs. To that end, the following objectives have been set:

To recognize those elements that affects the construction of a PLE.

To conduct an analysis of the studies and techniques in order to identify the learning strategies and styles of students in different learning contexts.

To determine techniques and adapt instruments in order to identify the learning strategies and styles of students using the e-learning mode.

This study was conducted under the parameters of a mixed research approach, which uses quantitative and qualitative techniques, as well as an interpretive approach. Hernández et al. ( 2010 ) states that joint investigations refer to a process of collecting, analyzing and linking quantitative and qualitative data in a single study or a series of investigations to answer a research question. This type of research allows the object of study to be analyzed in its natural context, from the point of view of the participants as they perceive it. On the other hand, the use of the interpretive approach involves the description and analysis of learning styles and strategies based on the attitudes, behavior, cognitive features, and the emotional, physiological and procedural characteristics of students using the e-learning mode (Rodríguez & Valldeoriola 2009 ).

The study was conducted with undergraduate students from the Panamerican University Foundation (Unipanamericana), who were taking their course of studies in e-learning mode. In the second half of 2013, during which the research instruments were applied, there were 285 students enrolled on the various programs offered by Unipanamericana in e-learning mode.

A non-probabilistic sample was used for this study. Questionnaires were sent to all students using the e-learning mode and 54 participated in the study, corresponding to 19 % of total students enrolled. Tables 1 and 2 below detail the universe and the corresponding sample:

Research techniques

A combination of techniques allowed us to collect the necessary data to answer the research question, such as the survey, in-depth interviews and a literature review.

The survey technique was conducted via online resources, where an electronic questionnaire was used to collect structured data through closed dichotomous questions, multiple choice questions and others with alternative ordinate answers of the Likert type. The latter were used to identify the students’ learning strategies.

The survey aimed to identify the learning strategies and styles of students using the e-learning mode at Unipanamericana.

The interviews allowed the respondents’ ideas, beliefs and assumptions (Meneses & Rodríguez 2011 ) of learning strategies used and their impact on the learning process to be approached and understood.

The purpose of the interview was to understand the students’ conceptions of learning strategies and to identify the strategies they use and their impact on the learning process.

The interview was semi-structured since it was conducted from a script that allowed the interviewer to prepare information and familiarize him/herself with the topic being investigated. The central questions were open, which encouraged the interviewee to express flexible and comprehensive answers.

The literature review involved finding research and articles related to the learning strategies and styles of students in different learning contexts. The search was performed in specialized databases using search criteria to filter the most relevant and recent research publications.

Types of research tool

As an instrument of the survey technique, a questionnaire was used. This was constructed on the basis of a literature review of studies and techniques that helped to identify the learning strategies and styles of students in different learning contexts. The CHAEA tests were analyzed; CHAEA tests are the Spanish version of the LSQ tool proposed by Honey and Mumford (1988, cited by Alonso, & Gallego, 2006 )) and the Index of Learning Styles Questionnaire by Felder and Soloman ( 2008 ). Likewise, the CEVEAPEU questionnaire was analyzed, which is used to assess the learning strategies of university students (Gargallo et al. 2009 ). A process of selection, classification and adaptation of the questions was conducted and new questions were asked; all of these focused on the aim of this study.

For the interview technique, a script was made to allow the researchers to direct their questions according to the study aim and variables. In addition to the script there was a protocol giving the interviewer general guidelines to consider before, during and after the interview.

The script consisted of 18 questions, of which 6 were closed and corresponded to the respondents’ general information, and a section intended for respondents to give their consent to participating in the process of data gathering and dissemination within the framework of this study. There were also 12 open questions focusing on learning strategies. Thus the relationship of the study objectives to the research question was evident. Finally, a section was assigned to the interviewer to assess the interview. Some of the issues presented in the script are based on scripts validated and implemented in other research: the development of an oral source (Pantaleón & Rey 2006 ) and the design of a system for the management and control of the production of content and learning objects, for e-learning at Unipanamericana (Parra, 2010 ).

On the other hand, the data obtained from the literature review were listed in a matrix outlining the most important aspects of selected publications (general topic or title of the project consulted, authors, year, country, educational institution and funding body, specialist database, URL data, document type, search criteria used, keywords, synthesis and contribution), thus allowing their objects of study to be contextualized, their status to be identified, their results compared and the respective document analysis to be performed.

Data gathering was conducted electronically as follows:

The questionnaire was made available on Google Drive and sent to students via the institution’s e-mail system. It was addressed to all students and was notified through different electronic media.

For the interviews, three students were selected from the active programs in e-learning mode at Unipanamericana, who voluntarily chose to participate in it. The interviews were conducted individually via Skype, following protocol and script, designed for the application of the instrument, where the interviewer created a bond of trust with the interviewees and thus achieved an in-depth interview.

Learning styles of students using the e-learning mode at Unipanamericana

Table 3 shows the predominant learning styles of the 54 students surveyed, defined from the model of learning styles by Felder and Silverman:

Following Felder and Silverman’s bipolar category, in Category 1, the active learning style predominated (89 % of the students surveyed), according to the Index of Learning Styles Questionnaire (Felder & Soloman, 2008 .); the students in whom this style predominates tend to retain and understand information dynamically through dialogues or by explaining to others, and they are generally more likely to work in groups. For their part, reflective students tend to think about and process information in silence before giving their point of view and generally prefer individual work. Of the respondents, 9 % can be found in this category, and 2 % in both learning styles.

In category 2, the intuitive style predominated (44 % of the students surveyed), while only 15 % of the respondents can be found in the sensitive style. However, the prevalence of both learning styles is evident (41 % of the students surveyed). Sensitive students tend towards fact-based learning through problem solving and memorization of situations via laboratories and workshops, whereas intuitive students are often interested in discovery, exploration and connections, are innovative and often have a flair for abstraction and mathematical operations.

In category 3, the visual learning style predominated (83 % of the students surveyed), that is, they are students who better remember what they see (pictures, graphs, charts, timelines, videos and flow charts, among others), while only 7 % of the respondents can be found in the verbal style. Verbal students generally tend to learn best through lectures, readings, discussions and other spoken or written expressions. However, the prevalence of both learning styles is 9 %. This implies that, in 92 % of the sample, the visual style predominates, something that is favored in e-learning since it has several educational resources and graphic materials.

Finally, in category 4, the predominance of the global style is evident (87 % of the students surveyed); they are students who tend to learn in blocks without connections, are often able to solve complex problems quickly, but may struggle to explain how they do so. Of the respondents, 13 % can be found in the sequential style. The latter style is characterized by linear learning, following logical steps in search of solutions to problems, and through connections. Among the students surveyed, the global and sequential styles were not found to exist equitably.

In relation to the gender variable, and according to the results presented in Table 4 , the predominant learning style among women is global with 86 %, followed by the visual and active with 79 % each. Meanwhile, among men, the predominant learning style is active with 100 %, followed by visual and global with 88 % each. This indicates that there is a higher prevalence for the same learning styles in both genders.

Learning strategies of students using the e-learning mode

The interview data were categorized retaining the classification of learning strategies (Gargallo et al. 2009 ) and, from these, the following scheme was generated: (Fig. 1 ).

Respondents expressed their interest in individual work; it allows them to optimize time because of the technical and timing difficulties involved in synchronous meetings. However, in group work they are characterized as leaders and active. Among the strategies for organizing information, the most commonly used are the development of conceptual maps, summaries, keywords and data banks. A technique used to optimize learning is the association of terms. In addition, those interviewed agreed that they are methodical and linearly follow instructions when undertaking an activity.

When they have doubts about a topic, the respondents stated that they initially turn to Internet sources and only turn to teachers when they require clarification of the instructions to undertake academic activities. As for the work environment, there is a preference for spaces of silence and tranquility at night-time, something that coincides with the data collected in the survey.

Undertaking activities is planned according to deadlines for delivery and the level of difficulty of the issues, giving priority to subjects of greater complexity. After receiving feedback from the teacher, the respondents said that they did not always explore the topic further unless, that is, the feedback was not clear or sufficiently detailed.

Finally, the respondents said that the role of the teacher was very important in terms of facilitating their education process.

This study identified the learning strategies and styles of students using the e-learning mode at Unipanamericana, which showed that the active, visual and global styles predominant.

One thing to consider when learning environments and educational resources involved in PLEs are provided – which is significant in the sample – is that students prefer an environment isolated from noise and distraction factors, so as to enable better concentration and enhanced learning. For this reason, it is important to consider these conditions at the time of designing and publishing educational resources on virtual platforms, seeking balance between the different resources and ensuring that they are not distracting from the true purpose of learning that the students hope to achieve.

As for learning strategies, the trend among students is to make enquiries and address their concerns through various online resources. Faced with this situation, they have various options: to improve the quality and ultimately the accuracy of the information published on the network, though this does not depend solely on the teachers and students at Unipanamericana: while it is a viable alternative, it is insufficient. In short, we still need to generate the culture for students to seek out and identify reliable sources like books, specialist databases, scientific articles published in indexed journals, both nationally and internationally, and, finally to promote respect for copyright and the use of standards such as those of the American Psychological Association (APA).

Among the learning strategies, worthy of note is the fact that the students have a structure and are organized to carry out their learning process, plan their activities and to devote extra time to study. As for self-regulation, when undertaking their activities, the students realize whether or not they have been done properly, that is, they independently reflect on their own learning. However, it is necessary to continue strengthening the self-assessment strategies currently implemented at the university.

This indicates that is necessary to recognize that every individual learns and constructs knowledge differently based on their cognitive abilities, interests and preconceptions. This implies that knowledge is unique to the individual and depends on the pace of learning and the meaning given to it. Hence the importance of shifting towards active, dynamic and collaborative learning, sharing experiences and generating new knowledge, supported by the use of ICTs. This is possible if educational institutions have techno-pedagogical resources and strategies that are tailored to the learning styles of each student, and identifying them will allow them to build more assertive learning environments that are better tailored to their needs and interests. It is also important to create action plans that allow educational resources, platforms and mentoring processes to be adapted to the learning strategies and styles of students using the e-learning mode. Of particular importance within these plans is the implementation of instruments at different stages of the students’ formative processes, report results available online to students and tutors, specialized study skills clubs from the predominant learning styles, time management resources and strategies, and the adaptation of resources to different formats for different devices, among others.

Finally, this study allowed a literature review to be conducted, which helped to determine the current status of the issue within the national and international context, and instruments to be made available to students using the e-learning mode at Unipanamericana to identify their learning styles and strategies, which are the cornerstones for building their PLEs.

Study limitations and prospects

During the course of the study, the greatest difficulty was encountered in the questionnaire implementation stage due to the timing of the academic recess for students in Colombia, which coincided with the data collection date. In the questionnaire implementation stage of future projects, it will be important to contact participants via email, social networks and institutional platforms to provide them with a preliminary summary of the study in order to encourage them to become part of the sample.

Based on the results of this study, a new project has been started. The new project seeks to design software to allow students to undertake activities, each designed according to the questions of the instruments used during the study. By using the software, the students will be able to undertake these activities and, on completion, the software will tell each student what his/her dominant learning style is and suggest a series of learning strategies.

Likewise, the need arises to perform new studies to delve into the role of the tutor in the students’ PLEs and learning styles, and into how the tutor will be able to guide the students to ensure that they are better used.

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

Description : To provide a detailed and accurate description of a particular phenomenon or population.
Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

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Speaker 1: Welcome to this overview of quantitative research methods. This tutorial will give you the big picture of quantitative research and introduce key concepts that will help you determine if quantitative methods are appropriate for your project study. First, what is educational research? Educational research is a process of scholarly inquiry designed to investigate the process of instruction and learning, the behaviors, perceptions, and attributes of students and teachers, the impact of institutional processes and policies, and all other areas of the educational process. The research design may be quantitative, qualitative, or a mixed methods design. The focus of this overview is quantitative methods. The general purpose of quantitative research is to explain, predict, investigate relationships, describe current conditions, or to examine possible impacts or influences on designated outcomes. Quantitative research differs from qualitative research in several ways. It works to achieve different goals and uses different methods and design. This table illustrates some of the key differences. Qualitative research generally uses a small sample to explore and describe experiences through the use of thick, rich descriptions of detailed data in an attempt to understand and interpret human perspectives. It is less interested in generalizing to the population as a whole. For example, when studying bullying, a qualitative researcher might learn about the experience of the victims and the experience of the bully by interviewing both bullies and victims and observing them on the playground. Quantitative studies generally use large samples to test numerical data by comparing or finding correlations among sample attributes so that the findings can be generalized to the population. If quantitative researchers were studying bullying, they might measure the effects of a bully on the victim by comparing students who are victims and students who are not victims of bullying using an attitudinal survey. In conducting quantitative research, the researcher first identifies the problem. For Ed.D. research, this problem represents a gap in practice. For Ph.D. research, this problem represents a gap in the literature. In either case, the problem needs to be of importance in the professional field. Next, the researcher establishes the purpose of the study. Why do you want to do the study, and what do you intend to accomplish? This is followed by research questions which help to focus the study. Once the study is focused, the researcher needs to review both seminal works and current peer-reviewed primary sources. Based on the research question and on a review of prior research, a hypothesis is created that predicts the relationship between the study's variables. Next, the researcher chooses a study design and methods to test the hypothesis. These choices should be informed by a review of methodological approaches used to address similar questions in prior research. Finally, appropriate analytical methods are used to analyze the data, allowing the researcher to draw conclusions and inferences about the data, and answer the research question that was originally posed. In quantitative research, research questions are typically descriptive, relational, or causal. Descriptive questions constrain the researcher to describing what currently exists. With a descriptive research question, one can examine perceptions or attitudes as well as more concrete variables such as achievement. For example, one might describe a population of learners by gathering data on their age, gender, socioeconomic status, and attributes towards their learning experiences. Relational questions examine the relationship between two or more variables. The X variable has some linear relationship to the Y variable. Causal inferences cannot be made from this type of research. For example, one could study the relationship between students' study habits and achievements. One might find that students using certain kinds of study strategies demonstrate greater learning, but one could not state conclusively that using certain study strategies will lead to or cause higher achievement. Causal questions, on the other hand, are designed to allow the researcher to draw a causal inference. A causal question seeks to determine if a treatment variable in a program had an effect on one or more outcome variables. In other words, the X variable influences the Y variable. For example, one could design a study that answered the question of whether a particular instructional approach caused students to learn more. The research question serves as a basis for posing a hypothesis, a predicted answer to the research question that incorporates operational definitions of the study's variables and is rooted in the literature. An operational definition matches a concept with a method of measurement, identifying how the concept will be quantified. For example, in a study of instructional strategies, the hypothesis might be that students of teachers who use Strategy X will exhibit greater learning than students of teachers who do not. In this study, one would need to operationalize learning by identifying a test or instrument that would measure learning. This approach allows the researcher to create a testable hypothesis. Relational and causal research relies on the creation of a null hypothesis, a version of the research hypothesis that predicts no relationship between variables or no effect of one variable on another. When writing the hypothesis for a quantitative question, the null hypothesis and the research or alternative hypothesis use parallel sentence structure. In this example, the null hypothesis states that there will be no statistical difference between groups, while the research or alternative hypothesis states that there will be a statistical difference between groups. Note also that both hypothesis statements operationalize the critical thinking skills variable by identifying the measurement instrument to be used. Once the research questions and hypotheses are solidified, the researcher must select a design that will create a situation in which the hypotheses can be tested and the research questions answered. Ideally, the research design will isolate the study's variables and control for intervening variables so that one can be certain of the relationships being tested. In educational research, however, it is extremely difficult to establish sufficient controls in the complex social settings being studied. In our example of investigating the impact of a certain instructional strategy in the classroom on student achievement, each day the teacher uses a specific instructional strategy. After school, some of the students in her class receive tutoring. Other students have parents that are very involved in their child's academic progress and provide learning experiences in the home. These students may do better because they received extra help, not because the teacher's instructional strategy is more effective. Unless the researcher can control for the intervening variable of extra help, it will be impossible to effectively test the study's hypothesis. Quantitative research designs can fall into two broad categories, experimental and quasi-experimental. Classic experimental designs are those that randomly assign subjects to either a control or treatment comparison group. The researcher can then compare the treatment group to the control group to test for an intervention's effect, known as a between-subject design. It is important to note that the control group may receive a standard treatment or may receive a treatment of any kind. Quasi-experimental designs do not randomly assign subjects to groups, but rather take advantage of existing groups. A researcher can still have a control and comparison group, but assignment to the groups is not random. The use of a control group is not required. However, the researcher may choose a design in which a single group is pre- and post-tested, known as a within-subjects design. Or a single group may receive only a post-test. Since quasi-experimental designs lack random assignment, the researcher should be aware of the threats to validity. Educational research often attempts to measure abstract variables such as attitudes, beliefs, and feelings. Surveys can capture data about these hard-to-measure variables, as well as other self-reported information such as demographic factors. A survey is an instrument used to collect verifiable information from a sample population. In quantitative research, surveys typically include questions that ask respondents to choose a rating from a scale, select one or more items from a list, or other responses that result in numerical data. Studies that use surveys or tests need to include strategies that establish the validity of the instrument used. There are many types of validity that need to be addressed. Face validity. Does the test appear at face value to measure what it is supposed to measure? Content validity. Content validity includes both item validity and sampling validity. Item validity ensures that the individual test items deal only with the subject being addressed. Sampling validity ensures that the range of item topics is appropriate to the subject being studied. For example, item validity might be high, but if all the items only deal with one aspect of the subjects, then sampling validity is low. Content validity can be established by having experts in the field review the test. Concurrent validity. Does a new test correlate with an older, established test that measures the same thing? Predictive validity. Does the test correlate with another related measure? For example, GRE tests are used at many colleges because these schools believe that a good grade on this test increases the probability that the student will do well at the college. Linear regression can establish the predictive validity of a test. Construct validity. Does the test measure the construct it is intended to measure? Establishing construct validity can be a difficult task when the constructs being measured are abstract. But it can be established by conducting a number of studies in which you test hypotheses regarding the construct, or by completing a factor analysis to ensure that you have the number of constructs that you say you have. In addition to ensuring the validity of instruments, the quantitative researcher needs to establish their reliability as well. Strategies for establishing reliability include Test retest. Correlates scores from two different administrations of the same test. Alternate forms. Correlates scores from administrations of two different forms of the same test. Split half reliability. Treats each half of one test or survey as a separate administration and correlates the results from each. Internal consistency. Uses Cronbach's coefficient alpha to calculate the average of all possible split halves. Quantitative research almost always relies on a sample that is intended to be representative of a larger population. There are two basic sampling strategies, random and non-random, and a number of specific strategies within each of these approaches. This table provides examples of each of the major strategies. The next section of this tutorial provides an overview of the procedures in conducting quantitative data analysis. There are specific procedures for conducting the data collection, preparing for and analyzing data, presenting the findings, and connecting to the body of existing research. This process ensures that the research is conducted as a systematic investigation that leads to credible results. Data comes in various sizes and shapes, and it is important to know about these so that the proper analysis can be used on the data. In 1946, S.S. Stevens first described the properties of measurement systems that allowed decisions about the type of measurement and about the attributes of objects that are preserved in numbers. These four types of data are referred to as nominal, ordinal, interval, and ratio. First, let's examine nominal data. With nominal data, there is no number value that indicates quantity. Instead, a number has been assigned to represent a certain attribute, like the number 1 to represent male and the number 2 to represent female. In other words, the number is just a label. You could also assign numbers to represent race, religion, or any other categorical information. Nominal data only denotes group membership. With ordinal data, there is again no indication of quantity. Rather, a number is assigned for ranking order. For example, satisfaction surveys often ask respondents to rank order their level of satisfaction with services or programs. The next level of measurement is interval data. With interval data, there are equal distances between two values, but there is no natural zero. A common example is the Fahrenheit temperature scale. Differences between the temperature measurements make sense, but ratios do not. For instance, 20 degrees Fahrenheit is not twice as hot as 10 degrees Fahrenheit. You can add and subtract interval level data, but they cannot be divided or multiplied. Finally, we have ratio data. Ratio is the same as interval, however ratios, means, averages, and other numerical formulas are all possible and make sense. Zero has a logical meaning, which shows the absence of, or having none of. Examples of ratio data are height, weight, speed, or any quantities based on a scale with a natural zero. In summary, nominal data can only be counted. Ordinal data can be counted and ranked. Interval data can also be added and subtracted, and ratio data can also be used in ratios and other calculations. Determining what type of data you have is one of the most important aspects of quantitative analysis. Depending on the research question, hypotheses, and research design, the researcher may choose to use descriptive and or inferential statistics to begin to analyze the data. Descriptive statistics are best illustrated when viewed through the lens of America's pastimes. Sports, weather, economy, stock market, and even our retirement portfolio are presented in a descriptive analysis. Basic terminology for descriptive statistics are terms that we are most familiar in this discipline. Frequency, mean, median, mode, range, variance, and standard deviation. Simply put, you are describing the data. Some of the most common graphic representations of data are bar graphs, pie graphs, histograms, and box and whisker graphs. Attempting to reach conclusions and make causal inferences beyond graphic representations or descriptive analyses is referred to as inferential statistics. In other words, examining the college enrollment of the past decade in a certain geographical region would assist in estimating what the enrollment for the next year might be. Frequently in education, the means of two or more groups are compared. When comparing means to assist in answering a research question, one can use a within-group, between-groups, or mixed-subject design. In a within-group design, the researcher compares measures of the same subjects across time, therefore within-group, or under different treatment conditions. This can also be referred to as a dependent-group design. The most basic example of this type of quasi-experimental design would be if a researcher conducted a pretest of a group of students, subjected them to a treatment, and then conducted a post-test. The group has been measured at different points in time. In a between-group design, subjects are assigned to one of the two or more groups. For example, Control, Treatment 1, Treatment 2. Ideally, the sampling and assignment to groups would be random, which would make this an experimental design. The researcher can then compare the means of the treatment group to the control group. When comparing two groups, the researcher can gain insight into the effects of the treatment. In a mixed-subjects design, the researcher is testing for significant differences between two or more independent groups while subjecting them to repeated measures. Choosing a statistical test to compare groups depends on the number of groups, whether the data are nominal, ordinal, or interval, and whether the data meet the assumptions for parametric tests. Nonparametric tests are typically used with nominal and ordinal data, while parametric tests use interval and ratio-level data. In addition to this, some further assumptions are made for parametric tests that the data are normally distributed in the population, that participant selection is independent, and the selection of one person does not determine the selection of another, and that the variances of the groups being compared are equal. The assumption of independent participant selection cannot be violated, but the others are more flexible. The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the method of analysis for a quasi-experimental design. When choosing a t-test, the assumptions are that the data are parametric. The analysis of variance, or ANOVA, assesses whether the means of more than two groups are statistically different from each other. When choosing an ANOVA, the assumptions are that the data are parametric. The chi-square test can be used when you have non-parametric data and want to compare differences between groups. The Kruskal-Wallis test can be used when there are more than two groups and the data are non-parametric. Correlation analysis is a set of statistical tests to determine whether there are linear relationships between two or more sets of variables from the same list of items or individuals, for example, achievement and performance of students. The tests provide a statistical yes or no as to whether a significant relationship or correlation exists between the variables. A correlation test consists of calculating a correlation coefficient between two variables. Again, there are parametric and non-parametric choices based on the assumptions of the data. Pearson R correlation is widely used in statistics to measure the strength of the relationship between linearly related variables. Spearman-Rank correlation is a non-parametric test that is used to measure the degree of association between two variables. Spearman-Rank correlation test does not assume any assumptions about the distribution. Spearman-Rank correlation test is used when the Pearson test gives misleading results. Often a Kendall-Taw is also included in this list of non-parametric correlation tests to examine the strength of the relationship if there are less than 20 rankings. Linear regression and correlation are similar and often confused. Sometimes your methodologist will encourage you to examine both the calculations. Calculate linear correlation if you measured both variables, x and y. Make sure to use the Pearson parametric correlation coefficient if you are certain you are not violating the test assumptions. Otherwise, choose the Spearman non-parametric correlation coefficient. If either variable has been manipulated using an intervention, do not calculate a correlation. While linear regression does indicate the nature of the relationship between two variables, like correlation, it can also be used to make predictions because one variable is considered explanatory while the other is considered a dependent variable. Establishing validity is a critical part of quantitative research. As with the nature of quantitative research, there is a defined approach or process for establishing validity. This also allows for the findings transferability. For a study to be valid, the evidence must support the interpretations of the data, the data must be accurate, and their use in drawing conclusions must be logical and appropriate. Construct validity concerns whether what you did for the program was what you wanted to do, or whether what you observed was what you wanted to observe. Construct validity concerns whether the operationalization of your variables are related to the theoretical concepts you are trying to measure. Are you actually measuring what you want to measure? Internal validity means that you have evidence that what you did in the study, i.e., the program, caused what you observed, i.e., the outcome, to happen. Conclusion validity is the degree to which conclusions drawn about relationships in the data are reasonable. External validity concerns the process of generalizing, or the degree to which the conclusions in your study would hold for other persons in other places and at other times. Establishing reliability and validity to your study is one of the most critical elements of the research process. Once you have decided to embark upon the process of conducting a quantitative study, use the following steps to get started. First, review research studies that have been conducted on your topic to determine what methods were used. Consider the strengths and weaknesses of the various data collection and analysis methods. Next, review the literature on quantitative research methods. Every aspect of your research has a body of literature associated with it. Just as you would not confine yourself to your course textbooks for your review of research on your topic, you should not limit yourself to your course texts for your review of methodological literature. Read broadly and deeply from the scholarly literature to gain expertise in quantitative research. Additional self-paced tutorials have been developed on different methodologies and techniques associated with quantitative research. Make sure that you complete all of the self-paced tutorials and review them as often as needed. You will then be prepared to complete a literature review of the specific methodologies and techniques that you will use in your study. Thank you for watching.

Methods for Quantitative Research in Psychology

Conducting Research

Psychological Research

August 2023

This seven-hour course provides a comprehensive exploration of research methodologies, beginning with the foundational steps of the scientific method. Students will learn about hypotheses, experimental design, data collection, and the analysis of results. Emphasis is placed on defining variables accurately, distinguishing between independent, dependent, and controlled variables, and understanding their roles in research.

The course delves into major research designs, including experimental, correlational, and observational studies. Students will compare and contrast these designs, evaluating their strengths and weaknesses in various contexts. This comparison extends to the types of research questions scientists pose, highlighting how different designs are suited to different inquiries.

A critical component of the course is developing the ability to judge the quality of sources for literature reviews. Students will learn criteria for evaluating the credibility, relevance, and reliability of sources, ensuring that their understanding of the research literature is built on a solid foundation.

Reliability and validity are key concepts addressed in the course. Students will explore what it means for an observation to be reliable, focusing on consistency and repeatability. They will also compare and contrast different forms of validity, such as internal, external, construct, and criterion validity, and how these apply to various research designs.

The course concepts are thoroughly couched in examples drawn from the psychological research literature. By the end of the course, students will be equipped with the skills to design robust research studies, critically evaluate sources, and understand the nuances of reliability and validity in scientific research. This knowledge will be essential for conducting high-quality research and contributing to the scientific community.

Learning objectives

Describe the steps of the scientific method.
Specify how variables are defined.
Compare and contrast the major research designs.
Explain how to judge the quality of a source for a literature review.
Compare and contrast the kinds of research questions scientists ask.
Explain what it means for an observation to be reliable.
Compare and contrast forms of validity as they apply to the major research designs.

This program does not offer CE credit.

More in this series

Introduces applying statistical methods effectively in psychology or related fields for undergraduates, high school students, and professionals.

August 2023 On Demand Training

Introduces the importance of ethical practice in scientific research for undergraduates, high school students, and professionals.

Profiling mathematics teacher educators' readiness for digital technology integration: evidence from Zambia

Open access
Published: 04 September 2024

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Angel Mukuka ORCID: orcid.org/0000-0003-0292-1324 1 &
Jogymol Kalariparampil Alex ORCID: orcid.org/0000-0002-0118-760X 2

Research on Mathematics Teacher Educators (MTEs) is crucial for enhancing the professional development of prospective mathematics teachers. However, there is a dearth of recent studies focusing on MTEs’ preparedness for technology integration, particularly within the Zambian educational context, and the wider Sub-Saharan African region. This study assessed the readiness of MTEs in Zambia to effectively integrate digital technology into mathematics education, examining their perceived technological proficiency and familiarity, perceived usefulness, and perceived ease of use. Using a predominantly quantitative cross sectional research design, responses were gathered from 104 MTEs across 16 colleges of education and 12 universities in Zambia through an online semi-structured questionnaire. The findings revealed that, on average, MTEs exhibited low to moderate familiarity with various mathematics-related software applications, e-learning management systems, and web-based video conferencing tools. Although technological proficiency and perceived ease of use were somewhat lacking, MTEs demonstrated awareness of the value of digital technology and expressed willingness to ensure that preservice mathematics teachers acquire the necessary information and skills for technology integration in mathematics teaching and learning. Furthermore, willingness to use technology in the classroom was significantly predicted by perceived usefulness of, and proficiency with, various digital tools. The study also revealed that individuals tend to perceive technology as easier to use as they become more technologically proficient. In light of these findings, it is suggested that access to technological support not only enhances MTEs’ perception of technology’s ease of use but also positively influences their inclination to incorporate it into instructional strategies.

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Introduction

Mathematics education faces persistent challenges worldwide, with many students at both school and tertiary levels perceiving it as one of the most challenging subjects. This trend is prominently reflected in both national and international assessments of student achievement in mathematics, consistently indicating subpar performance among students, albeit with notable exceptions observed in select East Asian countries (Bethell, 2016 ; Mullis et al., 2012 , 2020 ; Organisation for Economic Cooperation and Development [OECD], 2019 ). The emergence of the coronavirus disease 2019 (COVID-19) in recent years has exacerbated concerns surrounding academic performance in mathematics, highlighting the urgency for proactive measures to address potential future crises (Mukuka et al., 2021 ). The pivotal role of digital technology in mathematics education has become increasingly evident, not only during the COVID-19 era but since the advent of the twenty-first century. Digital tools have reshaped how we engage with information, altering our learning processes and prompting a re-evaluation of pedagogical practices (Chorney, 2018 ; Gravemeijer et al., 2017 ; Traore, 2021 ). This evolution is particularly pertinent for preservice teachers, who are poised to become change agents in the classroom. However, challenges persist, particularly in regions such as sub-Saharan Africa (SSA), where inadequate resources hinder the adoption of technology-based instruction (Iyamuremye et al., 2022 ; Jita & Sintema, 2022 ). Despite its potential, there remains a dearth of recent information regarding mathematics teacher educators’ (MTEs) readiness to integrate digital technology into their teaching practices, particularly in Zambia where no such study has been conducted (Mukuka, 2024 ). Research conducted by Appova and Taylor ( 2019 ) also indicates that this trend is quite prominent in other settings.

Given MTEs’ pivotal role in shaping the next generation of mathematics teachers, it is imperative to understand their readiness to use digital technology in their pedagogical practices. This study aimed to profile MTEs’ readiness for effective integration of digital technology in mathematics education by evaluating their perceived technological proficiency and familiarity, perceived usefulness, and perceived ease of use. By examining these factors, we sought to uncover the current landscape of digital technology integration in mathematics teacher education and inform efforts to enhance MTEs’ preparedness in this critical domain. Therefore, we sought answers to the following research questions:

What are MTEs’ perceptions of their technological proficiency, familiarity, usefulness, and ease of using digital technology in mathematics education?

To what extent do MTEs’ technological proficiency, perceived usefulness, and perceived ease of using digital technology influence their willingness to support preservice mathematics teachers in acquiring the necessary skills for effective technology integration in their future classrooms?

Literature review

The definition of “technology” has varied depending on the situation, and it is a very broad construct. Our study focuses on digital technology, which at times, is referred to as “technology” in this text. In accordance with Freiman’s ( 2014 ) simplistic perspective, we define digital technology as that which encompasses ‘hardware’ devices that are physically present (such as tablets, computers, printers, smartphones, projectors, etc.) along with ‘software’ or applications that provide user interfaces for such hardware. According to Sinclair and Robutti ( 2020 , p. 245), digital technology serves two roles in mathematics education. The first is to assist in the organization of the teacher’s work (by, for example, producing worksheets, printing tests, keeping track of students’ grades, etc.). The second is to encourage cutting-edge methods for creating and presenting mathematics lessons. In the context of this study, we place a greater emphasis on the latter, particularly mathematics software and other relevant digital tools and applications that offer user-friendly interfaces, within the teaching and learning process.

Role of digital technology in mathematics education

Literature is replete with studies that have highlighted the transformative potential of digital tools in reshaping pedagogical practices and enhancing learning outcomes in mathematics at both school and tertiary levels of education (Alex & Mukuka, 2024 ; Clark-Wilson et al., 2020 ; Drijvers & Sinclair, 2023 ). As indicated earlier, one area of focus within this paper concerns MTEs’ perceptions of their proficiency to use various digital applications, ranging from social media platforms to mathematics software. Specifically, the term ‘perceived technology proficiency’ refers to self-assessed confidence and ability to understand and use technology in mathematics teacher educational settings. This means that the term does not encompass dimensions such as actual skill levels and practical experience with technology.

Platforms such as Facebook, Twitter, WhatsApp, YouTube, and other online forums have emerged as spaces for educators and students to engage in collaborative learning, share resources, and seek assistance with mathematical concepts (Baya’a & Daher, 2015 ). These platforms facilitate asynchronous communication and enable learners to access support outside of traditional classroom settings, fostering a sense of community and collaboration among learners. In their study of a group of preservice mathematics teachers in Zambia, Mulenga and Marbàn ( 2020 ) found that social media plays a significant role in shaping the future of mathematics education, particularly regarding its integration into teaching practices and its potential to foster collaborative and innovative learning environments.

Similarly, video conferencing technologies have revolutionized the delivery of mathematics lessons, particularly in contexts where physical classroom attendance is limited or impractical. This was more pronounced and quite evident during the COVID-19 era where platforms like Zoom, Google Meet, and Microsoft Teams, among others enabled educators to conduct virtual mathematics lessons, demonstrations, and tutorials, thereby overcoming geographical barriers and expanding access to quality education (Asad et al., 2022 ; Betthäuser et al., 2023 ; Mukuka et al., 2021 ). There have been calls on the need to continue utilizing such initiatives, especially that such technologies have proved useful even in the post-COVID-19 era (Camilleri & Camilleri, 2022 ; Ng & Fang, 2023 ; Nikou, 2021 ).

In addition to communication and collaboration tools, mathematics educators have increasingly embraced specialized software applications designed to facilitate mathematical exploration and problem-solving. Programs such as GeoGebra, PHET simulations, Excel, and Graphmatica, among others offer dynamic visualization tools, computational capabilities, and interactive features that enhance students’ conceptual understanding and problem-solving skills (Gökçe & Güner, 2022 ; Uwurukundo et al., 2022 ; Yohannes & Chen, 2023 ). Research shows that these software applications provide opportunities for hands-on exploration of mathematical concepts, allowing learners to manipulate variables, plot graphs, and analyze data in real-time (Bokhove & Drijvers, 2012 ; Chorney, 2018 ; Hussein et al., 2022 ).

Opportunities and challenges of technology integration

Drawing from the preceding section, it is evident that many studies have explored the effectiveness of technology-based instruction in mathematics education, revealing promising outcomes. Research indicates that integrating digital applications such as social media platforms, online video conferencing tools, and specialized mathematics software applications into mathematics instruction enhances students’ engagement, motivation, and conceptual understanding (Drijvers & Sinclair, 2023 ; Mensah & Ampadu, 2024 ). Although digital tools such as social media platforms, web-based conferencing tools, and learning management systems are not typically classified as ‘mathematics action technologies’ that directly support learners in making sense of mathematical ideas (Lee & Hollebrands, 2008 ), it is noteworthy that such tools could be used for communication purposes. Additionally, they can serve as mediums for delivering mathematics lessons. This utilization fosters a sense of community and collaboration among learners and teachers. On the other hand, specialized mathematics software applications like GeoGebra, Graphmatica, and PHET simulations, among others, provide visual representations of abstract mathematical concepts. This results in enhanced accessibility and comprehension of abstract mathematical concepts for students. Lee and Hollebrands ( 2008 ) emphasize the importance of preparing teachers to use appropriate technology in teaching mathematics, aligning with the observation by Mensah and Ampadu ( 2024 ) that computer-assisted instruction promotes student-centered approaches and active engagement. Furthermore, technology-based instruction offers customized educational experiences designed to meet the unique needs and learning preferences of each student (Castillo & Polly, 2024 ).

Amidst the aforementioned roles and opportunities, integration of digital technology into mathematics education faces significant challenges. Studies by Sacristán ( 2017 ) and Timotheou et al. ( 2023 ) highlight the multifaceted interplay of factors that influence the impact of digital technologies on education and are crucial for effective change. These factors encompass the availability and quality of infrastructure, adequacy of educational technology, sufficiency of technological resources, efficacy of professional development initiatives, teachers’ self-efficacy in utilizing technology, and their attitudes toward it. In resource-constrained environments, accessing technology poses a major hurdle, with many schools lacking essential infrastructure like stable electricity and internet connectivity necessary for digital tool implementation (Drijvers & Sinclair, 2023 ). Additionally, both teachers and learners must possess digital literacy skills for effective technology utilization (Viberg et al., 2023 ). However, teachers often lack the requisite training and support to develop these competencies especially in low-resource settings. Even when digital tools and skills are available, integrating them into the curriculum in a manner that enhances learning presents some challenges (Adnan et al., 2024 ; Luneta, 2022 ). Moreover, equity concerns arise, most students do not have equitable access to digital resources outside of school, college or university, potentially exacerbating disparities in learning outcomes (Gottschalk & Weise, 2023 ).

In the context of SSA region, these challenges are particularly evident. For example, a study conducted by Agieyi ( 2021 ) on the integration of Information and Communications Technologies (ICT) into schools in this region revealed efforts to enhance teachers’ ICT skills, yet significant obstacles hindered classroom implementation. These barriers include inadequate training opportunities, insufficient technical support, and a lack of time allocated in the school schedule for ICT involvement. Similarly, in Zambia, despite initiatives aimed at leveraging technology in education, its impact has been constrained by challenges related to infrastructure, teacher training, curriculum integration, and self-efficacy beliefs among others (Bethell, 2016 ; Bwalya & Rutegwa, 2023 ; Mukuka et al., 2021 ).

Addressing these challenges requires a comprehensive approach that includes improving infrastructure, providing teacher training, and developing curriculum guidelines for the effective use of digital tools in mathematics education (Sacristán, 2017 ). It also requires addressing equity issues to ensure that all students can benefit from the advantages that digital technology can offer in mathematics education. The highlighted challenges also point to a renewed emphasis on the need to revisit the ways in which preservice mathematics teachers are being prepared to teach mathematics with technology as highlighted by McCulloch et al. ( 2021 ). This means that MTEs need to be proficient with technology-based instruction. However, there is little information available about the depth and breadth of MTEs’ proficiency and perspectives in fostering future teachers’ technological skills, not only in Zambia but across SSA and beyond (Appova & Taylor, 2019 ; Bethell, 2016 ; Luneta, 2022 ).

Most studies that have been conducted on technology integration in mathematics classrooms have concentrated on preservice and in-service teachers, even in well-resourced settings. While this has been an important step in the right direction, it suffices to pinpoint that teacher educators’ expertise should be a priority since teacher educators are the ones who get to interact with student teachers before they are sent into schools to teach. Additionally, teacher educators are in a better position to facilitate the creation of instructional strategies that are required for sustainable futures and to train prospective teachers in how to address some of the highlighted challenges. This is why this study focuses on profiling MTEs’ readiness with the integration of digital technology in their classroom practice as they train future teachers of mathematics.

There is also a need to hear MTEs’ views with regards to their familiarity with, and access to, various digital facilities as well as their willingness to equip their students (preservice teachers) with relevant digital skills. According to Fütterer et al. ( 2023 ), “familiarity with technology refers to the level of knowledge and experience that students and teachers have with various forms of technology, such as smart tablet computers or educational software”. Technology familiarity in the context of this study primarily refers to MTEs’ access to, and use of, various mathematics-related software, e-learning management systems, video conferencing tools, and social media platforms.

Understanding the current state of MTEs’ readiness with technology integration aligns with calls for initiatives to enhance mathematics teacher preparation (Alex & Mukuka, 2024 ) and acknowledges their role as agents of change (Chapman, 2021 ). Additionally, it affirms the necessity for MTEs to possess relevant knowledge beyond the scope of preservice teachers (Beswick & Goos, 2018 ). In Zambia, there is a lack of studies on MTEs’ capacity for integrating technology-based instruction. This exploratory study aims to fill that gap by examining the current situation. Our goal is to inform efforts to improve preservice mathematics teachers’ learning experiences. Furthermore, we aim to identify the necessary enhancements to MTEs’ technological skills in order to generate findings that are particularly relevant to lower-resourced contexts in developing education systems.

Theoretical perspectives

This study employed the Technology Acceptance Model (TAM) as a framework to explore the factors shaping MTEs’ readiness to assist preservice mathematics teachers in acquiring essential skills for effective technology integration. In addition to TAM, the Technological Pedagogical Content Knowledge (TPACK) framework was utilized to provide a comprehensive understanding of MTEs’ readiness for technology integration. These models complemented each other, enabling the examination of MTEs’ familiarity, proficiency, and perceptions regarding the utility and ease of using digital technologies in mathematics classrooms. While the TAM provided insights into MTEs’ perceptions of technology adoption, the TPACK framework allowed for an exploration of how MTEs’ pedagogical expertise intersected with their perceived technological proficiency. This holistic view of MTEs’ readiness for technology integration aimed to discern the current landscape of digital technology utilization among MTEs in Zambia and how their perceptions influence their support for preservice teachers. Insights from this research are also anticipated to inform initiatives aimed at enhancing technology integration in mathematics education.

Technology acceptance model

TAM stands as a pivotal framework for understanding the factors influencing individuals’ acceptance or rejection of technology (Marangunić & Granić, 2015 ). Introduced by Fred Davis in 1989, TAM posits that perceived usefulness and perceived ease of use are key determinants of individuals’ willingness to adopt technology (Davis, 1989 ). This model suggests that an individual’s decision to use technology is primarily influenced by its perceived usefulness and ease of use (Davis, 1989 ).

TAM proposes a three-step process for technology acceptance, where external elements (like system design features) initiate cognitive reactions (such as perceived ease of use and usefulness), leading to an emotional response (attitude toward using technology/intention), which then influences usage behavior (Davis, 1989 , 1993 ). Perceived ease of use and usefulness constitute the anticipation of positive behavioral results and the belief that the behavior will not be effort intensive. Davis ( 1989 ) defined perceived usefulness as the individual’s perception of how much the usage of a specific technology enhances performance. Perceived ease of use was characterized as the degree to which an individual perceives using a specific system as being uncomplicated.

External variables are system characteristics that impact users’ perceptions of ease of use and usefulness (Marangunić & Granić, 2015 ). In the realm of mathematics education, these external variables encompass factors like facilitating conditions within the user’s environment, which encourage system utilization. Such conditions may include resource availability, technical infrastructure, user competence, self-efficacy beliefs, and access to ICT tools (Bwalya & Rutegwa, 2023 ; Joo et al., 2018 ; Perienen, 2020 ). In this study, MTEs’ proficiency with digital technology was considered an external variable that could influence their perception of technology’s usefulness and ease of use.

Although TAM has evolved into different versions, such as TAM2 (Venkatesh & Davis, 2000 ), TAM3 (Venkatesh & Bala, 2008 ), and the Unified Theory of Acceptance and Use of Technology (UTAUT) (Venkatesh et al., 2003 ), we applied the original version (as illustrated in Fig. 1 ). This was due to its simplicity and alignment with our research objectives. This model’s straightforward approach made it the most suitable choice for this study. Specifically, we focused on perceived usefulness and perceived ease of use to investigate MTEs’ readiness for technology integration. The original TAM also allows for the inclusion of external variables, such as MTEs’ technology proficiency, which was assessed through the TPACK model as discussed later in this article.

Venkatesh and Davis ( 1996 ) Version of TAM (Source, Rondan-Cataluña et al., 2015 , p. 792)

Technological pedagogical content knowledge

As alluded to earlier, the TPACK model was used to understand the level of MTEs’ perceived proficiency with technology integration. This framework offers a structured approach to describe the knowledge essential for teachers to effectively incorporate technology into their teaching methodologies. Mishra and Koehler ( 2006 ) articulate that TPACK aims to tackle the complex nature of teacher knowledge, highlighting the necessary information teachers must possess to integrate technology into their instructional practices. Building upon Shulman’s ( 1986 ) Pedagogical Content Knowledge, the TPACK framework comprises seven components, as illustrated in Fig. 2 . Each of these components encompasses distinct facets of knowledge crucial for effective technology integration in teaching, from understanding subject matter and pedagogical techniques to leveraging technology to transform both content and pedagogy. Furthermore, the TPACK model has been utilized by prior researchers from different settings to evaluate teacher competency in technology integration ( see Aldemir et al., 2023 ; Clark-Wilson et al., 2020 ; Joo et al., 2018 ; Njiku, 2024 ). This highlights its relevance in assessing MTEs’ proficiency in incorporating technology. Illustrated in Fig. 2 , TPACK not only examines individual domains but also their intersections, providing a comprehensive perspective on the competencies that are imperative for successful technology integration in teaching practices.

TPACK Framework

While Joo et al. ( 2018 ) included all 7 TPACK model components as well as self-efficacy as external factors, this study only focused on technology components (TK, TCK, TPK, and TPACK) since MTEs’ mastery of mathematics content was not within the confines of this study. In addition, it was believed that MTEs’ familiarity with a range of digital technologies was cardinal because lack of access to technology is likely to restrict one’s acquaintance with various digital tools (Fütterer et al., 2023 ). Although concerns with access to various digital tools and platforms have been recognized in an earlier study (Mukuka et al., 2021 ), no study has been conducted in Zambia to profile MTEs’ readiness to integrate technology into their pedagogical practices.

Hypothesized relationships among study variables

The conceptual model that is shown in Fig. 3 illustrates the structural connections among the variables that were investigated for providing answers to the second research question. As discussed earlier, these structural relationships were informed by insights from the TAM model (Fig. 1 ). Additionally, we enhanced our understanding by incorporating proficiency with digital technology as an external variable, assessed using the TPACK framework (Fig. 2 ).

Hypothesized structural relationships among the studied constructs [Adapted from Joo et al., 2018 ]

In line with the conceptual model depicted in Fig. 3 , and the second research question, the following hypotheses were formulated and tested at the 5% level of significance.

Hypothesis 1 (H1)

Proficiency with digital technology has a positive influence on MTEs’ perceived usefulness of technology in mathematics teaching.

Hypothesis 2 (H2)

Proficiency with digital technology positively affects MTEs’ perceived ease of using technology in mathematics teaching.

Hypothesis 3 (H3)

Willingness to support the development of technological skills among preservice teachers is positively influenced by MTEs’ proficiency, perceived usefulness, and perceived ease of using technology in mathematics teaching and learning.

Research design and setting

This paper reports the findings from an exploratory study that aimed to profile MTEs’ perspectives regarding digital technology integration. A cross sectional survey design was employed. According to Creswell ( 2014 ), cross sectional survey designs are well-suited for exploratory research because they provide an overview of the situation without requiring long-term data collection. With our limited budget and personnel, this design allowed us to survey MTEs across different provinces, covering a wide geographic area within a short period of time. The survey respondents were mathematics teacher educators (lecturers) teaching at either private or public colleges and universities across the 10 provinces of Zambia. Teachers in Zambia undergo training to teach mathematics across four distinct educational levels: early childhood, primary, junior secondary, and senior secondary education. Early childhood education caters to children aged 3 to 6 years, while primary education (Grades 1–7) serves children aged 7 to 13, and secondary education caters to learners aged 14 to 18 (Ministry of Education, 2000 ; Ministry of Education, Science, Vocational Training and Early Education [MOESVTEE], 2013 ). It is noteworthy that these age ranges are not absolute, with exceptions occurring in certain situations. For instance, some children may enter grade one at 6 or even 5 years, especially in urban areas, while delays in entering the primary education are common in rural areas where early childhood education centers are scarce.

Additionally, there is no specialized training for teachers at the early childhood and primary education levels; teachers trained for these levels receive training in all subjects, including mathematics. Conversely, teachers trained for junior and senior secondary levels undergo specialized training to teach specific subjects. Nonetheless, the focus of this research was on educators at the tertiary level who train prospective teachers in mathematics instruction for junior and senior secondary levels. As noted in prior literature (e.g., Tabakamulamu et al., 2007 ), two distinct pathways exist for teaching mathematics at the secondary school level: one through colleges of education and another through universities. Teachers who graduate from colleges of education with a diploma are certified to teach mathematics to students in grades 8 and 9. University-trained teachers, on the other hand get a bachelor’s degree and are eligible to teach mathematics to students in both junior and senior secondary schools (Grades 8–12). A bachelor’s degree holder with relevant teaching experience is also eligible to teach at a college of education; whereas, a master’s degree is required minimum qualification to teach at the university. This means that a bachelor’s degree with relevant experience is the minimum qualification to teach at a college of education.

Research participants and data collection

The survey was created in Google Form and sent to the targeted respondents online. Snowball and convenience sampling techniques were deemed appropriate for selecting the study participants. The researchers were aware of the discrepancy between the study approach employed and the sampling techniques used. Quantitative studies demand probability (random) sampling techniques, albeit qualitative research fares well with non-probability sampling techniques like the ones employed in this study. Since participation in the study was entirely voluntary and the researchers aimed to recruit as many participants as possible, the nature of the study precluded the use of random sampling. The MTEs who could easily be identified were sent a link to a questionnaire, and they then forwarded it to other individuals in their departments and other institutions. Researchers also worked closely with officials in the Ministry of Education to identify more respondents. As referenced in another source (Mukuka, 2024 ), the process of data collection took place between mid-June 2023 and early August 2023. During this period, the authors concluded their data collection efforts, feeling they had explored all available avenues and could no longer gather further responses.

Using the sampling method outlined above, 104 MTEs from 16 colleges of education and 12 universities, across all the 10 provinces of Zambia turned up for the study. Although our sample size met the 10-times minimum sample size rule for structural equation modeling analysis (Barclay et al., 1995 ), we were cognizant of the fact that this rule has been criticized for its failure to account for the population size and other power analysis procedures (Hair et al., 2021 ; Kock & Hadaya, 2018 ). As reported elsewhere (Mukuka, 2024 ), our justification of the sufficiency of this sample lies in its representativeness of the population being studied. First, the population of MTEs in accredited teacher education institutions is comparatively small in contrast to the population of teacher educators in other subject combinations. Second, this sample covers all the 10 provinces of Zambia. Since the bulk of teacher training institutions have been established in two provinces (Lusaka and Copperbelt) that are largely urban, we did not anticipate receiving many responses from other provinces that are predominantly rural and have fewer teacher training institutions. Nonetheless, all the ten provinces have been represented in the sample. Third, participation in the study was voluntary. Only those willing to participate turned up to complete the questionnaire. Above all, this sample size aligns with the suggested inverse approach to power analysis as advised by Hair et al. ( 2021 ) and Kock and Hadaya ( 2018 ), considering the path coefficients derived from analogous previous research (Joo, et al., 2018 ). Thus, it is improbable that an alternative sample from this population would yield markedly different results.

Among the 104 respondents, 82 (78.8%) were male; while, 22 (21.2%) were female. It was further noted that 51 (49%) were from colleges of education; while, 44 (42.3%) came from universities and 9 (8.7%) did not disclose the institutional level at which they were teaching. In terms of qualifications, 73 (70.2%) of the respondents were master’s degree holders; while, 23 (22.1%) had bachelor’s degrees and only 6 (5.8%) had doctorate degrees. It was also noted that 2 (1.9%) did not disclose their qualifications. Regarding the institutional ownership, 70 (67.3%) came from public institutions; while, 33 (31.7%) came from privately owned institutions and only one respondent did not disclose. Among participants, the range of teaching experience spanned from 1 to 37 years, with an average of 9.5 years and standard deviation of 6.8 years.

Formulation and validation of questionnaire items

The questionnaire items were sourced from reputable and dependable academic references, integrating foundational principles from TAM (Davis, 1989 ) and TPACK (Mishra & Koehler, 2006 ). Furthermore, insights were gleaned from other studies that explored similar constructs and utilized the TAM and/or TPACK frameworks ( See , Camilleri & Camilleri, 2022 ; Joo et al., 2018 ; Schmid et al., 2020 ; Schmidt et al., 2009 ; Taylor & Todd, 1995 ). Structurally, the questionnaire encompassed four sections: demographic data (previously addressed in the preceding sub-section), familiarity with diverse digital technologies, proficiency in technology-based instruction within mathematics classrooms, and perceptions regarding the usefulness, ease of use, and willingness to incorporate technology within the classroom setting. The names of variables, item quantities, and reliability values derived for the current study are shown in Table 1 .

A five-point Likert scale gauged MTEs’ familiarity with technology. MTEs were tasked with indicating their level of familiarity with various digital technologies pertinent to mathematics classrooms, rating from 1 (not at all familiar) to 5 (completely familiar). Familiarity was categorized into three components: selected mathematics software (SMS), e-learning management systems and web-based conferencing tools (eLMS-CT), and social media platforms (SMP). The seven SMS applications that were explored included GeoGebra, PHET simulations, Excel, Graphmatica, Photo math, Geometer’s sketch pad, and Microsoft math solver. The six eLMS-CT included Zoom, Google Meet/Google classroom, Moodle e-learning management, Webex cisco, Clanned online learning platform, and Microsoft teams. Facebook, WhatsApp, and YouTube constituted SMPs. The selection of these technologies was predicated on both the researchers’ understanding of the most prevalent and extensively utilized tools and the existing literature in mathematics education research. We were aware that simply asking respondents to indicate their familiarity with various digital technologies might not provide a comprehensive understanding of their utilization in mathematics classrooms. Therefore, in addition to rating their familiarity, respondents were also presented with two open-ended questions. These questions prompted them to specify the particular digital tools they had previously used and the specific mathematics topics for which these technologies were employed.

Proficiency in incorporating technology-based instruction within mathematics classrooms was evaluated by utilizing four out of the seven components of the TPACK model (Mishra & Koehler, 2006 ; Schmid et al., 2020 ; Schmidt et al., 2009 ). These components encompass TK, TCK, TPK, and TPACK, as outlined in the provided questionnaire, openly accessible in a data repository at ( https://data.mendeley.com/datasets/3x8gs6nkk8/1 ). It is worth noting that only the four components related to technology were employed, as the study did not delve into MTEs’ proficiency in mathematical content. Respondents were asked to express their agreement level with the provided statements using a scale from 1 (indicating strong disagreement) to 5 (indicating strong agreement). These statements pertained to their perceived competencies in digital technologies such as computers, tablets, mobile phones, and projectors, among others. Nonetheless, the potential limitations of self-reported questionnaire items in assessing technological proficiency have been acknowledged. It is also important to understand that this study adopted an exploratory approach, aiming to glean insights that could serve as a foundation for future research endeavors in the Zambian context, where such investigations have not been previously conducted. In the final segment of the questionnaire, MTEs were prompted to express their level of agreement concerning perceived usefulness (PU), perceived ease of use (PE), and inclination toward integrating technology (IT) into their instructional methods (Davis, 1989 ; Taylor & Todd, 1995 ).

Before dissemination to the target participants, the questionnaire underwent scrutiny by a select group of experienced colleagues to identify potential weaknesses. This group comprised two seasoned scholars and three PhD candidates actively involved in research on technology integration in mathematics education. As detailed elsewhere (Mukuka, 2024 ), these colleagues were tasked with assessing the clarity, relevance, sufficiency, and coherence of the questionnaire items. Following their feedback via email and phone discussions, the instrument underwent refinement and was made available in both hard copy and online formats. Although a hard copy version was accessible, the questionnaire was primarily administered via a Google Form, with the link shared among identified MTEs who, in turn, disseminated it among their colleagues within their respective departments.

Data analysis

Descriptive statistics, and partial least squares structural equation modeling (PLS-SEM) were employed as methods of data analysis. The Statistical Package for Social Sciences (SPSS) version 27 was used to generate descriptive statistics. PLS-SEM, on the other hand, was employed to evaluate the significance of the structural relationships hypothesized in Fig. 3 .

First, reliability analysis was carried out in SPSS version 27 using Cronbach Alpha. This was done to guarantee internal consistency among all the items chosen to assess a specific variable/construct. Since all the Cronbach Alpha values displayed in Table 1 exceeded the suggested cutoff point of 0.7 (Adams & Wieman, 2010 ; Taber, 2018 ), it can be inferred that all the items on each variable were internally consistent. It was deemed reasonable to compute descriptive statistics like the mean, standard deviations, skewness, and kurtosis for each construct rather than performing it for every individual item. Skewness and kurtosis offered some insights into the nature of the distribution of data; whereas, standard deviation indicated how data values were distributed around the mean. Based on skewness and kurtosis values displayed in Table 2 , each variable’s departure from normality falls within the acceptable range of random fluctuations (Kline, 2009 ).

On the other hand, PLS-SEM was used to uncover major predictors of MTEs’ willingness to incorporate digital technology in their classroom practice, with a view to improving prospective mathematics teachers’ competencies and skills in regard to digital technology integration. The fact that proficiency, perceived usefulness, perceived ease of use and willingness to incorporate technology were set as latent variables justifies the use of PLS-SEM. We employed a consistent PLS-SEM methodology as opposed to the conventional PLS-SEM algorithm, which is based on a composite model. Consistent PLS-SEM is more reliable in terms of minimizing bias and improving accuracy in calculating path coefficients and related coefficients of determination (Dijkstra & Henseler, 2015 ; Dijkstra & Schermelleh-Engel, 2014 ). This is due to the adjustment of the correlations between reflective components.

Finally, it suffices to indicate that the quantitative analysis of the two open-ended questionnaire items was limited to a few of the digital tools that MTEs could access and use. To create a bar graph (Fig. 4 ), the number of times each digital tool was mentioned was counted.

Digital technologies used by MTEs for purposes of mathematics teaching and learning

Ethical clearance

Prior to giving the questionnaire to the intended participants, an appropriate ethical committee at the lead author’s institution of affiliation provided ethical clearance with protocol number (FEDSECC027-06-23). Participation in this study was voluntary. The participants were given a thorough description of the goal of the study, emphasizing the significance of their contribution of accurate and pertinent information. By participating, MTEs consented to have their responses examined and published while keeping their personal information anonymous.

The results are structured into three segments. The initial two sections provide descriptive analyses addressing research question 1; while, the third section delves into research question 2 by presenting data that explore the hypothesized structural relationships. Section one encompasses descriptive analyses focusing on MTEs’ familiarity with various digital technologies and their integration into mathematics teaching and learning. Section two examines MTEs’ technological proficiency, perceptions of usefulness and ease of use of digital technology, and their willingness to incorporate it into pedagogical practices. The third section presents findings regarding the predictive roles of MTEs’ perceived technological proficiency, usefulness, and ease of use of technology on their willingness to integrate it into pedagogical practices.

Familiarity with digital technology

On average, the results shown in Table 2 indicates that respondents’ familiarity with social media platforms (SMP) was the highest ( M = 4.27, SD = 0.898). MTEs’ familiarity with e-learning management systems and conferencing tools (eLMS-CT) was between low and moderate ( M = 2.64, SD = 0.801). Selected mathematics software (SMS) applications, which had an average level of familiarity between very low and low ( M = 2.17, SD = 0.648), was the least in terms of familiarity. Even though SMPs scored higher than the other two categories, further data analysis showed that most MTEs did not use them for mathematics teaching and learning purposes. This became evident during the analysis of an open-ended questionnaire item where MTEs were asked to mention some of the digital technologies, they had been using for purposes of mathematics teaching and learning. Out of the 161 mentions, Footnote 1 SMPs appeared 40 times (or 24.8%), on average (Fig. 4 ). Nonetheless, majority of the MTEs who cited SMPs for academic purposes only used them as communication tools to reach out to their students. On the other hand, a mathematics software was cited 56 times (34.8%) out of the total 161 mentions (Fig. 4 ). Results show that GeoGebra and excel were mostly used to teach topics like analytic geometry, statistics, and graphs of various functions. The findings presented in Fig. 4 reveal minimal references to PHET simulations ( n = 4), Graphmatica ( n = 3), and Photo math ( n = 2). Additionally, none of the respondents reported using Microsoft Math Solver or Geometer’s Sketchpad. It has also been demonstrated that e-learning management systems and conferencing tools were the most frequently cited technologies ( n = 65), accounting for 40.4% of all mentions. We also observed that, mostly during the COVID-19 outbreak, video conferencing platforms like Zoom and Google Classroom were used to deliver lessons to students; whereas, e-learning management systems like Moodle were used for sharing lecture notes with students.

Proficiency, perceived usefulness, and perceived simplicity of technology

According to the findings in Table 2 , MTEs’ proficiency with technology-based instruction ranged from low to moderate on average ( M = 3.08, SD = 0.746). The reported ease of using digital technology by MTEs also ranged from low to moderate on average ( M = 3.16, SD = 0.909). However, the findings indicate that MTEs’ desire to use technology ( M = 3. 88, SD = 0.893) and perceived usefulness of digital technology ( M = 3.89, SD = 0.799) were both rather high. This suggests that even though MTEs’ knowledge of technology-based instruction and their perception of its ease of use were somewhat lacking, they were not only aware of its usefulness but also willing to make sure that preservice mathematics teachers had the knowledge and skills they needed to use technology in their future mathematics classrooms.

Predictors of MTEs’ willingness to technology integration

The second research question was addressed by examining the significance of the hypothesized structural relationships among the study variables, as depicted in Fig. 3 . Before evaluating the structural model, the validity and reliability of the measurement model Footnote 2 were scrutinized concerning the four constructs and their corresponding indicators. Perceived usefulness and perceived ease of use were evaluated with six indicators each; while, MTEs’ proficiency in technology-based instruction was assessed with sixteen indicators. Conversely, MTEs’ willingness to integrate technology into teaching methods was evaluated with three indicators.

We adhered to the guidelines outlined by Hair et al. ( 2019 ) for assessing the reliability and validity of the reflective measurement model. When running a consistent PLS-SEM model (Dijkstra & Henseler, 2015 ), it is recommended to retain only indicators with factor loadings exceeding 0.708. However, achieving this condition can be challenging at times due to diverse respondent perspectives, attitudes, experiences, and competencies within the same study. Consequently, only indicators jeopardizing the model’s validity and reliability were excluded from the final analysis based on their individual factor loadings below 0.5. After the initial measurement model assessment, three indicators related to technological proficiency and one indicator linked to perceived usefulness of technology were excluded from the final analysis due to compromised average extracted variance (AVE) by their respective factor loadings that were less than 0.5.

Subsequently, internal consistency was verified by examining both Cronbach’s alpha and composite reliability for each construct. At that point, it was found that all constructs yielded composite reliability values exceeding 0.70 but below 0.95. Furthermore, the AVEs, used to ascertain convergent validity for each construct, surpassed the recommended threshold of 0.5 with the lowest being 0.503 for perceived usefulness and the highest being 0.690 for the dependent variable (MTEs’ willingness to integrate technology). Regarding discriminant validity, the model met the requirement wherein the square root of the AVE for each construct exceeded its correlations with other constructs beneath it (Fornell & Larcker, 1981 ). Variance inflation factors (VIFs) ranged from 1.839 to 4.991. Since all extracted VIFs for all indicators were below 5, there were no indications of multicollinearity between any pair of indicators for each construct (Hair et al., 2017 ).

Upon establishing the reliability and validity of the measurement model, the explanatory and predictive power of the structural model was assessed based on the coefficient of determination, R 2 , and Q 2 . Notably, f 2 is not reported in this paper as it is deemed equivalent to the regression coefficients (path coefficients) detailed in Table 3 (Hair et al., 2019 ).

According to Hair et al. ( 2011 ), an R 2 value of 0.75 signifies a significant model fit, 0.50 indicates a moderate model fit, and 0.25 suggests a weak model fit. However, the significance of R 2 values may vary depending on the discipline and setting of a particular study. For example, in certain circumstances, an R 2 value of 0.1 may suffice (Raithel et al., 2012 ). In the present study, R 2 values of 0.276 for perceived usefulness of technology, 0.474 for MTEs’ willingness to utilize digital technology, and 0.624 for perceived ease of use of digital technology all demonstrate a satisfactory model fit as they exceed the recommended thresholds.

Concerning the predictive power of the model, Hair et al. ( 2019 ) recommended that Q 2 values for a specific outcome variable should surpass zero. They further proposed that Q 2 values exceeding 0, 0.25, and 0.5 represent low, moderate, and high predictive utility of the PLS-SEM model. In the context of this study, the Q 2 values derived from the PLSPredict procedure indicate small (0.195), moderate (0.293), and large (0.529) predictive relevance of the model regarding the perceived usefulness of digital technology, willingness to use technology, and perceived ease of use of digital technology, respectively.

After confirming that all prerequisites for executing and analyzing the PLS-SEM results were fulfilled, conclusions were drawn regarding the proposed structural connections among the variables under study. Table 3 shows the path coefficients ( β ), the t -statistics, and p -values associated with each of the five direct structural relationships that were examined.

Based on the path coefficients displayed in Table 3 , and considering 5% level of significance, it can be inferred that only one structural relationship (perceived ease of use → willingness) is insignificant ( β = 0.194, p = 0.144). On the other hand, MTEs’ willingness to use technology-based instruction in their classrooms is significantly influenced by their perception of the usefulness of digital technology ( β = 0.297, p = 0.015). Similarly, MTEs’ perceived ease of use is significantly influenced by their perceived technological proficiency ( β = 0.790, p < 0.001). Additionally, MTEs’ proficiency with digital technology is a significant predictor of perceived usefulness ( β = 0.525, p < 0.001) as well as their willingness to incorporate technology in their classrooms ( β = 0.299, p = 0.025).

This study sought to profile MTEs’ readiness to technology integration by identifying the kind of digital technologies that they were familiar with, had access to, and how well-versed they were in technology-based classroom instruction. In addition, the study looked at the structural relationships among four factors, including proficiency, perceived utility, perceived ease of use, and desire to use technology in the context of preservice mathematics teacher training.

The study’s findings show that, on average, MTEs had low to moderate familiarity with a variety of software apps related to mathematics, e-learning management systems, and video conferencing tools. On the other hand, MTEs had a very high level of familiarity with social media networks such as WhatsApp, Facebook, and YouTube. Even though the majority of MTEs claimed to be quite familiar with social media platforms, subsequent analysis of the data showed that they were not really used for mathematics teaching and learning purposes. In cases where social media like WhatsApp was used, respondents indicated that it was just used to transmit general information in the form of announcements, not necessarily as a mode of delivering mathematics lessons. This is in line with research by Amhag et al. ( 2019 ) who found that teacher educators did not predominantly use digital technologies for didactic purposes. This suggests a need to raise awareness among MTEs on the efficacy of using social media such as Facebook for engaging students in learning mathematics (Baya’a & Daher, 2015 ). A study conducted in Zambia by Mulenga and Marbàn ( 2020 ) found that social media had a significant role in shaping the future of mathematics education, particularly in terms of how it is integrated into teaching practices and its potential to foster collaborative and innovative learning environments.

Low familiarity was attributed, among other things, to weak ICT skills, limited internet access, and a lack of infrastructure that is technologically advanced. These results also confirm the findings of a study by McCulloch et al. (2018) in highlighting how having limited access to technology is a prevalent concern that has a negative effect on someone's intention to use technology in their classrooms. Secondary school mathematics teachers and pupils have also been found to have limited expertise and access to digital tools, particularly in low-resource contexts like sub-Saharan Africa (Bethell, 2016 ; Iyamuremye et al., 2022 ; Luneta, 2022 ; Mukuka et al., 2021 ).

Despite the limited access and familiarity that MTEs have exhibited with most mathematics software applications, it is noteworthy that a significant portion of these educators have been utilizing Microsoft Excel and GeoGebra in their classrooms, as evident in the results displayed in Fig. 4 . This usage is particularly remarkable given the low-resource settings, such as Zambia, in which these educators operate. Furthermore, studies conducted by Munyaruhengeri et al. ( 2023 ) and Uwurukundo et al. ( 2022 ) corroborate the benefits and limitations of such applications in the teaching and learning of mathematics in similar settings. These findings affirm the potential of these applications to foster conceptual understanding among mathematics learners, even in challenging environments.

Additionally, it has been noted that MTEs’ perceived ease of use and proficiency with technology-based instruction, overall, ranged from low to moderate. This somewhat supports the claim made by Kopp et al. ( 2019 ) that a sizable portion of teachers in higher education institutions have minimal expertise using technology for instructional purposes. On the other hand, the results show that MTEs' readiness to use technology in their classroom instruction and their perception of its usefulness were both relatively high. This suggests that despite their low proficiency and fears about how easy it is to use technology, MTEs were not only aware of its benefits but also eager to make sure that prospective mathematics teachers had the knowledge and skills they needed to use it in their classrooms. This aligns with the findings of a study by Adnan et al. ( 2024 ), which highlights the importance of educators being role models for effective technology use as well as emphasizing the need for raising technological proficiency among teacher educators.

The findings of this study confirm those of earlier studies regarding the predictability of perceived usefulness of technology and proficiency with technology-based instruction on one’s willingness to use it in their classroom practice (Alsofyani et al., 2012 ; Davis, 1989 ; Joo et al., 2018 ; McCulloch et al., 2018 ). Additionally, it has been demonstrated that some external factors can affect an individual’s perceived simplicity and usefulness of technology (Joo et al., 2018 ). Findings of this study revealed that MTEs' proficiency with technology is a significant predictor of their beliefs of its usefulness and ease of use. Accordingly, MTEs start to appreciate the value and simplicity of the many digital technologies that are associated with mathematics as they get more adept at using them. We have also discovered that, despite MTEs’ limited exposure to and familiarity with digital technology, their awareness of its value and desire to incorporate it into their teaching strategies serve as a clear demonstration of the importance of technology in mathematics education as observed by other scholars in the field (Camilleri & Camilleri, 2022 ; Ng & Fang, 2023 ; Nikou, 2021 ).

Study limitations

Despite all the benefits this study has to offer, we are aware that there are certain restrictions as well. First, only MTEs who train secondary school teachers were the subject of the study. As a result, conclusions might not be applied to the preparation of primary school and early childhood education teachers. Second, this cross sectional study used an online questionnaire to obtain self-reported data. This might have prevented some MTEs from participating due to limited or no access to internet and appropriate digital tools. Moreover, we acknowledge that relying solely on self-reported data to assess MTEs’ technological proficiency may not provide a comprehensive understanding of their actual capabilities, as individuals may report skills, they do not actively practice. Third, it is important to recognize that the findings of this study are applicable within the specific context of Zambia and may not be extrapolated to settings markedly divergent from the Zambian context. Despite these limitations, it is important to remember that this study is timely because it is the first of its sort in Zambia and other comparable situations especially in the SSA region. It serves as a foundation for further research into MTEs’ proficiency with technology-based instruction and their readiness to use it. Additionally, it has been emphasized that no other sample from the study’s target population could have produced results that would be significantly different from those found in this study. This is so because the sample used in the current study is thought to be representative of the MTEs’ population in Zambia.

Study implications and future directions

After establishing the current state of MTEs’ proficiency with technology-based instruction, we advise that future studies in this domain concentrate on enhancing MTEs’ digital literacy and affective skills such as self-efficacy beliefs (Clark-Wilson et al., 2020 ; Joo et al., 2018 ; Njiku et al., 2022 ). This might be done by involving them in the process of developing lessons that include technology into their teaching practices (Psycharis & Kalogeria, 2018 ). It is quite likely that preservice mathematics teachers will acquire the necessary skill set for using technology-based instruction in their future classrooms if MTEs get adequate technical support.

It is undeniable that MTEs and prospective teachers of mathematics may both still struggle to effectively use digital tools for purposes of teaching and learning mathematics. As a result, we agree with Kopp et al. ( 2019 ) that it is important to distinguish between digital competencies that are learned for personal use (like social media) and those that are required for teaching and learning. It will be beneficial to begin by equipping MTEs with the necessary digital skills and providing their access to the necessary digital tools. This is due to the fact that if MTEs continue to display insufficient expertise, the potential of digital technology in mathematics teaching and learning will be hardly realized. According to Helliwell and Ng ( 2022 ), teacher educators are essential in ensuring that prospective teachers have the tools they need to perform at their best as competent teachers.

This study has also shown the importance of improving MTEs’ access to various types of digital technologies. Enhancing student learning outcomes has also been shown to be strongly correlated with the availability of digital infrastructure and teachers’ knowledge with appropriate digital technologies (Betthäuser et al., 2023 ; Jaekel et al., 2021 ; König et al., 2020 ; Mukuka et al., 2021 ). We think that access to and familiarity with digital technologies at universities and colleges will boost research capabilities in addition to improving the technology-based teaching skills of both the MTEs and their students.

The findings imply that having access to technology in the classroom and having access to high-quality technology support will not only enable MTEs to view technology as simple to use but will also have a positive impact on their willingness to incorporate technology into their teaching methods (Liu et al., 2017 ). However, according to Pollack et al. ( 2018 ), time, quality, and cost are some of the factors that drive digital transformation. As a result, achieving high-quality digital transformation within a reasonable period is only doable with a suitably high budget because under-funding may be associated with quality loss and/or prolonged periods of development. Therefore, it is vital to remember that low-resource environments like Zambia might not be able to handle the ever-increasing complexity due to how swiftly technology is expanding. As such, education systems in low-resource contexts need to focus on establishing essential infrastructure for the future while identifying what is beneficial in the short term.

In conclusion, this study shows that there is no need to assume that all teacher educators are technologically proficient, neither should we also assume that all higher education institutions are technologically advanced. Instead, there should be more MTEs’ capacity building initiatives to help them equip preservice mathematics teachers with the technical skills they will need to use in their future classrooms.

Data availability

The data that support the findings of this study are openly available on Mendeley Data Repository at https://data.mendeley.com/datasets/3x8gs6nkk8/1 .

The total number of mentions ( n = 161) is above the sample size ( n = 104) in the sense that some respondents mentioned more than one form of digital technology that they had used before.

A comprehensive procedure for establishing the validity and reliability of the measurement model along with the associated supplementary files has been described in a dedicated standalone data article authored by Mukuka ( 2024 ), which can be accessed via the provided link https://data.mendeley.com/datasets/3x8gs6nkk8/1 .

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Acknowledgements

We extend our gratitude to all respondents who participated in this study. Additionally, we would like to express our appreciation to our colleagues who aided in identifying Mathematics Teacher Educators across various colleges and universities in Zambia.

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Relationship between the inner setting of CFIR and the delivery of the Healthy School Recognized Campus initiative: a mixed-methods analysis

Allyson Schaefers 1 na1 ,
Lucy Xin 1 na1 ,
Paula Butler 2 ,
Julie Gardner 2 , 3 ,
Alexandra L. MacMillan Uribe 1 ,
Chad D. Rethorst 1 ,
Laura Rolke 1 , 4 ,
Rebecca A. Seguin-Fowler 5 &
Jacob Szeszulski 1

Implementation Science Communications volume 5 , Article number: 96 ( 2024 ) Cite this article

Metrics details

Introduction

Healthy School Recognized Campus (HSRC) is a Texas A&M AgriLife Extension initiative that promotes the delivery of multiple evidence-based physical activity and nutrition programs in schools. Simultaneous delivery of programs as part of HSRC can result in critical implementation challenges. The study examines how the inner setting constructs from the Consolidated Framework for Implementation Research (CFIR) impact HSRC program delivery.

We surveyed ( n = 26) and interviewed ( n = 20) HSRC implementers ( n = 28) to identify CFIR inner setting constructs related to program acceptability, appropriateness, and feasibility. Using a concurrent mixed-methods design, we coded interviews using the CFIR codebook, administered an inner setting survey, tested for relationships between constructs and implementation outcomes via chi-square tests, and compared quantitative and qualitative results.

Stakeholders at schools that implemented one program vs. more than one program reported no differences in acceptability, appropriateness, or feasibility outcomes (p > .05); however, there was a substantial difference in reported program minutes (1118.4 ± 951.5 vs. 2674.5 ± 1940.8; p = .036). Available resources and leadership engagement were related to HSRC acceptability (r = .41; p = .038 and r = .48; p = .012, respectively) and appropriateness (r = .39; p = .046 and r = 0.63; p = .001, respectively). Qualitative analyses revealed that tangible resources (e.g., curriculum, a garden) enabled implementation, whereas intangible resources (e.g., lack of time) hindered implementation. Participants also stressed the value of buy-in from many different stakeholders. Quantitative results revealed that implementation climate was related to HSRC acceptability (r = .46; p = .018), appropriateness (r = .50; p = .009), and feasibility (r = .55; p = .004). Learning climate was related to HSRC appropriateness (r = .50; p = .009). However, qualitative assessment of implementation climate subconstructs showed mixed perspectives about their relationship with implementation, possibly due to differences in the compatibility/priority of different programs following COVID-19. Networks/communication analysis showed that schools have inner and outer circles of communication that can either benefit or hinder implementation.

Few differences were found by the number of programs delivered. Implementation climate (i.e., compatibility, priority) and readiness for implementation (i.e., resources and leadership engagement) were important to HSRC implementation. Strategies that focus on reducing time-related burdens and engaging stakeholders may support HSRC’s delivery. Other constructs (e.g., communication, access to knowledge) may be important to the implementation of HSRC but need further exploration.

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Contributions to the literature

The simultaneous delivery of multiple evidence-based programs can result in critical implementation challenges.

Mixed methods approaches can quantify the magnitude of association between implementation barriers and outcomes while also providing a nuanced understanding of how implementation strategies can address those barriers.

Readiness for implementation (i.e., resources and leadership engagement) is important to the delivery of multiple programs as part of the Healthy School Recognized Campus initiative.

Implementation strategies that focus on reducing time-related burdens and engaging stakeholders may be beneficial for supporting the Healthy School Recognized Campus initiative.

Reviews of school- and evidence-based programs for improving physical activity and nutrition show reductions in obesity prevalence by up to 8% [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ]. Many models and frameworks (e.g., Whole School, Whole Community, Whole Child) emphasize the delivery of multiple programs [ 10 , 11 , 12 ], which can result in critical implementation challenges (e.g., limited resources and communication barriers) [ 13 , 14 , 15 ]. Despite challenges, most schools deliver numerous programs within the same school day or year. Thus, it is important to understand how to support simultaneous implementation of programs.

The Consolidated Framework for Implementation Research (CFIR) examines five domains that affect implementation: intervention characteristics, outer setting, inner setting, characteristics of individuals, and implementation processes [ 16 , 17 , 18 , 19 ]. Although all CFIR constructs affect implementation, within schools, the inner setting has a major impact on program delivery and may be critically important when assessing the simultaneous delivery of multiple evidence-based programs [ 20 ]. Furthermore, implementation strategies that target the inner setting have the potential to improve delivery of multiple programs [ 21 , 22 ].

CFIR is commonly used to assess barriers/facilitators related to the implementation of school-based programs [ 20 , 23 , 24 , 25 ]. One systematic review identified several inner setting factors – administrative support, staff engagement, and access to resources – as central to supporting implementation [ 20 ]. Qualitative findings highlighted important lessons including: (1) conduct a readiness assessment, (2) identify wellness champions, (3) build on existing curricula, and (4) conduct ongoing training [ 20 ]. However, this study broadly focused on all CFIR constructs. Thus, limited inner setting information was provided.

Qualitative methods provide context, whereas quantitative methods describe the magnitude of a relationship between program barriers/facilitators and implementation outcomes [ 26 , 27 , 28 , 29 ]. Mixed methods approaches that bridge quantitative and qualitative methods can generate new insights [ 28 ]. For example, one mixed methods study quantified inner setting barriers to program implementation – lack of time/resources, staff buy-in, administrator support – but also found that outer setting educators could be utilized to overcome those barriers [ 30 ]. This type of nuanced understanding of implementation processes is especially important with increased complexity, such as when programs are concurrently delivered.

To elucidate inner setting factors related to concurrently implementing school-based physical activity and nutrition programs, we conducted a mixed methods study that examined the implementation of a Texas A&M AgriLife Extension initiative, Healthy School Recognized Campus (HSRC).

Study design and participants

HSRC is a program that rewards schools for delivering health programs, including an evidence-based school-wide walking program, one additional adult program, and one additional youth program. Outside of the evidence-based walking program, schools fill out an application at the beginning of the school year to choose between evidence-based programs and ones easier to implement (full list of programs and their evidence base can be found at https://texas4h-hsrc.com/ ). Programs are delivered by Extension agents (i.e., agents) with the support of school staff. School staff often only implement one program, while agents implement two or more at each school. Schools that complete programs receive a banner and a proclamation at a local school board meeting. Not all schools that enroll in HSRC become recognized, only those that complete selected programs by a specific deadline (i.e., May 1).

We utilized a cross-sectional, concurrent mixed methods design consisting of surveys and/or interviews grounded in CFIR (spring of 2022). Integration of methods occurred during the design (i.e., aligning qualitative and quantitative constructs) and data analysis (i.e., comparing and contrasting results) phases and are reported following both guidelines (Supplemental Table 1). Texas A&M’s Institutional Review Board approved this study (IRB2022-0390 M).

We recruited a convenience sample of HSRC program implementers (e.g., teachers, agents) from eight elementary schools in rural East Texas. Participants completed a survey, interview, or both based on their interest. Inclusion criteria were being at least 18 years old and speaking English.

Surveys and interviews

When designing the survey and interview guide, we aligned CFIR constructs by selecting and using existing instruments that contained as many inner setting constructs as possible. We assessed inner setting constructs (Definitions—Table 1 ) and implementation outcomes (i.e., acceptability, appropriateness, feasibility) via validated survey measures that used Likert scales (strongly disagree to strongly agree) [ 31 , 32 ]. Program minutes were assessed via three questions that asked, “How many [weeks, days/week, and minutes/day] did students participate in [program]?” Surveys ( n = 26), collected using REDCap, lasted about 20–30 min. Participants received a $20 gift card.

Utilizing the CFIR website, two researchers (JS, AS) developed an interview guide that asked questions about how inner setting constructs affected program delivery: (a) school leaders, staff, and students’ perceptions; “What do you think are leaderships’ impressions of the HSRC program?” (b) schools’ characteristics (e.g., organizational structure, space); “How do you think the physical design of the school – playgrounds, gyms – affected the implementation?”(c) culture (i.e., shared beliefs and values); “How do you think the culture of your school affected the implementation of HSRC?”(d) resources; “What resources are available at your school to implement HSRC?” Interviews were conducted at elementary schools ( n = 13) or online ( n = 7), audio-recorded, and lasted 30–60 min. Participants received a $50 gift card.

We used NVivo to transcribe and review audio files. Applying a directed content analysis and iterative categorization approach [ 33 , 34 ], we used a priori codebook, based on CFIR inner setting constructs, to deductively code transcripts. Two researchers (AS, LR) independently coded four transcripts and discussed line-by-line discrepancies to consensus. One researcher (AS) coded the remaining 16 transcripts. Two researchers (AS, LX) independently read code queries noting important findings, summarizing constructs, and highlighting quotes. Three researchers (AS, LX, JS) constructed themes synthesizing the results. We compared themes between stakeholders that implemented one program vs. more than one program.

Statistical methods

We scored CFIR inner setting constructs and implementation outcomes using established protocols [ 31 , 32 ]. For constructs missing less than 75% of the data (seven total responses), we imputed missing values as the average of all other responses for that construct. We calculated program minutes as the days/week, times total weeks, times average session length, summed across all programs. We conducted descriptive statistics and chi-square tests, in SPSS 27, to assess relationships between CFIR constructs and implementation outcomes. We also compared the direction of quantitative analysis (i.e., positive or negative association) with findings from the qualitative analysis, when applicable.

Five of the eight schools completed 2 evidence-based programs, but all schools completed at least one (Table 3 ). Most participants ( n = 28; n = 2 interview only, n = 8 survey only, n = 18 both) were female and classroom teachers (Table 2 ). Schools ( n = 8) had on average 327.1 ± 158.3 students (14.9% Black/African American; 30.1% Hispanic; and 50.0% White), included 75.4% economically disadvantaged students, were Title I (100%), and on average implemented 2.1 ± 1.2 programs (Table 3 ). When comparing stakeholders at schools that implemented one program vs. more than one program, there were no differences in qualitative themes, acceptability, appropriateness, or feasibility outcomes (p > 0.05); however, there was a substantial difference in reported program minutes (1,118.4 ± 951.5 vs. 2,674.5 ± 1,940.8; p = 0.036).

Implementation climate

Quantitatively, implementation climate was associated with the acceptability, appropriateness, and feasibility of HSRC (Table 4 ). The only implementation climate subconstruct measured was learning climate , which was associated with appropriateness, but not discussed in interviews.

Qualitatively, within implementation climate, interviewees shared different perspectives on schools’ tension/need for change (i.e., adoption of HSRC) based on the community’s and students’ needs (Table 5 —Quote 1). An Extension agent (i.e., agent) also noted that some teachers would become interested in programs after seeing the positive effects, such as students keeping each other and teachers accountable for health behaviors.

Most interviewees valued the compatibility of HSRC programs with the schools’ current curriculums, as they were aligned with the state educational standards (Texas Essential Knowledge & Skills [TEKS]). One agent used the fact that HSRC programs were TEKS-aligned to promote adoption (Table 5 —Quote 2). Although programs aligned with state learning requirements, the programs’ timelines did not necessarily match teachers’ scheduled lesson plans or state testing schedules (Table 5 – Quotes 3 & 4). However, an agent noted that not all grade levels participate in state tests (Table 5 – Quote 5).

Not all school stakeholders viewed HSRC as a relative priority . When HSRC was presented to the School Health Advisory Council (SHAC), they only expressed interest in certain aspects of the initiative and were apprehensive about implementing the full program (Table 5 – Quote 6). Due to the timing of these interviews, COVID-19 restrictions still limited most in-person activities, resulting in HSRC being ranked as a lower priority. Many interviewees also stated that competing priorities (e.g., staff responsibilities, school sports) took precedence (Table 5 —Quote 7 & 8). Organizational incentives and rewards and goals and incentives were not often discussed.

Readiness for implementation

Quantitatively, leadership engagement and available resources were associated with acceptability and appropriateness (Table 4 ). Access to knowledge and information was not measured.

Qualitatively, schools were generally optimistic and demonstrated indicators of their readiness for implementing HSRC. Related to leadership engagement , school leadership supported schools’ participation in HSRC, however, engagement varied. Sometimes, principals knew that staff implemented HSRC, but they did not involve themselves or push for more school-wide programming (Table 6 —Quote 1). Some principals’ involvement stopped short ( after providing approval, whereas some principals participated in the programs themselves (e.g., team captain for the walking challenge) or sought out new health-related opportunities (Table 6 —Quote 2). Interviewees expressed that endorsement from leadership was imperative to launch HSRC, and leadership approval usually guaranteed implementation (Table 6 – Quote 3).

For available resources , there appeared to be two categories – tangible and intangible. Tangible resources were readily available for program implementation, either through the school, the agent, or community donations (Table 6 —Quote 4). From the school’s perspective, the agent provided most, if not all, of the materials needed for HSRC (e.g., marketing materials, curricula). From the agent’s perspective, schools already had most of the items that they needed (e.g., pencils and printing capabilities). For items that needed to be purchased, agents sought out small grants, Extension funding, or local community donations.

Intangible resources included volunteer support and time, but it was a lack of these resources that seemed to negatively affect program implementation. Many interviewees recognized the positive impact volunteers had on implementation. Volunteers helped repair the facilities (e.g., gardens), taught program lessons, and even provided funding. However, agents and school staff both mentioned the need for more volunteers (Table 6 —Quote 5). Interviewees also discussed how the time needed for orienting schools, lesson planning, and teaching program lessons served as barriers to implementation. Principals and agents commented on time as a barrier more than school staff (Table 6 —Quote 6).

Regarding access to knowledge , most school staff stated that their agent provided them with the information needed for program implementation. Many highlighted the helpfulness and accessibility of their agent (Table 6 —Quote 7), which agents also described as one of their own goals (Table 6 —Quote 8). For this reason, programs that initially felt overwhelming became easier to implement (Table 6 —Quote 9). For agents, access to knowledge was less readily available. One agent discussed how new agents faced challenges in implementing HSRC due to inaccessible program information scattered across platforms, inefficient communication with schools, and uncertainties about how to implement HSRC. From the agents’ perspective, Extension leadership served as the main source of knowledge for HSRC. One agent discussed connecting with other agents about questions, but they also recommended setting up more frequent meetings. Similarly, a couple of school staff suggested having meetings or a discussion board with implementers from different schools to share experiences and ideas.

Culture, structural characteristics and networks & communications

Quantitatively, culture effort, but not culture or culture stress, was marginally related to HSRC’s acceptability and appropriateness (p < 0.10; Table 4 ). Structural characteristics and networks and communications were not included in the survey.

Qualitatively for culture , many implementers highlighted how living in a small community fostered an emphasis on agricultural programming (Table 7 —Quote 1). Many also commented on the positive culture of support that they saw for HSRC (Table 7 —Quote 2). Principals highlighted the positivity and willingness of teachers to implement HSRC (Table 7 – Quote 3), compared to teachers who identified the principal as the driving force (Table 7 – Quote 4).

For structural characteristics , most interviewees stated that being in a smaller school, compared to a larger school, was beneficial for implementation (Table 7 —Quote 5). Agents also reported that implementing the program in larger schools was more difficult due to their own time constraints, financial barriers, and lack of volunteers (Table 7 —Quote 6). However, being in a rural setting negatively impacted schools’ ability to implement some programs, such as the walking challenge (Table 7 —Quote 7).

For communication , there seemed to be both an inner and outer circle. The inner circle, involved with HSRC implementation, was typically made up of a school administrator, agent, and a few staff. The agent was generally the HSRC expert, and they would share program information. In some instances, the principal decided on which staff would facilitate communication with the agent (Table 7 —Quote 8). In other cases, the agent worked with an existing contact or friend (Table 7 —Quote 9). Most interviewees stated that only school staff involved in HSRC – the inner circle – knew enough about the programs to talk about them. The outer circle – school staff who did not implement HSRC and parents – might have noticed the HSRC activities but were unaware of the larger initiative. Parents’ main source of HSRC information came from their students (Table 7 —Quote 10). Agents expressed feeling like they were also part of the outer circle because they were unaware of everything happening at the school (e.g., school culture, competing priorities).

Three schools reported implementing a single HSRC program, whereas five schools reported implementing multiple HSRC programs. However, few differences were found in our results by the number of programs delivered. Furthermore, many teachers did not know about other programs being delivered simultaneously, and as a result interviewees did not discuss related challenges. Thus, many of our identified implementation barriers match the previous literature on barriers to the implementation of single program [ 9 , 10 , 16 ], although our qualitative findings provide additional context.

Several inner setting constructs, including resources, leadership, and communication seemed to be more important than other constructs, such as culture. Although implementation climate appeared important in the quantitative analysis, in the qualitative analysis, subconstructs from implementation climate (e.g., compatibility, priority) presented conflicting findings that may have been related to implementation right after COVID-19. In general, qualitative analyses added depth that helped us understand better how inner setting constructs function as a part of the multicomponent HSRC initiative.

Within readiness for implementation, both leadership engagement and available resources were important for delivery; however, interviews provided deeper insight. Resources for HSRC fell into two categories – tangible and intangible. Tangible resources were readily available, whereas time, an intangible resource, was a barrier to HSRC delivery. Our study adds to the current literature [ 9 , 10 , 16 ], as it demonstrates that time affects the acceptability and appropriateness of delivering multiple school-based physical activity and nutrition programs but may not relate to program minutes. Implementation strategies that reduce time-related burdens and improve time management strategies may support future implementation efforts.

Schools involved many stakeholders in HSRC delivery, and each stakeholder had different roles/responsibilities, which hindered agents from getting HSRC adopted. Agents described needing to customize their approach for each school, including working through existing connections (e.g., friends) to get buy-in. Previous research has emphasized the role of leadership as gatekeepers and the need for their engagement and support for program adoption [ 20 , 24 , 40 ]. We found that principals also choose which teachers implement programs, these teachers were not always aware of all the programs being delivered at their schools. Furthermore, some principals stayed involved with the programs once adopted, whereas other principals passed those responsibilities to school staff. More research is needed to understand the most effective role of school leadership: a one-time authority figure or an ongoing facilitator.

Finally, we found that schools had an inner and outer circle of communication, and agents felt that they belonged to both circles, which made it difficult to bridge gaps between all stakeholders involved with program delivery. Previous research found that strong communication between leadership and other program stakeholders leads to successful implementation, whereas ineffective communication inhibits implementation [ 24 ]. Additional research is needed to better understand the purpose of having an inner and outer communication circle and to determine if there is a need to bridge the gap between the two groups, potentially via more centralized communication systems.

Limitations

Not all programs available as part of HSRC are evidence-based. However, easier to implement programs are included as a way for schools to work up to more complex (e.g., longer) evidence-based interventions. As few validated instruments to measure CFIR’s inner setting exist, all constructs measured in the qualitative analysis could not be measured through the survey. Some sections of interviews were coded as multiple constructs, but we reached a consensus on where best to discuss them within this paper. A consensus was also developed during the coding process instead of calculating inter-rater reliability. The CFIR team has recently added new constructs to the inner setting, which do not have validated measures (e.g., mission alignment). These constructs may also be important to consider and should be tested in future studies in relationship to additional implementation outcomes (e.g. adherence/fidelity). The small sample size and inclusion of only rural schools may limit this study’s generalizability to larger and more urban schools. Not everyone completed both the interview and survey, and as a result, qualitative and quantitative perspectives may not be perfectly aligned. However, a majority did complete both activities (64%).

Conclusions

This study utilized the CFIR framework in conjunction with a mixed methods approach to evaluate barriers and facilitators for the simultaneous implementation of multiple school-based physical activity and nutrition programs as part of HSRC. Few differences were found by the number of programs delivered or in comparison to previous studies evaluating the implementation of a single program. However, our analyses found that readiness for implementation (i.e., resources and leadership engagement) was vital to successful program implementation. Other constructs may need more research. Future research can use these findings to begin to develop implementation strategies that support the successful implementation of HSRC or other initiatives that aim to implement multiple concurrent physical activity and nutrition programs.

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

Consolidated Framework for Implementation Research

Community Preventive Services Task Force

Healthy School Recognized Campus

Research Electronic Data Capture

School Health Advisory Council

Texas Essential Knowledge & Skills

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Acknowledgements

The authors wish to thank all the Extension agents who supported this study .

AS, LX, ALMU, CR, and RASF were funded (in part) by the Institute for Advancing Health Through Agriculture at Texas A&M University.

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Allyson Schaefers and Lucy Xin are co-first authors who equally contributed to this work.

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Institute for Advancing Health Through Agriculture (IHA), Texas A&M University, 17360 Coit Rd, Dallas, TX, 75252, USA

Allyson Schaefers, Lucy Xin, Alexandra L. MacMillan Uribe, Chad D. Rethorst, Laura Rolke & Jacob Szeszulski

Texas A&M AgriLife Extension, 600 John Kimbrough Boulevard, College Station, TX, 77843, USA

Paula Butler & Julie Gardner

Texas 4-H Youth Development, 1470 William D Fitch Parkway, College Station, TX, 77845, USA

Julie Gardner

Department of Population and Health Sciences, Duke University School of Medicine, 215 Morris Street, Durham, NC, 27701, USA

Laura Rolke

Institute for Advancing Health Through Agriculture (IHA), Texas A&M University, 1500 Research Parkway, Centeq Building B, College Station, TX, 77845, USA

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AS, LR, and JS conceptualized and designed this study. AS, LR, LX, and JS acquired, analyzed, and interpreted both the qualitative and quantitative data. AS, LX, PB, JG, ALMU, CR, LR, RSF, and JS drafted and substantially revised this manuscript. AS, LX, PB, JG, ALMU, CR, LR, RSF, and JS have approved the submitted version (and any substantially modified version that involves the author's contribution to the study). AS, LX, PB, JG, ALMU, CR, LR, RSF, and JS have agreed both to be personally accountable for the author's own contributions and to ensure that questions related to the accuracy or integrity of any part of the work, even ones in which the author was not personally involved, are appropriately investigated, resolved, and the resolution documented in the literature.

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Schaefers, A., Xin, L., Butler, P. et al. Relationship between the inner setting of CFIR and the delivery of the Healthy School Recognized Campus initiative: a mixed-methods analysis. Implement Sci Commun 5 , 96 (2024). https://doi.org/10.1186/s43058-024-00627-3

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Published: 02 September 2024

Quantitative microbiology with widefield microscopy: navigating optical artefacts for accurate interpretations

Georgeos Hardo 1 ,
Ruizhe Li 1 &
Somenath Bakshi 1

npj Imaging volume 2 , Article number: 26 ( 2024 ) Cite this article

Metrics details

Cellular imaging
Imaging and sensing
Phase-contrast microscopy
Single-cell imaging
Wide-field fluorescence microscopy

Time-resolved live-cell imaging using widefield microscopy is instrumental in quantitative microbiology research. It allows researchers to track and measure the size, shape, and content of individual microbial cells over time. However, the small size of microbial cells poses a significant challenge in interpreting image data, as their dimensions approache that of the microscope’s depth of field, and they begin to experience significant diffraction effects. As a result, 2D widefield images of microbial cells contain projected 3D information, blurred by the 3D point spread function. In this study, we employed simulations and targeted experiments to investigate the impact of diffraction and projection on our ability to quantify the size and content of microbial cells from 2D microscopic images. This study points to some new and often unconsidered artefacts resulting from the interplay of projection and diffraction effects, within the context of quantitative microbiology. These artefacts introduce substantial errors and biases in size, fluorescence quantification, and even single-molecule counting, making the elimination of these errors a complex task. Awareness of these artefacts is crucial for designing strategies to accurately interpret micrographs of microbes. To address this, we present new experimental designs and machine learning-based analysis methods that account for these effects, resulting in accurate quantification of microbiological processes.

Quantitative image analysis of microbial communities with BiofilmQ

Biofilm viability checker: An open-source tool for automated biofilm viability analysis from confocal microscopy images

Sopa: a technology-invariant pipeline for analyses of image-based spatial omics

Introduction.

Widefield fluorescence microscopy is a cornerstone of quantitative microbiology, allowing for noninvasive, real-time imaging of individual cells. This technique’s capacity to measure the size, shape, and content of individual microbial cells has advanced several areas of quantitative microbiology research, including studies on size regulation and division control in bacteria 1 , 2 , 3 , regulation and noise in gene expression 4 , 5 , 6 , and analysis of interactions between cells and their environments 7 , 8 . Additionally, imaging individual molecules within cells using this technique has enabled the study of the dynamics and organisation of individual genes, mRNAs and proteins, and has facilitated the construction of accurate distributions of their abundance 9 , 10 . In essence, live-cell widefield microscopy plays a pivotal role in developing a comprehensive understanding of biological processes within and between microbial cells, offering insights into their organisation, dynamics, and regulation across different scales.

However, careful scrutiny is required for the extraction of quantitative microbiological information from microscopy data. The size of most microbes (particularly bacterial cells) is comparable to the dimensions of the microscope’s point-spread function (PSF) 11 , resulting in significant diffraction effects on bacterial cell images (blur). Moreover, the thickness of bacterial cells is roughly equivalent to the depth of field (DoF) of a microscope objective. Consequently, 2D widefield images of microbes contain projected 3D information containing diffraction from the 3D PSF. The interplay of projection and diffraction effects can bias the estimation of cell size, shape, and intensity. Additionally, these factors hinder the quantification of low copy-number molecules like mRNAs and transcription factors from single-molecule counting experiments 10 as molecules at varying depths exhibit varying degrees of defocus, overlap in the 2D projection, and coalesce into a single blurred spot due to diffraction. Systematically analysing these effects to understand their impact on the accurate interpretation of microscopy data has proven challenging due to the lack of accurate ground-truth information.

To address this challenge, we utilised SyMBac (Synthetic Micrographs of Bacteria), a virtual microscopy platform (which we introduced in a previous work 12 ) capable of generating synthetic bacterial images under various conditions. This tool allows us to assess diffraction and projection effects through forward simulation. The SyMBac-generated images come with precise ground-truth data, enabling us to accurately quantify errors and biases in different measurements and offer control over a wide range of parameters, encompassing optics, physics, and cell characteristics (size, shape, intensity distribution and fluorescent label type). Consequently, we can analyse how these factors affect image formation and feature extraction. Moreover, the virtual microscopy setup allows us to explore imaging parameters that may be difficult or impractical to realise in actual experiments but are crucial for identifying important variables by amplifying their effects.

In this paper, we use SyMBac to systematically investigate the impact of projection and diffraction on the accurate quantification of three key aspects: (1) cell dimensions, (2) fluorescence intensity of individual cells and (3) counts of individually labelled entities per cell. To validate the findings from our virtual microscopy experiments, we conducted targeted real experiments with variable optical settings. Our analysis revealed previously unrecognised artefacts arising from the interplay of projection and diffraction effects. These artefacts introduce significant errors and biases in the estimation of cell size, intensity, and molecule counts, proving challenging to rectify. Recognising these effects and devising appropriate mitigation strategies is crucial for accurate quantification of microbiological processes from microscopy data. To this end, we have demonstrated that understanding these effects enables designing ‘smart-microscopy’ experiments, along with analytical protocols that minimise their impact while facilitating accurate data interpretation for estimating cell size and content measurements.

Digital widefield fluorescence microscopy experiments

We employed the SyMBac virtual microscopy platform to conduct digital experiments mimicking widefield epifluorescence microscopy, the technique typically used for time-resolved live-cell microbial imaging 13 , 14 . In this configuration, microbial cells are sandwiched between a glass coverslip and a biocompatible material like agarose or PDMS, as they are imaged through the cover glass via the microscope’s objective lens, which can be either upright or inverted (Fig. 1a ).

a Schematic optical paths for sample illumination (blue) and emission (green) collection on the camera for image formation in an epi-fluorescence setup. Emitters in the midplane of the cell are in focus. b A stepwise illustration of image formation of a cell uniformly filled with fluorescent emitters. Light from emitters at various planes of the cell is diffracted by the corresponding plane of the 3D point spread function (PSF). Images from multiple planes at various sample depths are projected on top of each other to form the final 2D image of the cell. Further details on the image formation process are given in Supplementary Information 1 . All scale bars are 0.5 μm.

In these settings, the microscope objective has a dual role: it focuses the excitation beam, illuminating the sample through the cover glass and collects emitted photons from the entire sample, focusing them on the camera to form the image (Fig. 1a ). The excitation light illuminates the entire sample, inducing fluorescence throughout. The objective collects emitted light from various planes along the sample’s Z-axis within its depth of field. Each of these planes in the Z-axis introduces blurring due to the 3D PSF, resulting in the projected 2D image, which comprises contributions from each Z-plane. Each contribution is differentially blurred according to its relative distance from the focal plane and the corresponding slice of the 3D PSF (Fig. 1b ). The interplay of projection and diffraction effects in image formation presents significant challenges in accurately extracting the ground-truth distribution of the emitters, as elaborated below.

Effects of projection and diffraction on cell size estimation

We start by examining how projection and diffraction impact the quantification of cell size and shape from 2D fluorescence images. The extent of blurring due to “diffraction effects” is linked to the 3D PSF’s size, which depends on the imaging wavelength, the numerical aperture of the objective lens, and any aberrations within the optical system. Consequently, diffraction effects exhibit wavelength-dependent characteristics for a fixed objective lens. In our digital simulations and real experiments, we employed PSFs of different wavelengths to investigate how diffraction impacts error and bias in measurements. Conversely, the manipulation of the depth of field in the imaging setup reveals the influence of “projection effects.” Using SyMBac, we can selectively toggle projection or diffraction effects, thus allowing us to model each effect in isolation by either capturing light from an infinitesimally thin plane or omitting convolution with the PSF, as shown in Fig. 2a, g . These “nonphysical” experiments are instrumental in identifying and understanding each underlying effect and its contribution independently.

a Synthetic images of a stained cell membrane demonstrate the independent and combined effects of diffraction and projection on 2D image formation (scale bar = 1 µm). Diffraction effects were simulated using the experimentally measured instrumental PSF (iPSF) of our imaging system. b Radial profiles of intensity (across the cell width) from each panel from a are compared to show the relative shifts caused by projection and diffraction effects. The black dotted line indicates the true position of the cell boundary. c Radial profiles of synthetic-cell images with two wavelengths of iPSFs are shown. Lower wavelengths (green) cause smaller shifts, as expected from a smaller size of the PSF. d Example images of a cell stained with fluorescent d -amino acids HADA and RADA are shown. As expected, intensity traces across the cell’s width show RADA (red) emission is more diffracted than HADA (blue) emission, and the diffraction is biassed towards the centre of the cell. e A plot showing the average measured width of a population of cells stained with HADA and RADA (error bar = 99% CI). Inter-peak distances from radial profiles of RADA images consistently underestimate the width more than HADA images. f Comparison of radial profiles before and after deconvolution shows that deconvolution does not shift and correct the peak position; it only makes the profile sharper. g Synthetic images of a digital cell, uniformly filled with fluorescence emitters, show the effects of diffraction and projection on 2D image formation (scale bar = 1 µm). h We compare the radial intensity profile (across the cell width) with and without projection and diffraction effects corresponding to the panels in g . The black dotted line indicates the true position of the cell boundary. i Trendlines from synthetic data show that the observed/true width ratio is dependent on the cell width, with the error growing rapidly for narrow cells. The trends, however, occur in opposing directions for membrane-stained cells and cytoplasm-labelled cells. Estimated widths are calculated from the interpeak distance in membrane-stained cells and full width at half maximum (FWHM) of the radial profile of cytoplasm-labelled cells.

Errors and biases in size estimation from membrane-stained images

To define cell boundaries, quantitative microbiologists often use a membrane stain, a fluorescent dye that highlights the cell membrane (or the cell wall, or a tagged fluorescent protein which localises to the cell’s periplasm), creating a bright outline in the image 15 . Researchers have developed algorithms to identify the cell boundary by either setting a threshold on the brightness of the membrane-stained cells or by locating the brightest contour 16 , 17 . To assess the errors and biases in our estimation of cell boundaries from images of membrane-stained cells, we generated digital images of bacteria stained with a membrane marker. When we isolate the effects of projection and diffraction in synthetic images of a membrane-stained cell, we observe that projection causes a notable shift of the intensity distribution towards the cell’s centre. This shift is further illustrated in Fig. 2b , in the corresponding radial intensity profile. Such a shift leads to an underestimation of cell dimensions, especially cell width, which is typically estimated from the interpeak distance. Diffraction further exacerbates this intensity shift towards the centre, resulting in an even greater underestimation of width. The magnitude of this shift is influenced by the imaging wavelength, as expected due to diffraction (as shown in Fig. 2c ). Note: In this discussion, we have focused on cell width estimation from the interpeak distance of radial intensity profiles of such images, due to its pronounced error sensitivity compared to cell length and its quadratic influence on cell volume, significantly affecting overall size estimation.

Our digital experiments indicate that in a typical widefield imaging setup using a 515 nm emission fluorescent dye and a 1.45 NA objective, the width of a 1 µm wide cell is underestimated by approximately 20%, and a 0.5 µm wide cell is underestimated by 40% (Fig. 2c ). The extent of underestimation is higher for dyes with longer wavelength (Fig. 2c ) and for cells narrower than 0.6 µm in width, stained with a red fluorescent dye (emission wavelength = 700 nm), two separate peaks are not observable due to diffraction blur (Fig. 2i ), meaning the width cannot even be estimated. These findings underscore the major biases and limitations of this method for cell size estimation in existing literature.

To validate the predictions from our digital experiments, we labelled the peptidoglycan layer of individual E. coli cells with two distinct stains emitting at different wavelengths (HADA = 450 nm and RADA = 580 nm), both being fluorescent d -amino acids (FDAAs). We expect these stains to integrate into the same location in the peptidoglycan layer. However, radial intensity profiles revealed a notable inward shift in the intensity peaks of the longer wavelength dye (RADA) compared to the shorter-wavelength counterpart (HADA) (inset - Fig. 2d ), consistent with our simulated profiles in Fig. 2c . Analysing 137 cells, we found that RADA, with the longer wavelength, led to significantly more underestimation of cell width compared to HADA (see Fig. 2e , with additional image examples in Supplementary Information 2 ). These results validate our prediction about diffraction effects on width estimation. However, since the effects of diffraction on the peak position is dependent on the extent of projection, these effects cannot be eliminated by deconvolution using the PSF, as 2D deconvolution is unable to eliminate the projection effects (shown in Fig. 2f and Supplementary Information 3 ). 3D deconvolution would partially address this problem, but it is not compatible with single-plane widefield images that are typically acquired during time-resolved imaging of microcolonies. Instead, using superresolution imaging where diffraction effects are minimised (such as SIM, STED, or PALM 18 , 19 , 20 , 21 ) could help, or employing an imaging system with a shallower depth of field compared to the cell depth (such as a confocal microscope) could also reduce the effects of projection and mitigate the resulting shift from diffraction effects (detailed in Supplementary Information 4 ).

Errors and biases in size estimation from images of cells uniformed filled with markers

Alternatively, researchers often use thresholding algorithms to segment bacterial cell images based on uniformly distributed fluorescence of molecules within the cytoplasm 22 , 23 , 24 , 25 , 26 , 27 . Various thresholding algorithms are employed to segment cells from their fluorescence images, but each has biases and sensitivities that are challenging to quantify and correct (Supplementary Information 5 ). To quantitatively assess the impact of projection and diffraction on extracting cell dimensions from these types of images, we rely on estimating cell width from the full width at half maximum (FWHM) of the radial profile of the intensity.

Unlike in our previous analysis of membrane-stained cells, projection and diffraction have opposite effects on size quantification for cytoplasm-stained cells. Projection effects cause the intensity distribution to shift toward the centre, leading to a bias towards underestimation of cell width from FWHM, while diffraction effects result in light bleeding out, making the radial profile wider than their projected version (see Fig. 2g, h ). We demonstrate that increasing the depth of projection leads to an underestimation of cell dimensions beyond a critical cell width (Supplementary Information 4 ), while higher imaging wavelengths result in increased image blur from diffraction, leading to a bias towards overestimated dimensions. The diffraction effect is also apparent in brightfield/phase-contrast images. In Supplementary Information 6 , we compare radial profiles of phase-contrast images of the same cell collected with different emission filters. The results reveal that phase-contrast images collected with blue emission filters exhibit significantly sharper features and narrower profiles than those collected with red emission filters. Results from image segmentation of phase-contrast or brightfield images of bacteria are affected by such biases and should be corrected for 28 , 29 .

It is important to note that both imaging approaches (membrane-stained or cytoplasm-labelled) exhibit biases in cell dimension estimation that strongly depend on the actual cell dimensions. Figure 2i shows that the relative width-estimation bias from the membrane image decreases as cell width increases, while the estimates from the cytoplasmic marker exhibit an opposite, but less pronounced effect. In the case of membrane-stained images, the shifts from projection and diffraction happen in the same direction, while they oppose each other in case of cytoplasmically-labelled images. An accurate model of the imaging system can be used to calculate correction factors for a given wavelength, which could then be applied to estimate the true dimensions from the observed profile. Virtual microscopy platforms, such as SyMBac, could be utilised to simulate these effects to computationally estimate such correction factors (Supplementary Information 7 ). However, it is difficult to recover the outline of an individual cell to accurately estimate size and shape using this approach. In the following section, we explore methods for incorporating these effects into training deep learning image segmentation models, enabling the models to accurately estimate cell sizes and shapes from 2D images.

Deep learning approaches for precise quantification of cell dimensions

There has been a surge in the popularity of deep learning approaches for cell image segmentation 30 , 31 , 32 , 33 , 34 , 35 . However, the accuracy of these models is inherently linked to the quality of their training data. Generating training data for microscopic images of microbes presents unique challenges compared to standard computer vision tasks. Here, projection and diffraction effects are comparable to object dimensions and, as a result, impede computational boundary identification, as mentioned in our previous work 12 . Manual annotation is also affected because 2D images lack clear boundaries and contain intensity gradients. In essence, the images are blurry. To evaluate the performance of human annotators, we provided them with synthetic images with accurate ground truths and conducted a benchmarking experiment. Supplementary Information 8 details this experiment and the corresponding results, revealing that human annotator performance is not only highly variable but also consistently exhibits an underestimation bias stemming from projection effects.

Inaccuracies and biases in training data, whether originating from computational thresholding or human annotation, compromise the integrity of object-image relationships, thereby leading to the corrupted performance of deep-learning models. The subsequent analysis shows that the highly versatile Omnipose algorithm (specifically bact_fluor_omni) 30 , when trained on human-annotated synthetic fluorescence images, compromises its efficacy in cell segmentation (Fig. 3 ). This phenomenon parallels findings from our recent publication 12 , where we demonstrated that the segmentation outputs from pretrained models inherit biases from their training datasets, resulting in significant variability in segmentation outcomes and marked deviations from the ground-truth distribution.

a SyMBac can be used to generate synthetic training-data, containing realistic images and accompanying perfect ground-truth, to retrain image segmentation models. Illustrative examples of synthetic images and ground-truth pairs are shown for training Omnipose to learn cell masks from images of cytoplasm-stained samples (top) and images of membrane-stained samples (bottom). b Using synthetic data as ground truth, we can check the performance of the pretrained bact_fluor_omni model. To alleviate the effects of human annotation quality, we retrained the model on samples of simulated agar-pad data generated using SyMBac. Examples of validation data, with ground-truth masks and mask outputs from the pretrained and retrained models are shown. To compare ground-truth masks and output masks, each is coloured based on its total area, and the colurmap is given below (scale bar = 2 µm). c Comparison of the output distribution of cell sizes shows that the pretrained model does not reconstruct the underlying ground truth distribution, whereas the output distribution from the SyMBac-trained model more closely mimics the underlying distribution. d To show that synthetic data also boosts segmentation accuracy on real data, we analysed patches of densely packed cells to find groups of cells aligned across their long axis. Since cell width is tightly controlled, we can use these patches of aligned cells to estimate a value for the true population mean width (full analysis is given in Supplementary Information 10 ). We then generated training data matching the real data’s experimental parameters and retrained Omnipose. The resulting distribution of widths for isolated cells and cells within dense colonies is plotted for both the pretrained and retrained model, showing that retraining on synthetic data makes width estimation more accurate. (Ground truth: 0.94 ± 0.066 μm, pretrained: 1.2 ± 0.10 μm, SyMBac trained: 0.94 ± 0.062 μm). e Using synthetic data of membrane-stained cells as ground truth, we trained an Omnipose model to segment cells. We compared the output widths to those widths measured by calculating the interpeak distance between the labelled cell walls/membranes, as shown in Fig. 2 . (Mask colour represents cell width, and the colurmap is given below, scale bar = 2 µm). f The fractional underestimation of a membrane-stained cell’s width (given by the interpeak distance) is highly dependent upon the width itself, and the imaging wavelength. This is true for a cell imaged in widefield, where the DoF is approximately equal to its width (Width DoF in the legend). Training Omnipose on synthetic data of membrane-stained cells makes the deep-learning model (DL) insensitive to the scale of the cell, as well as the imaging wavelength, unlike the interpeak distance method (error bar = 1 SD). g Comparison of the output mask width distribution of the two simulated datasets to the ground-truth mask width distribution shows that when trained on appropriate synthetic data, the entire population distribution can be faithfully reconstructed irrespective of the imaging wavelength.

The virtual microscopy pipeline offers an advantage in addressing the issue of user subjectivity and bias in training data. One can generate realistic synthetic microscopic images of microbes accompanied by accurate ground-truth information (Fig. 3a ). Training deep-learning models with such synthetic training data enables the models to learn precise object-image relationships (detailed in Supplementary Information 9 , Supplementary Information 10 , and ref. 12 ) and mitigates the problem of inaccuracies and user subjectivity in traditional training data. The same Omnipose model, when retrained with synthetic data, produces a segmentation output that more accurately predicted the ground-truth information in the test data, as demonstrated in the ground-truth mask comparisons (Fig. 3b ) and input-output size distributions (Fig. 3c ). The comparison of cell size distributions indicates that Omnipose training data contain enlarged cell masks.

To experimentally verify and validate the enhanced performance of the retrained Omnipose model compared to the pretrained version, we devised a new assay that leverages the tight width regulation of bacteria 36 . This involved placing a high density of cells on agar pads, capturing images of both isolated cells and cell clusters, and then estimating the ground-truth widths of individual cells based on their average width in aligned space-filling patches (further explained in Supplementary Information 10 ). The average cell widths estimated from the patches were tightly distributed (0.94 ± 0.066 μm). The estimated mean width from the patch analysis should match the average widths of isolated individuals, as the cells were not grown on the agarose pad and therefore, were not allowed to differentially adjust to the imaging environment. Subsequently, the widths obtained from this analysis were compared with those derived from the segmentation outputs of both the pretrained Omnipose model (1.2 ± 0.10 μm) and the retrained model using synthetic images (0.94 ± 0.062 μm). The results demonstrate that the retrained Omnipose model exhibits both higher precision and accuracy in estimating cell widths compared to its pretrained counterpart (Fig. 3d ). The comparison of masks presented in Supplementary Information 11 reveals that the original Omnipose model generates substantially larger masks for isolated cells than for cells within clusters, resulting in significant variability and bias in the predicted cell width. In contrast, the output masks from the Omnipose model retrained with synthetic data demonstrate robust performance.

Motivated by these results, we explored an additional application of this approach in the analysis of membrane-stained images; we retrained the Omnipose model with pairs of synthetic fluorescent images of membrane-stained cells and corresponding ground truths (Fig. 3a —bottom). The estimated cell outline from the contour of the membrane-stained images (as described in ref. 37 ) significantly underestimated the cell area compared to the ground truth masks (Fig. 3e ). The relative error in width estimation was size and wavelength dependent (Fig. 3f ), consistent with the previous discussion. Conversely, the comparison of output masks from the retrained Omnipose and the ground-truth cell masks illustrates the high accuracy and precision of the deep-learning model. The model robustly learns the offset created by diffraction and projection as a function of size, and the estimated width closely tracks the ground truth across a wide range of input widths and in a wavelength-independent manner (Fig. 3f, g ). The combination of these digital experiments and real experiments illustrates how synthetic training images can capture the subtle effects of projection and diffraction and augment our capabilities of estimating true cell sizes using deep-learning models.

Quantifying fluorescence intensities of individual cells

Next, we address the issue of quantifying the intensity of individual cells from their fluorescence images. Measuring the total fluorescence intensity of labelled molecules within a cell is crucial for estimating their abundance. This capability enables researchers to monitor the dynamics of cellular processes using time-resolved single-cell image data 38 . The variation in signal intensities among individual cells within the population and over time offers insights into the key regulatory variables and noise sources 39 .

Usually, for the sake of experimental simplicity, microcolonies of microbial cells are cultivated on agarose pads 27 . This setup enables the tracking of individual cell intensities over time and the comparison of intensities among colony cells at different time points. However, such experimental designs, including microfluidic devices with densely packed cells 40 , 41 , introduce a significant artefact in single-cell intensity measurements due to a combination of diffraction and projection effects from the imaging system. The PSF of an imaging system disperses light away from its source. In the context of a cell filled with fluorescent emitters, the emitted light extends beyond the true cell boundaries, making solitary cells appear dimmer (see Fig. 4 a, b). In densely packed clusters, the dispersed light is erroneously attributed to neighbouring cells. We previously termed this phenomenon ‘light bleedthrough’ 42 . Light bleedthrough substantially distorts intensity estimates of cells within a colony, leading to misinterpretations of the strength and noise in gene expression levels, as explained below.

a The radial intensity profile of a simulated fluorescence cell illustrates how intensity is lost from the cell contours due to diffraction effects (scale bar = 0.5 μm). b Example snapshots of simulated fluorescence images of a growing microcolony using a 100× 1.49 NA objective’s instrumental point spread function (iPSF). All cells in the simulation have identical ground truth intensities. Isolated cells and individual cells in small microcolony sizes show low cell intensities, while as the colony grows larger, cells in dense regions, such as at the centre of the colony, begin receiving more light contributions from surrounding cells, artificially increasing their perceived intensity. (Scale bar = 2 μm). c As colony size increases, the mean observed intensity of each cell in the colony also increases (Error bars = 99% CI). Relative changes in intensity compared to isolated individual cells are shown on the left-hand y -axis. Cells approach the true mean intensity as the colony size increases, as shown on the right-hand y -axis. d A false-coloured image of cells on a real agarose pad showing ‘preformed’ microcolonies of various sizes, along with a single cell (white arrow). The relative intensity scale is shown on the right. Important features to note are the similarity to the simulated data shown in ( b ) (Scale bar = 10 μm). e The intensity distribution of cells depends on the size of the clusters they belong to. Isolated individual cells have low mean intensities, while cells from preformed microcolonies with more than 50 cells have 3× higher mean intensities. f Experimental data shows that the average intensity of cells increases with the population size of microcolonies (shown in orange). The trend from simulated colonies is shown in blue.

With the SyMBac virtual microscopy system, we can quantify these effects and verify them through experiments on real microcolonies (see example images of synthetic microcolonies in Fig. 4 , real examples in Fig. 4d ). Crucially, while measuring the instrumental PSF (iPSF) of one’s microscope is a standard procedure, they are not typically imaged over a domain large enough to capture the effects of light bleedthrough at long distances (> ~15 μm for high NA objectives), since the signal to noise ratio becomes low. Thus, we pursued analytical fits to the iPSF to extend its range for simulating long-range diffraction effects. The most suitable method involves extracting the pupil, followed by reconstructing a phase-retrieved PSF which includes appropriate aberrations 43 . However, as detailed in Supplementary Information 12 , although the reconstructed PSF effectively captured the aberrations in our system, it failed to replicate the long-range effects observed in the iPSF. A theoretical PSF (tPSF) model 44 gave a much better fit to the entire iPSF (Supplementary Information 13 ). However, since we are interested in simulating the long-range effects of diffraction, one must extrapolate the function domain of the fitted PSF. We found that the tPSF did not extrapolate well when fitted to a crop of the iPSF. We, therefore, resorted to an ad hoc empirical function fit, which we call an “effective” PSF (ePSF), which we verified was able to extrapolate to the entire function domain despite being fitted on only a small crop of the iPSF (see Supplementary Information 14 ). All simulations of light bleedthrough effects in microcolonies were carried out using this ePSF model.

Colony size affects single-cell intensity quantification

Our simulations suggest that, due to the loss from light bleedthrough, an isolated cell appears only 30% as bright as its true intensity (Fig. 4c ). 70% of the intensity is lost to the surroundings and can end up in nearby cells. As the microcolony size increases, more neighbouring cells contribute to the intensity of cells within the colony through the light bleedthrough effect. Consequently, the mean intensity of cells within a simulated microcolony rises monotonically with colony size, reaching 70% of the true intensity in very large colonies (>1000 cells, see Fig. 4b, c ). As the colony size tends to infinity, the mean intensity of an individual cell should converge to the true mean intensity, since all the lost intensities are allocated to other cells within the colony. These simulations predict that individuals within a colony of a hundred cells should appear, on average, 2–2.5 times brighter than isolated cells (Fig. 4c ).

To validate these predictions, we conducted experiments with microcolonies on agar pads, comparing the intensity of cells within colonies of different sizes with that of isolated cells. To ensure a consistent intensity distribution among all cells, we placed a high density of cells on agar pads and captured instantaneous images of cell clusters, rather than allowing colonies to form gradually, which could introduce temporal intensity variations. This method allowed us to obtain ‘preformed microcolonies’ of varying sizes while maintaining the original cellular content distribution. As expected from the analysis of simulated microcolonies, snapshots of real cell clusters clearly show higher intensity in cells from larger colonies compared to isolated cells (see Fig. 4d ). The intensity distributions of cells in large ‘preformed colonies’ (number of cells >300) do not overlap with those of isolated individuals (see Fig. 4e ). The trend in Fig. 4f , which illustrates the mean intensity of cells relative to their preformed colony sizes, is qualitatively similar to the trend predicted from the digital experiments. Nevertheless, the magnitude of bleedthrough effects witnessed in the experimental microcolonies exceeds that of the simulated colonies. This disparity may arise from the mismatch between the long-distance tails of the ePSF and the actual iPSF of the system, the possible contribution of scattering in the imaging medium, or field-dependent aberrations not captured in our simulations.

Light bleedthrough affects noise and correlations in single-cell intensity measurements

The light bleedthrough effect goes beyond its impact on mean intensity, introducing subtle local variations in individual cell intensities. Since the degree of bleedthrough depends on the number of neighbouring cells, the intensity of individual cells varies based on their position within the colony (Fig. 5 ). Cells closer to the centre, receiving contributions from more neighbours, appear brighter in images than those near the edges (see Fig. 4b, d ). Consistent with the predictions from our digital simulations of microcolonies, the experimental data reveal a correlation between spatial intensity patterns, the number of neighbouring cells, and intra-colony position, (see Fig. 5a–c ). Additional example images of microcolonies from imaging experiments are shown in Supplementary Information 15 .

a Schematic representation of a cell (green) some distance from the centre of the microcolony, with its neighbouring cells labelled (lighter green). The intensity of individual cells depends on their position within the microcolony, given by d c / D , where dc is the distance from the colony centre, and D is the colony diameter, and the number of direct neighbours ( cell N ). b Cells closer to the centre of a simulated colony appear brighter than cells at the periphery due to light bleedthrough (Error bars = 99% CI, data sample averaged for colonies of size 20–1000 cells). The position-dependent trend predicted from simulated microcolonies (green) is consistent with experimental results (orange). c Simulated cells with more neighbours appear brighter (Error bars = 99% CI, data sample averaged for colonies of size 20–250) consistent with experiments (orange). d Two simulated colonies with CVs of 0.01 and 0.22, respectively, along with their convolution with the iPSF, showing that their observed CVs are very similar despite markedly different underlying cell intensity distributions. e At low noise, true CV < 0.15, where the underlying cell intensity distribution is uniform, the PSF causes artificial position-dependent variation in cell intensities (increasing CV). Conversely, when the input CV is high (true CV > 0.15), the PSF acts as a blurring filter, lowering the variance in the population by allocating intensities from brighter cells to neighbouring dimmer cells (lowering CV).

Such phenomena, where the intensity of individuals appears to be dependent on their position or number of neighbouring cells, can lead to misinterpretations in quantifying intensity correlations and cellular heterogeneity 5 , 8 . It may wrongly suggest that an individual cell’s intensity is influenced by interactions with neighbouring cells, incorrectly implying nonexistent biological mechanisms. In studies using intensity distribution patterns as evidence of cell-cell interactions, researchers should consider the confounding influence of optical effects and implement appropriate controls to differentiate genuine biological interactions from optical artefacts 7 . The use of digital control experiments via virtual microscopy platforms, like SyMBac, can help identify potential artefacts specific to a given experimental design, including optical specifications and sample configurations.

Light bleedthrough effects also cause a major artefact in noise estimation from single-cell data, which is somewhat counterintuitive. In the absence of true population variability (coefficient of variation, CV = 0), positional factors within the microcolony and the number of neighbouring cells can artificially introduce variability and result in a higher estimated CV (Fig. 5d ). Conversely, when substantial variation exists among cells, the PSF acts as a smoothing filter, redistributing intensity from brighter to dimmer cells (see Fig. 5d, e ), leading to an underestimation of inherent variability. These paradoxes emphasise the complexities introduced by diffraction effects in the temporal quantification of gene expression variability. They produce similar results across different underlying distributions (further examples in Supplementary Information 16 ) and present challenges for correction because the effect’s magnitude and direction depend on an unknown ground truth CV, as well as the size and shape of the microcolonies.

It is conceivable that one could leverage deconvolution to correctly assign light to specific pixels in the image. In actual image formation, the PSF has an infinite range, leading to long-range diffraction effects accumulating within dense microcolonies. This results in diffracted light potentially ending up several pixels away from the original point source. However, deconvolution methods applied in the literature sometimes use kernel sizes far smaller than the data and thus merely result in a sharpening of the image, failing to accurately reassign light from beyond the kernel’s boundaries. This phenomenon is illustrated using experimental and simulated images in Supplementary Information 17 and 18 . As shown in Fig. 5e , where deconvolution is performed with a kernel measuring 125 × 125 pixels, only a marginal improvement in noise estimation accuracy is seen. Ideally, the deconvolution should use a kernel size as large as the data being deconvolved. Since such a large iPSF is unattainable, deconvolution with the full ePSF was performed. While it gave a marked improvement over the iPSF, it was unable to fully recover the underlying ground truth intensity distribution in experimental data (Supplementary Information 17 ).

Microfluidic imaging platforms for robust intensity quantification

Given the challenges associated with accurately knowing the PSF and the exact configuration of cells within a microcolony, the task of estimating the true intensities of individual cells, especially for quantifying noise or correlations, becomes nearly impossible. Additionally, the influence of projection and scattering effects and potential inhomogeneities in the growth environment 45 is hard to eliminate. Therefore, we suggest that, considering knowledge of diffraction effects, researchers could design their experiments differently. For instance, utilising a structured imaging platform, where cells are maintained at a fixed distance from each other, can help minimise the bleedthrough effects.

To systematically analyse the constraint on such an imaging platform, in our simulations on an array of digital cells, we explored how the extent of intensity bleedthrough depends on the inter-cell distance in such an array (Fig. 6a ). The percentage bleedthrough contribution from neighbouring cells is plotted as a function of distance along the short and long axes of cells ( x and y , respectively) (Fig. 6b ). The heatmap illustrates that in a closely packed array, shown in the left-top corner, the intensity of individual cells receives an additional ~100% contribution from neighbours, causing cells to appear 2x brighter than isolated cells—a finding consistent with our earlier discussion. To reduce the light bleedthrough effects to <1% of the true intensity, cells need to be at least 10 μm apart from each other (a conservative estimate based on the ePSF).

a A simulated array of cells with controllable x and y cell pitch. The grid corresponds to the heatmap in panel b , with increased x and y spacing between cells lowering the intensity bleedthrough from neighbours. b The heatmap shows the overall intensity bleedthrough percentage of a cell within an ordered array of neighbours as a function of inter-cell distance. c Characterisation of intensity bleedthrough from distant cells within the mother machine microfluidic device. A schematic representation of the mother machine is given, along with a phase-contrast image taken of the same device, with the (mCherry) fluorescence channel overlaid to indicate labelled and unlabelled cells. Varying the spacing between mother machine trenches affects the amount of light bleedthrough incurred. d Bleedthrough from within a single trench in the mother machine; an unlabelled cell’s intensity is measured and its apparent intensity increases as the number of additional labelled cells within a trench increases, despite it being unlabelled.

Microfluidic devices, such as the ‘mother machine’ 2 , provide a viable solution for maintaining cells at a fixed, constant distance from one another. This device keeps cells in short vertical arrays placed at a specific distance apart. By selecting the appropriate spacing between these arrays through specific device design and optimisation, researchers can effectively eliminate the bleedthrough effect, allowing for accurate estimation of the heterogeneity and fluctuation dynamics of intensities from individual cells 46 .

To assess the effect of bleedthrough in these scenarios, we conducted experiments by mixing unlabelled cells with fluorescently labelled cells in the mother machine (black and red coloured cells in Fig. 6c and d respectively). Details of the experimental design, analysis, and results are shown in Supplementary Information 19 . Intensities of unlabelled cells, as a function of the number and distance of their neighbouring fluorescent cells, were calculated to estimate the percentage bleedthrough effect. The results from this analysis, along with data from a previous paper using a similar approach 46 , show a quantitative match with the simulated trends. A distance of >10 μm between trenches is sufficient to reduce the extent of bleedthrough to below ~1%. Microfluidic device design and performance verification, using digital microscopy experiments, should be routinely employed to estimate and eliminate unwanted optical effects in microscopy data.

Counting single molecules

Quantifying the abundance of low-copy tagged molecules introduces unique challenges. When the collective fluorescent signal from these tagged molecules approaches the background autofluorescence of the cell, interpreting intensity values in terms of abundance becomes complex. In the case of species with moderately low copy numbers per cell (approximately 50–100 copies per cell), some researchers have employed techniques like background deconvolution 4 . However, these methods fall short of achieving single-cell resolution since they deconvolve the entire distribution along with autofluorescence levels. Moreover, these distribution deconvolution techniques are ineffective for proteins with very low copy numbers (less than 20), which often play critical roles in gene expression regulation, including gene copy numbers, transcription factors (TFs), mRNAs and plasmids 47 . To reliably quantify the abundance of low-copy proteins, it is essential to count individual fluorescently tagged molecules within a cell 48 .

Accurately determining the copy number of labelled molecules remains a formidable task due to the interaction of the diffraction limit and the 2D projection of 3D-distributed emitters. In 2D images, individually tagged molecules manifest as diffraction-limited, blurry spots, with the extent of blur contingent upon their distance from the focal plane. Consequently, when spots are positioned closer to each other than the resolution limit (in the XY plane, regardless of their position in Z, due to projection) they can merge into a single spot in the projected image. Adding to the complexity, the 3D characteristics of the PSF make it difficult to detect out-of-focus spots (Fig. 7a ). Both of these effects collectively contribute to an underestimation of the molecule count, even when there are only two copies per cell.

a Schematic of an epifluorescence single molecule imaging setup, where the position of emitters within the cell determines the extent of defocus in their image and determines their detection probability. b Molecules in a cell exist in three dimensions. Shown are nine molecules in a digital cell and their ground truth positions projected in xy . Upon convolution with the PSF, the resultant image is a projection of all nine molecules, of which only three are in focus. The remaining six molecules are dim and hard to detect, and two of them are very close. c Simulated sampling of points within a digital cell shows ‘naive’ detection bounds and sources of undercounting. If points had an SNR lower than the 99th percentile of the background PSNR, they were considered too dim to detect. Additionally, if two molecules are within 1 Rayleigh criterion of one another, they are considered too close to resolve, and thus these molecules are lost due to diffraction. The remaining population of molecules are considered countable. d Relative contributions of each mode of undercounting (lost to diffraction and lost to defocus) are plotted as a function of the true count of molecules in a narrow cell ( r = 0.5 μm) and a thicker cell ( r = 1 μm). The resolvable fraction decreases rapidly with increasing density of molecules, whereas the detectable fraction stays constant.

In Fig. 7b , we illustrate the extent of undercounting from various sources using digital imaging experiments. We employ a “naive counting” criterion, as described in the Methods section, which includes the enumeration of molecules that are out of focus, those that are undercounted due to proximity to diffraction-limited spots, and the cumulative count of both individual and cluster molecules perceived as singular due to the diffraction limit. This approach allows us to identify error sources that are influenced by cell dimensions (spot density and projection) and experimental setups (diffraction and depth of field). The results in Fig. 7c show that, when the count is small ( n = 5), most spots are isolated, resulting in minimal losses due to diffraction effects. However, increasing the cell thickness (from cell radius = 0.5 μm to radius = 1 μm) leads to a significant fraction of spots becoming undetectable as they get blurred and dimmed due to the defocused PSF. On the other hand, as the molecular count increases, there is a corresponding increase in the proportion of molecules that are undercounted due to the diffraction limit since an increase in spot density leads to an increase in the fraction of spots being unresolvable from their neighbours. However, the proportion of molecules lost due to defocus remains constant, dependent solely on the volume fraction of the cell situated outside the focal plane (Fig. 7d ).

This digital experiment reveals that the combined effects of projection and diffraction lead to substantial undercounting, even for molecules present in very low quantities; in an average-sized bacterium, a single snapshot may incorrectly count only two molecules as a single entity approximately 5% of the time (Supplementary Information 20 ). The proportion of undercounting escalates rapidly with the increase in the number of molecules present per cell, as depicted in Fig. 7d , and for a copy number of 15 molecules per cell, one underestimates by 40%.

Smart-microscopy approaches for improving counting performance

The term ‘smart-microscopy approaches’ denotes utilising domain knowledge of a specific imaging system and subject to craft targeted microscopy solutions, encompassing both acquisition and analysis. To improve counting performance, knowledge of the depth-dependent detection probability and the cell volume can be leveraged to calculate a correction factor, addressing the loss of molecules due to defocus. At the focal plane, a molecule will be most in focus, and given that it is bright enough, will exceed a threshold SNR for detection. The probability of exceeding this SNR threshold decreases as the molecule shifts out of the focal plane. We call this probability function D ( z ). We derived this empirical depth-dependent detection probability function for our imaging system from the instrumental PSF (shown in Fig. 8a and detailed in Supplementary Information 21 ).

a The depth-dependent probability function D ( z ) of an imaging system is shown in blue. The cell’s cross-sectional density is given in red as a ( z ). The overlapping area between these two profiles (given by the cross-correlation a ( z ) ★ D ( z )) gives an estimate of the fraction of the molecules which will be observed. To maximise the number of molecules detected, one can shift the objective by an optimal amount, given by δz optimal , which is where the two functions have maximum overlap. b A schematic showing a cell in the optimal focal position relative to the detection probability function, thus detecting the maximum number of molecules possible. The true number of molecules can then be estimated by multiplying the observed count (green) by a correction factor (accounting for the lost molecules, shown in black), which intuitively is the reciprocal of the overlapping area (full derivation in Supplementary Information 21 ). Another approach to detecting more molecules is to modify a ( z ) by physically compressing the cell (using Microfluidics-Assisted Cell Screening (MACS)), bringing the entire cell’s volume within the maximum region of D ( z ). c Applying the correction factor or compressing the cell using MACS improves the counting performance compared to the naive estimate. Both of these approaches reduce the error from defocus, but undercounting errors at higher counts occur due to diffraction effects. d A schematic architecture of the Deep-STORM single molecule localisation network is shown, which was trained using synthetic single molecule images. e Applying Deep-STORM to molecule counting improves performance, but combining it with MACS leads to near-perfect detection and counting up to a higher density of molecules.

Upon closer examination, we observed that this function is offset from the objective’s focal plane because of the asymmetric nature of the iPSF along the Z axis. To maximise the number of detectable molecules within a cell, it is necessary to optimise the overlap between the cell’s cross-section and this function. A cell’s cross-sectional density is given in red as a ( z ) (Fig. 8a ). The integral of a ( z ) between two z positions within the cell will give the volume fraction, and hence the fraction of molecules between those positions (assuming a uniform distribution of emitters within the cell). The detection probability D ( z ) can be shifted by focusing the microscope’s objective up and down. Thus, the overlapping area between these two profiles (given by the cross-correlation a ( z ) ★ D ( z ) gives an estimate of the fraction of the molecules which will be observed, for all shifts of D ( z ). To maximise the number of molecules detected, one can shift the objective by an optimal amount, given by δz optimal , which is where the two functions have maximum overlap (Fig. 8a ).

Once the focal plane is adjusted, we can compute the fraction of molecules lost to the out-of-focus volume to find an empirical correction factor (Fig. 8b ). This correction leads to improved counting performance, but only on averaged counts, as demonstrated in Fig. 8d . Alternatively, using microfluidic platforms to flatten cells can bring a larger number of spots into focus (Fig. 8b ). Additionally, the expanded cross-section of the flattened cells in the imaging plane slightly reduces the undercounting effect caused by the diffraction limit (Fig. 8c ), consistent with previous findings in the work of Okumus et al. (Microfluidics-Assisted Cell Screening—MACS) 10 , 49 .

To further improve the counting performance, we explored the potential of designing an image analysis pipeline that leverages knowledge of defocus and spatial patterns from simulated data to enhance counting accuracy. To pursue this, we retrained Deep-STORM, a well-established deep-learning network designed for super-resolving single-molecule images 50 . Deep-STORM leverages a convolutional neural network architecture to super-resolve single molecules based on local intensity patterns and spatial relationships. We have trained the Deep-STORM model using simulated synthetic images, which contain a varying number of spots with appropriate defocus depending on their position within the digital phantom cells (Fig. 8d ). This training enabled the model to consistently and accurately count molecules to a larger copy-number (Fig. 8e ) compared to the naive counting estimates and the performance demonstrated in previous research in this field 10 .

Just as observed with deep-learning models used for cell segmentation (discussed in the “Deep-learning approaches for informed cell segmentation” section), training these models with realistic synthetic data significantly enhances their ability to detect single molecules. Our previous analysis demonstrates that flattening the cells using platforms like MACS reduces the fraction of defocused spots and emulates a situation in which most spots are in focus (Fig. 8b ). Indeed, Deep-STORM models, when implemented in a simulated MACS type scenario, performed reliably up to a very large number of molecules per cell (>~25 molecules/cell, Fig. 8e ).

The advancement of quantitative microbiology relies heavily on the accurate interpretation of microscopy data. We have employed virtual microscopy experiments and targeted real experiments to systematically explore the challenges and potential pitfalls associated with using microscopy data to quantify the size and content of microbial cells. Our focus was on projection and diffraction effects, particularly significant for microbial cells due to their size.

Our findings reveal significant impacts of projection and diffraction on the performance of image segmentation algorithms in accurately identifying cell outlines from fluorescence and brightfield images of bacteria. Both traditional segmentation techniques and machine-learning approaches experience biases in cell size estimation. The extent and direction of this bias depend on various factors, including labelling methodologies, imaging configurations and the cell’s dimensions, which makes it difficult to correct. However, we found that the bias and error can be mitigated when using machine-learning methods trained with synthetic data that incorporates these effects.

Timelapse imaging methodologies, commonly employing agar pads and microfluidic devices, are frequently utilised for investigating live-cell gene expression dynamics and heterogeneity 39 , 40 , 41 , 51 . Using digital image simulations and experimental fluorescence imaging of cell clusters, we found that the accurate quantification of true cellular fluorescence signals in clustered configurations (‘microcolonies’), is difficult due to diffraction-induced misallocation of light intensity from adjacent cells. Such distortions impact both the estimation of expression variation and correlation analyses conducted on these platforms 5 , 7 , 8 , 52 . Deconvolution can improve, but not entirely eliminate, these artefacts and its fidelity to ground truth strictly depends on the precision and size of the deconvolution kernel. In this case, experimental design changes, such as the use of imaging platforms like microfluidic devices, where cells can be kept at specified distances, can reduce such distortions 42 , 46 .

Similar challenges arise in the quantification of low copy number moieties, such as mRNA, plasmids, or proteins, complicating the accurate counting of more than five individual molecules. Caution is warranted when interpreting ‘single-molecule’ images and results from estimated molecular ‘counts.’ To address these challenges, alternative experimental designs and deep-learning-based analysis protocols were proposed and substantial improvements in counting accuracy were demonstrated.

In summary, the analysis presented here underscores the critical importance of understanding the artefacts and aberrations incorporated into microscopy data to extract meaningful information about microbiology, whether it involves the shape and size of cells or their content from intensity measurements or single-molecule counting. We advocate for the routine use of digital experiments with virtual microscopy platforms to test limitations of experimental design and potential optical illusions, ensuring ‘informed’ interpretations of imaging data. This knowledge can further inform the design of ‘smart microscopy’ experiments, leveraging domain knowledge to create appropriate imaging platforms and machine-learning models trained with relevant ‘synthetic images.’ The analysis and discussion presented in this paper should guide improved experiment design and help with quantitative interpretation of microscopy experiments in microbiology.

Computational methods

Virtual fluorescence microscopy using symbac.

In this study, image simulations were conducted utilising the SyMBac Python library 12 . Unless specified otherwise, all virtual fluorescence microscopy images were generated following a consistent workflow: 1. The 3D spherocylindrical hull of a digital cell was positioned within a defined environment—either (a) isolated, (b) among scattered cells, or (c) within a microcolony if colony growth simulation data were available. 2. Fluorescent emitters were uniformly sampled within the cell volume and indexed within a 3D array, the value at each index denoting the emitter count. For cells with homogeneously distributed fluorescence, a “density” value was established, defined as the average number of emitters per volumetric element within a cell. Thus, the total number of molecules within a cell was calculated as the product of this density and the cell volume. 3. Subsequently, diffraction and projection effects were simulated through the convolution of this dataset with a point spread function (PSF). Convolution was executed employing either a theoretical, effective, or instrumentally measured PSF (tPSF, ePSF, or iPSF respectively). The PSF_generator class within SyMBac was used to generate synthetic PSFs in accordance with the model from Aguet 44 . To simulate the projection and out-of-focus light characteristic of a widefield fluorescence microscope, the centre of the point spread function (PSF) is assumed to be aligned with the midplane of the cell. Each slice of the PSF is accordingly convolved with the corresponding slice of the cell, as illustrated in Fig. 1b , Supplementary Information 22 , and Supplementary Information 23 . If using a tPSF or ePSF, convolution is done at a high resolution, and then downsampled to the pixel size of the simulated camera in order to capture the high-frequency features of the kernel.

To artificially modulate the depth of field of the microscope and thereby mitigate projection artefacts, the number of PSF planes convolved with the cell can be truncated. For instance, in a 1 µm wide cell simulated at a pixel size of 0.0038 µm, there would be 263 slices in the Z-direction. To generate an image devoid of projection artefacts, only the middle Z-slice of the cell is convolved with the middle Z-slice of the 3D PSF. This method is applicable for both simulated and empirically measured PSFs. To eliminate diffraction effects, the PSF can be substituted with an identity kernel, which, upon convolution, reproduces the original data. To modulate the effect of diffraction continuously, the frequency of light employed to simulate the kernel can be arbitrarily adjusted.

Simulations of fluorescence images of individual cells

To preclude errors stemming from length underestimation in width assessments, digital cells with a fixed length of 6 μm were utilised. The cell width was manipulated to range between 0.5 and 3.0 μm, while the simulated depth of field was adjusted between 3 μm (for the widest cell) and 0.0038 μm (for a single Z-slice). The PSF generator was configured to “3d fluo” mode for 3D convolution, employing the model from Aguet 44 . Additionally, an identity kernel served as the PSF for a theoretical undiffracted microscope with an imaging wavelength of 0 μm.

To simulate images of cells with cytoplasmic fluorescent markers, 3D spherocylindrical cells were rendered, and emitters sampled as described above. To simulate membrane fluorescent cells, fluorescent emitters were sampled only within a single pixel layer corresponding to the outermost cell volume. We ensured to render images at a high resolution, allowing accurate drawing of the cell membrane. Rendering at a lower resolution, even a single pixel would be significantly thicker than the true thickness of the cell membrane.

Simulated images of fluorescent single cells, either with cytoplasmic markers or membrane markers, were generated at different wavelengths, widths and depths of focus. It is important to note here that when the depth of field is changed, this is a simulation of a non–physical effect. In actuality, the volume of out-of-focus light captured by the microscope is determined by the objective lens. By adjusting the number of Z-PSF layers with which the 3D cell volume is convolved, the non-physical manipulation of out-of-focus light collection by the microscope’s objective is simulated. Despite its non-physical nature, this is a valuable exercise for identifying sources of measurement bias and error. A similar argument applies to diffraction: the use of an identity kernel simulates an image devoid of diffraction effects. Though non-physical, this is instrumental in examining how an image is compromised by the microscope’s PSF. In real experiments, both projection and diffraction effects co-occur; hence, the comparative analysis is limited to simulated images that incorporate both phenomena.

Cell size quantification and analysis

Following the simulation of individual cells, errors in size estimation attributable to diffraction and projection were quantified using two methodologies. For cells marked with cytoplasmic fluorescence, a binary mask of the resultant synthetic image was generated employing Otsu’s thresholding algorithm 53 . Dimensions along the two principal axes of the binary object were then calculated to determine length and width. In contrast, for synthetic images featuring fluorescent membrane markers, dimensions were determined by measuring the inter-peak distance along the one-dimensional intensity profile, which was aligned with the two principal axes of the cell.

Simulations of fluorescence images of microcolonies of cells

The agar pad simulation feature of SyMBac was used to generate microcolony simulations 12 , each of which was terminated when reaching a size of 1000 cells. All microcolonies are restricted to monolayers. This pipeline leverages the CellModeller platform, which is integrated into SyMBac, for the creation of ground-truth microcolonies 54 . For these simulations, a constant cell width of 1 μm was maintained, with cellular division programmed to occur at a target length of 3.5 μm ± Uniform (−0.25 μm, 0.25 μm) resulting in sequences of densely packed, proliferating colonies.

Individual cells in each colony simulation contain uniformly distributed fluorescent emitters. To control the coefficient of variation (CV) of intensity among the cells within a microcolony, we fixed the mean density of emitters within a cell but varied the variance of a truncated (at 0) normal distribution in order to sample single-cell intensities with a desired CV. The CV was sampled between 0 and 0.3. Synthetic images from these colonies were generated with 3D convolution in the same manner as described in the previous section, but with multiple PSFs: (1) a theoretical PSF being rendered for a 1.49NA objective, a refractive index of 1.518, a working distance of 0.17 mm, and with imaging wavelengths of 0.4 μm, 0.55 μm and 0.7 μm for separate simulations. (2) the same ground-truth data were convolved with an instrumental PSF captured from a Nikon 100× 1.49NA Plan Apo Ph3 objective lens with the same parameters described, imaged at 0.558 μm wavelength light (bandwidth 40 nm) and (3) the effective PSF fit of the instrumental PSF to simulate long range diffraction effects. This generated synthetic microscopy images and corresponding ground-truth masks of microcolonies under varied imaging conditions. More details on simulation and examples can be seen in Supplementary Video 1 .

Colony image intensity quantification and analysis

Quantification of single-cell intensities from synthetic microcolonies.

Calculating the intensity of each cell within the synthetic microcolony images did not require segmentation because the ground truth mask positions are available from the simulations. Thus, for each ground truth mask, the average intensity in the corresponding position in the synthetic microscope image was enumerated and used to calculate the CV, which could be compared to the ground truth CV. To assess whether the ground truth CV can be recovered under ideal circumstances, we performed Richardson–Lucy deconvolution (with 100 iterations) using the original PSF 55 , 56 . The deconvolved CV can then be compared to the ground truth CV by enumerating the deconvolved image’s average intensity within each ground truth mask position.

The distance of each cell from the centre of the colony was calculated by calculating each cell’s Euclidean distance to the mean position of all cells within the colony (the colony centroid). The distance was normalised by dividing by the maximum Feret’s radius of the colony as calculated by Scikit-image’s regionprops function 57 . The number of neighbours for each cell was calculated by first dilating all cell masks by 4 pixels to ensure that neighbouring cell masks touch. The mask image was then converted into a region adjacency graph, where each node is a cell, and edges represent a neighbour connection between two cells (cells that touch). The graph is then traversed and each node’s degree (corresponding to that cell’s neighbour number) is enumerated (Fig. 5c ).

Quantification of single-cell intensities from experimental microcolonies

Experimental microcolony data were analysed using the same methods as synthetic microcolonies but were first segmented in phase contrast using the Omnipose model to generate masks (example given in Supplementary Information 24 since only average intensity per cell is required, it is not critical to have very accurate size estimation). For datasets generated this way, there is no ground truth intensity estimation. Fluorescence images were first background subtracted by subtracting the mean of the lowest 5% of pixel intensities within the image. Mean cell intensity was defined as the sum of the pixel intensities within each mask, divided by the cell mask area. Deconvolution was performed using the iPSF and the ePSF, and the intensity of deconvolved cells recorded. Since no ground truth data exists, we did not estimate the CV of real data but rather focussed on showing the effects of colony size, cell neighbour number, and cell position within a colony on the observed cell intensity. These values were quantified using the same methods as for synthetic colonies.

Manual annotation platform and analysis

To assess the effects of projection and diffraction on the performance of manual (human) annotation of cells (for the purposes of training data preparation), five individuals were each asked to annotate the same dataset of 600 simulated cells, where the ground truth was known but not disclosed to the annotators. The cells had an average width of 1 µm, and were partitioned into 4 possible groups: projection “off” cells (cells where the imaging DoF is 1 pixel wide)/projection “on” cells (where the depth of field contains the entire 3D cell), and cells imaged with a fluorescent emitter capable of emitting 0.2 µm wavelength light, and a 0.6 µm wavelength light emitter, distributed with a density of 0.4 emitters per volume element within each cell. One-hundred fifty of each cell type were scattered with uniform random position and orientation on a 2048 × 2048 plane with a pixel size of 0.065. Convolution for the two wavelengths was performed once again with the Aguet PSF model. Camera noise was added after convolution using SyMBac’s camera class, using a baseline intensity of 100, a sensitivity of 2.9 analogue-digital units/electron, and a dark noise variance of 8. Annotators ran a Python script which presented them with a Napari window 58 and a layer upon which to label cells. The order in which the images with various effects were displayed was randomised.

Deep-learning models for image segmentation

In addition to comparing human annotation accuracy, we sought to test the accuracy of a pretrained model (in this case, Omnipose’s bact_fluor_omni model) on simulated images where the perfect ground truth dimension of each cell is known. We generated 200 images containing on average, 200 synthetic cells per image (approximately 40,000 total cells) according to the same method described in the previous section, but with areas of synthetic cells varying between 0.15 and 3.5 µm 2 . The PSF model used an imaging wavelength of 600 nm. Ground truth mask and image pairs were saved. Images were then segmented according to the recommended Omnipose documentation with the bact_fluor_omni model. Ground truth cells were matched with their prediction, and the IoU for each cell was calculated.

We then assessed the benefit of training a model on synthetic data matching one’s experimental setup exactly. The performance gained by training a model on an independent set of synthetic images with perfect ground truth available was checked by generating a test set of 200 images according to the aforementioned method. These were used to train a new model according to the Omnipose documentation for 4000 epochs. The 4000th epoch model was then used to segment the original test data, and ground truth cells were matched with their predictions, and the IoUs calculated once again.

Analysis of cell wall labelled cells on agar pads

After the acquisition of cells labelled with FDAAs, images were segmented with Omnipose. Since size estimation of the cell by segmentation is not important, the pretrained bact_phase_omni model was sufficient to segment the cells. To ensure that all the signal from the fluorescently labelled cell wall was captured, cell masks were binary dilated. After this, all individual cells were cropped, and Scikit-image’s regionprops function 57 was used to calculate the orientation of the cells and rotate them.

Simulations of fluorescence images of individual molecules within cells

Fluorescent single-molecule images of single cells were generated in the same manner as described before but with very few emitters per cell (1–30). These low-density fluorescent cells were convolved with the tPSF (to capture high-frequency information, since long-range effects are not needed for this analysis) using the layer-by-layer technique previously described. All analyses were performed on 3 cell types: (1) A typical 1 µm wide, 1 µm deep, 5 µm long cell, (2) an enlarged 2 µm wide, 2 µm deep, 5 µm long cell, (3) a cell trapped by the MACS 10 platform, 2 µm wide, 0.6 µm deep, 5.5 µm long.

We employed two techniques to count the single molecules in these cells. The first approach, which we term the naive approach, involved sampling fluorescent emitters within the cell and partitioning the emitters into 3 groups: (1) Molecules lost to depth of field; these were defined as molecules more than 0.25 µm away from the centre of the cell. (2) Molecules lost to diffraction; these were defined as molecules residing within 1 Rayleigh diffraction limit of at least one other molecule (with a modification term for the defocus, approximated by the model for the broadening of a Gaussian beam 59 ). (3) Resolved molecules; these are the sum of any remaining resolvable single molecules and clusters of molecules within 1 Rayleigh diffraction limit of another (appearing as a single molecule). Rather than applying image processing techniques to count spots, this approach allowed us to identify and partition different sources of miscounting error.

The second approach we applied was Deep-STORM 50 , a deep learning method for super-resolution single-molecule localisation. A more sophisticated method such as this should perform better than the naive method since it can learn to use defocus, changes in local intensity, and local spatial patterning information to better estimate the number of molecules in a region. We trained Deep-STORM by downloading and modifying the ZeroCostDL4Mic 60 implementation for local use. While Deep-STORM is typically trained on simulated data and comes with its own simulator, it does not take into account thick samples such as the depth of entire bacterial cells where defocus is appreciable. Therefore, we generated our own synthetic training data by reducing the number of fluorescent emitters in each cell to between 1 and 30. Individual models were trained for the regular cell and the MACS cell, both with SNRs (signal-to-noise ratios) of 8, which is typical for a bacterial single-molecule experiment.

All image simulation and image analysis methods made heavy use of scikit-image, NumPy, CuPy and SciPy 57 , 61 , 62 , 63 .

Methods for experimental validation

Strain preparation.

For imaging cells labelled with membrane stains, we used the strain E. coli MG1655 7740 ΔmotA with no fluorescent reporter. Cells were grown overnight from a glycerol stock in LB medium at 37 °C with 250 RPM shaking. The following day, cells were diluted by 100× into 1 mL of fresh LB. The fresh LB was supplemented simultaneously with both HADA and RADA to a final concentration of 1 mM each. HADA and RADA get incorporated into the bacterial cell wall during growth, allowing imaging of only the cell outline using fluorescence microscopy 64 , 65 . Cells were allowed to grow in the presence of the FDAAs for 2 h, after which a 300 µL aliquot was spun down and washed with phosphate-buffered saline (PBS) according to the protocol in 66 , taking care to ensure that cells were kept on ice between washes and when not being used.

For imaging microcolonies of fluorescently tagged cells, we used the strain E. coli MG1655 7740 ΔmotA with a constitutively produced cyan fluorescent protein (SCFP3A, FPbase ID: HFE84) under the control of prpsL. Cells were grown overnight from a glycerol stock in LB medium at 37 °C. The following day, cells were diluted by 200× in fresh LB and grown to an OD or 0.1–0.2 to ensure large cell size. Once the desired OD was reached, 1 mL of cells were spun down at 4000× g for 5 min, and the pellet resuspended in PBS for imaging.

Single-cell imaging on agar pad

Agar pads were prepared according to the protocol described in Young et al. 27 . Since only snapshot microscopy was to be performed, agar pads were instead prepared with PBS instead of growth medium, and were kept as consistently thick as possible. Agar pads were cut to approximately 22 × 22 mm, and placed upon a 22 × 40 mm coverslip. Cells on the agar pad were imaged using a Nikon ECLIPSE Ti2 inverted microscope using a 100× (NA = 1.49) objective with F-type immersion oil ( n = 1.518) with a second 1.5× post-magnification lens inserted, for an effective magnification of 150×. The camera used was an ORCA-Fusion C14440-20UP digital CMOS camera from Hamamatsu, with a pixel size of 6.5 µm × 6.5 µm. Cells stained with HADA were imaged with excitation light: 365 nm, 435 nm filter, 100% power, 1 second exposure. RADA was imaged with excitation light: 561 nm, 595 nm filter, 100% power, 0.5 s exposure. Focussing and field of view selection was again done using phase contrast, but special care was taken to account for chromatic aberration by adjusting the Z-plane offset between the focussed phase contrast image and the RADA and HADA images. This was crucial to ensuring that the cell wall was in focus in each image.

Imaging microcolonies on agar pads

Since cells can change their intensities during growth on an agar pad, we image preformed colonies to image the effects of diffraction on the cells (example images shown in Supplementary Information 11 and Supplementary Information 15 ). To generate preformed microcolonies, a higher OD of cells (0.1–0.2) was preferred. 3 µL of cell suspension was pipetted directly onto the agar pad and allowed to “dry” for 5 min, after which a second 22 × 40 mm coverslip was placed upon it. Agar pads were then immediately imaged using the ECLIPSE Ti2 inverted microscope using a 100× (NA = 1.49) objective. This enabled us to collect samples of cell clusters (preformed colonies) of various sizes. To avoid photobleaching, well-separated fields of view were first selected and focussed on phase contrast. Fluorescent images were captured by excitation with 440 nm light at an LED power of 50% for 900 ms (light source: Lumencore Spectra III Light Engine), and with a filter wavelength of 475 nm. Images were captured as multidimensional 16-bit ND2 files for further analysis.

Imaging cells in the mother machine

The mother machine chips were prepared and loaded with cells according to the protocol described in Bakshi et al. 46 . A single mother machine lane was supplied fresh LB by a syringe pump at 15 ul/min. Cells in the mother machine were imaged using the Nikon ECLIPSE Ti2 inverted microscope with a 40× (NA = 0.95) objective lens with a 1.5× post-objective magnification lens. The time-lapse images were acquired using the Hamamatsu ORCA-Fusion Digital CMOS camera, with a pixel size of 6.5 μm × 6.5 μm. Samples were illuminated with a brightfield light source and a fluorescence light source (Lumencor Spectra III) at 3 min intervals for 5 h. Fluorescence images were captured at fast scan mode with a 594 nm excitation LED at 100% power for 100 ms exposure time, and a 632 nm filter.

Point spread function acquisition

Our microscope’s (a Nikon ECLIPSE Ti2) point spread function was captured using fluorescent 0.1 µm TetraSpeck Microspheres from Invitrogen. Slides with fluorescent microspheres were prepared according to 67 , with the only changes being a bead dilution of 1000×, and the use of Fluoromount-G Mounting Medium from Invitrogen. PSFs were captured using 0.70 NA, 0.95 NA, and 1.49 NA objective lenses, with magnifications of 20×, 40×, and 100×, respectively. PSFs were captured with and without the addition of a 1.5× post-magnification lens. Z-stacks were taken of the beads with 0.05 µm spacing. The most in-focus Z-stack was determined by taking the radial profile of the PSF and finding the Z-slice with the highest peak intensity and narrowest FWHM. Intensity peaks were then found and beads were selected to maximise the crop area. Bead stacks were then centred around the mean peak intensity and averaged to produce a low noise iPSF.

Data availability

Sample datasets, including instrumental point spread functions, microscope images of membrane-stained cells and microcolonies, synthetic benchmarking data and mother machine data have been uploaded to https://zenodo.org/records/10525762 68 .

Code availability

All code written for this paper, and used to generate figures is uploaded to https://github.com/georgeoshardo/projection_diffraction 69 . For backward compatibility, the version of SyMBac used in this paper has been frozen and included in this repository.

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Acknowledgements

We thank Prof. Bartlomiej Waclaw, Prof. Ricardo Henriques, Dr. Diana Fusco, Dr. Temur Yusunov, and Kevin J. Cutler for their feedback on this work and the members of Bakshi Lab for their helpful feedback on this study. All figures included in the present paper are original and contain no third party material.

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G.H. and S.B. conceived of the study. G.H. designed the computational models and deep learning tools. G.H. performed the point spread function, microcolony, and single-cell agar pad experiments and analysed the corresponding data. R.L. performed mother machine experiments and analysis. G.H. and S.B. wrote the paper. All co-authors contributed to the final version of the paper.

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Correspondence to Somenath Bakshi .

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Hardo, G., Li, R. & Bakshi, S. Quantitative microbiology with widefield microscopy: navigating optical artefacts for accurate interpretations. npj Imaging 2 , 26 (2024). https://doi.org/10.1038/s44303-024-00024-4

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The chapter describes how learning strategy training can affect the process and outcome of learning, with special emphasis on an exemplary research study. Because learning strategies are intended to influence the process of learning, any useful theory of learning strategies must be based on an underlying theory of human learning.
LEARNING STRATEGIES: AN OVERVIEW
RESEARCH ISSUES As stated in the Introduction, learning strategies are behaviors that are intended to manipulate a person's cognitive processes during learning. Cook's (1982) study is an example of a successful strategy-training program in which there is evidence of students learning to select relevant information and build connections.
Learning strategies and styles as a basis for building personal
This paper presents the results and reflections from a study conducted on students using the e-learning mode from the Panamerican University Foundation. The aim of the study was to identify learning strategies and styles as a basis for building personal learning environments (PLEs). This study was conducted under the parameters of a mixed research approach, which uses quantitative and ...
Quantitative Research
Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
Comprehensive Guide to Quantitative Research Methods in Education
For example, in a study of instructional strategies, the hypothesis might be that students of teachers who use Strategy X will exhibit greater learning than students of teachers who do not. In this study, one would need to operationalize learning by identifying a test or instrument that would measure learning. ... In quantitative research ...
Methods for quantitative research in psychology
Learning objectives. Describe the steps of the scientific method. Specify how variables are defined. Compare and contrast the major research designs. Explain how to judge the quality of a source for a literature review. Compare and contrast the kinds of research questions scientists ask. Explain what it means for an observation to be reliable.
(PDF) THE IMPACT OF EFFECTIVE TEACHING STRATEGIES ON ...
Table (2) illust rates that the degree of e ffective teaching strategies on producing good and fast. learning outcomes are high and it demonstrates that the using of effect ive teaching strategies ...
Profiling mathematics teacher educators' readiness for digital
Research on Mathematics Teacher Educators (MTEs) is crucial for enhancing the professional development of prospective mathematics teachers. However, there is a dearth of recent studies focusing on MTEs' preparedness for technology integration, particularly within the Zambian educational context, and the wider Sub-Saharan African region. This study assessed the readiness of MTEs in Zambia to ...
TA Training: Grading & Delivering Feedback on Quantitative Assignments
Research. We conducted multiple assessments of these online modules to measure participants' learning gains and skill development. In a pilot study with 300 Computer Science TAs, we randomly assigned half to complete the modules prior to the beginning of the semester while the other half were used as controls.
Relationship between the inner setting of CFIR and the delivery of the
Reviews of school- and evidence-based programs for improving physical activity and nutrition show reductions in obesity prevalence by up to 8% [1,2,3,4,5,6,7,8,9].Many models and frameworks (e.g., Whole School, Whole Community, Whole Child) emphasize the delivery of multiple programs [10,11,12], which can result in critical implementation challenges (e.g., limited resources and communication ...
(PDF) "The Journey to Learning: Through the Learning ...
"The Journey to Learning: Through the Learning Styles of the Senior High School Academic Strand Students A.Y. 2019-2020" March 2020 DOI: 10.13140/RG.2.2.10443.62240
Quantitative microbiology with widefield microscopy: navigating optical
Time-resolved live-cell imaging using widefield microscopy is instrumental in quantitative microbiology research. It allows researchers to track and measure the size, shape, and content of ...
Quantitative strategies of different loss functions aggregation for
p>Deep learning models have been successfully applied to many visual tasks. However, they tend to be increasingly cumbersome due to their high computational complexity and large storage requirements.

ORIGINAL RESEARCH article

Introduction

Participants

Learning Strategy Questionnaire

Focus Groups

Quantity and Quality

Active Processing and Monitoring

Habits and Flexibility

Metacognitive Knowledge

Author Contributions

Conflict of Interest Statement

Supplementary Material

Relationship between learning strategies and academic performance: a comparison between accreditation of prior experiential learning (APEL) and regular entry undergraduates

Design/methodology/approach

Research limitations/implications

Practical implications

Originality/value

Introduction

Literature review

Research questions

Methodology

Recommendations

Suggestion for future studies

Acknowledgements

Corresponding author

Report an issue or find answers to frequently asked questions

Learning strategies and styles as a basis for building personal learning environments

Introduction

Problem statement

Justification

Research techniques

Types of research tool

Learning styles of students using the e-learning mode at Unipanamericana

Learning strategies of students using the e-learning mode

Study limitations and prospects

Author information

Corresponding author

Additional information

Competing interests

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Quantitative Research – Methods, Types and Analysis

Quantitative Research

Quantitative Research Methods

Descriptive Research Design

Correlational Research Design

Quasi-experimental Research Design

Experimental Research Design

Survey Research

Quantitative Research Analysis Methods

Statistical Analysis

Regression Analysis

Factor Analysis

Structural Equation Modeling

Time Series Analysis

Multilevel Modeling

Applications of Quantitative Research

Characteristics of Quantitative Research

Examples of Quantitative Research

How to Conduct Quantitative Research

When to use Quantitative Research

Purpose of Quantitative Research

Advantages of Quantitative Research

Limitations of Quantitative Research

About the author

Muhammad Hassan

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Methods for Quantitative Research in Psychology

August 2023