assignment problem disadvantages

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

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Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

Is homework a necessary evil?

After decades of debate, researchers are still sorting out the truth about homework’s pros and cons. One point they can agree on: Quality assignments matter.

By Kirsten Weir

March 2016, Vol 47, No. 3

Print version: page 36

• Schools and Classrooms

Homework battles have raged for decades. For as long as kids have been whining about doing their homework, parents and education reformers have complained that homework's benefits are dubious. Meanwhile many teachers argue that take-home lessons are key to helping students learn. Now, as schools are shifting to the new (and hotly debated) Common Core curriculum standards, educators, administrators and researchers are turning a fresh eye toward the question of homework's value.

But when it comes to deciphering the research literature on the subject, homework is anything but an open book.

The 10-minute rule

In many ways, homework seems like common sense. Spend more time practicing multiplication or studying Spanish vocabulary and you should get better at math or Spanish. But it may not be that simple.

Homework can indeed produce academic benefits, such as increased understanding and retention of the material, says Duke University social psychologist Harris Cooper, PhD, one of the nation's leading homework researchers. But not all students benefit. In a review of studies published from 1987 to 2003, Cooper and his colleagues found that homework was linked to better test scores in high school and, to a lesser degree, in middle school. Yet they found only faint evidence that homework provided academic benefit in elementary school ( Review of Educational Research , 2006).

Then again, test scores aren't everything. Homework proponents also cite the nonacademic advantages it might confer, such as the development of personal responsibility, good study habits and time-management skills. But as to hard evidence of those benefits, "the jury is still out," says Mollie Galloway, PhD, associate professor of educational leadership at Lewis & Clark College in Portland, Oregon. "I think there's a focus on assigning homework because [teachers] think it has these positive outcomes for study skills and habits. But we don't know for sure that's the case."

Even when homework is helpful, there can be too much of a good thing. "There is a limit to how much kids can benefit from home study," Cooper says. He agrees with an oft-cited rule of thumb that students should do no more than 10 minutes a night per grade level — from about 10 minutes in first grade up to a maximum of about two hours in high school. Both the National Education Association and National Parent Teacher Association support that limit.

Beyond that point, kids don't absorb much useful information, Cooper says. In fact, too much homework can do more harm than good. Researchers have cited drawbacks, including boredom and burnout toward academic material, less time for family and extracurricular activities, lack of sleep and increased stress.

In a recent study of Spanish students, Rubén Fernández-Alonso, PhD, and colleagues found that students who were regularly assigned math and science homework scored higher on standardized tests. But when kids reported having more than 90 to 100 minutes of homework per day, scores declined ( Journal of Educational Psychology , 2015).

"At all grade levels, doing other things after school can have positive effects," Cooper says. "To the extent that homework denies access to other leisure and community activities, it's not serving the child's best interest."

Children of all ages need down time in order to thrive, says Denise Pope, PhD, a professor of education at Stanford University and a co-founder of Challenge Success, a program that partners with secondary schools to implement policies that improve students' academic engagement and well-being.

"Little kids and big kids need unstructured time for play each day," she says. Certainly, time for physical activity is important for kids' health and well-being. But even time spent on social media can help give busy kids' brains a break, she says.

All over the map

But are teachers sticking to the 10-minute rule? Studies attempting to quantify time spent on homework are all over the map, in part because of wide variations in methodology, Pope says.

A 2014 report by the Brookings Institution examined the question of homework, comparing data from a variety of sources. That report cited findings from a 2012 survey of first-year college students in which 38.4 percent reported spending six hours or more per week on homework during their last year of high school. That was down from 49.5 percent in 1986 ( The Brown Center Report on American Education , 2014).

The Brookings report also explored survey data from the National Assessment of Educational Progress, which asked 9-, 13- and 17-year-old students how much homework they'd done the previous night. They found that between 1984 and 2012, there was a slight increase in homework for 9-year-olds, but homework amounts for 13- and 17-year-olds stayed roughly the same, or even decreased slightly.

Yet other evidence suggests that some kids might be taking home much more work than they can handle. Robert Pressman, PhD, and colleagues recently investigated the 10-minute rule among more than 1,100 students, and found that elementary-school kids were receiving up to three times as much homework as recommended. As homework load increased, so did family stress, the researchers found ( American Journal of Family Therapy , 2015).

Many high school students also seem to be exceeding the recommended amounts of homework. Pope and Galloway recently surveyed more than 4,300 students from 10 high-achieving high schools. Students reported bringing home an average of just over three hours of homework nightly ( Journal of Experiential Education , 2013).

On the positive side, students who spent more time on homework in that study did report being more behaviorally engaged in school — for instance, giving more effort and paying more attention in class, Galloway says. But they were not more invested in the homework itself. They also reported greater academic stress and less time to balance family, friends and extracurricular activities. They experienced more physical health problems as well, such as headaches, stomach troubles and sleep deprivation. "Three hours per night is too much," Galloway says.

In the high-achieving schools Pope and Galloway studied, more than 90 percent of the students go on to college. There's often intense pressure to succeed academically, from both parents and peers. On top of that, kids in these communities are often overloaded with extracurricular activities, including sports and clubs. "They're very busy," Pope says. "Some kids have up to 40 hours a week — a full-time job's worth — of extracurricular activities." And homework is yet one more commitment on top of all the others.

"Homework has perennially acted as a source of stress for students, so that piece of it is not new," Galloway says. "But especially in upper-middle-class communities, where the focus is on getting ahead, I think the pressure on students has been ratcheted up."

Yet homework can be a problem at the other end of the socioeconomic spectrum as well. Kids from wealthier homes are more likely to have resources such as computers, Internet connections, dedicated areas to do schoolwork and parents who tend to be more educated and more available to help them with tricky assignments. Kids from disadvantaged homes are more likely to work at afterschool jobs, or to be home without supervision in the evenings while their parents work multiple jobs, says Lea Theodore, PhD, a professor of school psychology at the College of William and Mary in Williamsburg, Virginia. They are less likely to have computers or a quiet place to do homework in peace.

"Homework can highlight those inequities," she says.

Quantity vs. quality

One point researchers agree on is that for all students, homework quality matters. But too many kids are feeling a lack of engagement with their take-home assignments, many experts say. In Pope and Galloway's research, only 20 percent to 30 percent of students said they felt their homework was useful or meaningful.

"Students are assigned a lot of busywork. They're naming it as a primary stressor, but they don't feel it's supporting their learning," Galloway says.

"Homework that's busywork is not good for anyone," Cooper agrees. Still, he says, different subjects call for different kinds of assignments. "Things like vocabulary and spelling are learned through practice. Other kinds of courses require more integration of material and drawing on different skills."

But critics say those skills can be developed with many fewer hours of homework each week. Why assign 50 math problems, Pope asks, when 10 would be just as constructive? One Advanced Placement biology teacher she worked with through Challenge Success experimented with cutting his homework assignments by a third, and then by half. "Test scores didn't go down," she says. "You can have a rigorous course and not have a crazy homework load."

Still, changing the culture of homework won't be easy. Teachers-to-be get little instruction in homework during their training, Pope says. And despite some vocal parents arguing that kids bring home too much homework, many others get nervous if they think their child doesn't have enough. "Teachers feel pressured to give homework because parents expect it to come home," says Galloway. "When it doesn't, there's this idea that the school might not be doing its job."

Galloway argues teachers and school administrators need to set clear goals when it comes to homework — and parents and students should be in on the discussion, too. "It should be a broader conversation within the community, asking what's the purpose of homework? Why are we giving it? Who is it serving? Who is it not serving?"

Until schools and communities agree to take a hard look at those questions, those backpacks full of take-home assignments will probably keep stirring up more feelings than facts.

Further reading

• Cooper, H., Robinson, J. C., & Patall, E. A. (2006). Does homework improve academic achievement? A synthesis of research, 1987-2003. Review of Educational Research, 76 (1), 1–62. doi: 10.3102/00346543076001001
• Galloway, M., Connor, J., & Pope, D. (2013). Nonacademic effects of homework in privileged, high-performing high schools. The Journal of Experimental Education, 81 (4), 490–510. doi: 10.1080/00220973.2012.745469
• Pope, D., Brown, M., & Miles, S. (2015). Overloaded and underprepared: Strategies for stronger schools and healthy, successful kids . San Francisco, CA: Jossey-Bass.

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Education scholar Denise Pope has found that too much homework has negative effects on student well-being and behavioral engagement. (Image credit: L.A. Cicero)

A Stanford researcher found that too much homework can negatively affect kids, especially their lives away from school, where family, friends and activities matter.

“Our findings on the effects of homework challenge the traditional assumption that homework is inherently good,” wrote Denise Pope , a senior lecturer at the Stanford Graduate School of Education and a co-author of a study published in the Journal of Experimental Education .

The researchers used survey data to examine perceptions about homework, student well-being and behavioral engagement in a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California communities. Along with the survey data, Pope and her colleagues used open-ended answers to explore the students’ views on homework.

Median household income exceeded $90,000 in these communities, and 93 percent of the students went on to college, either two-year or four-year.

Students in these schools average about 3.1 hours of homework each night.

“The findings address how current homework practices in privileged, high-performing schools sustain students’ advantage in competitive climates yet hinder learning, full engagement and well-being,” Pope wrote.

Pope and her colleagues found that too much homework can diminish its effectiveness and even be counterproductive. They cite prior research indicating that homework benefits plateau at about two hours per night, and that 90 minutes to two and a half hours is optimal for high school.

Their study found that too much homework is associated with:

* Greater stress: 56 percent of the students considered homework a primary source of stress, according to the survey data. Forty-three percent viewed tests as a primary stressor, while 33 percent put the pressure to get good grades in that category. Less than 1 percent of the students said homework was not a stressor.

* Reductions in health: In their open-ended answers, many students said their homework load led to sleep deprivation and other health problems. The researchers asked students whether they experienced health issues such as headaches, exhaustion, sleep deprivation, weight loss and stomach problems.

* Less time for friends, family and extracurricular pursuits: Both the survey data and student responses indicate that spending too much time on homework meant that students were “not meeting their developmental needs or cultivating other critical life skills,” according to the researchers. Students were more likely to drop activities, not see friends or family, and not pursue hobbies they enjoy.

A balancing act

The results offer empirical evidence that many students struggle to find balance between homework, extracurricular activities and social time, the researchers said. Many students felt forced or obligated to choose homework over developing other talents or skills.

Also, there was no relationship between the time spent on homework and how much the student enjoyed it. The research quoted students as saying they often do homework they see as “pointless” or “mindless” in order to keep their grades up.

“This kind of busy work, by its very nature, discourages learning and instead promotes doing homework simply to get points,” Pope said.

She said the research calls into question the value of assigning large amounts of homework in high-performing schools. Homework should not be simply assigned as a routine practice, she said.

“Rather, any homework assigned should have a purpose and benefit, and it should be designed to cultivate learning and development,” wrote Pope.

High-performing paradox

In places where students attend high-performing schools, too much homework can reduce their time to foster skills in the area of personal responsibility, the researchers concluded. “Young people are spending more time alone,” they wrote, “which means less time for family and fewer opportunities to engage in their communities.”

Student perspectives

The researchers say that while their open-ended or “self-reporting” methodology to gauge student concerns about homework may have limitations – some might regard it as an opportunity for “typical adolescent complaining” – it was important to learn firsthand what the students believe.

The paper was co-authored by Mollie Galloway from Lewis and Clark College and Jerusha Conner from Villanova University.

Media Contacts

Denise Pope, Stanford Graduate School of Education: (650) 725-7412, [email protected] Clifton B. Parker, Stanford News Service: (650) 725-0224, [email protected]

Branch and Bound Algorithm

Last updated: March 18, 2024

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1. Overview

In computer science, there is a large number of optimization problems which has a finite but extensive number of feasible solutions. Among these, some problems like finding the shortest path in a graph  or  Minimum Spanning Tree  can be solved in polynomial time .

A significant number of optimization problems like production planning , crew scheduling can’t be solved in polynomial time, and they belong to the NP-Hard class . These problems are the example of NP-Hard combinatorial optimization problem .

Branch and bound (B&B) is an algorithm paradigm widely used for solving such problems.

In this tutorial, we’ll discuss the branch and bound method in detail.

2. Basic Idea

Branch and bound algorithms are used to find the optimal solution for combinatory, discrete, and general mathematical optimization problems. In general, given an NP-Hard problem, a branch and bound algorithm explores the entire search space of possible solutions and provides an optimal solution.

A branch and bound algorithm consist of stepwise enumeration of possible candidate solutions by exploring the entire search space. With all the possible solutions, we first build a rooted decision tree. The root node represents the entire search space:

Here, each child node is a partial solution and part of the solution set. Before constructing the rooted decision tree, we set an upper and lower bound for a given problem based on the optimal solution. At each level, we need to make a decision about which node to include in the solution set. At each level, we explore the node with the best bound. In this way, we can find the best and optimal solution fast.

Now it is crucial to find a good upper and lower bound in such cases. We can find an upper bound by using any local optimization method or by picking any point in the search space. On the other hand, we can obtain a lower bound from convex relaxation  or  duality .

In general, we want to partition the solution set into smaller subsets of solution. Then we construct a rooted decision tree, and finally, we choose the best possible subset (node) at each level to find the best possible solution set.

3. When Branch and Bound Is a Good Choice?

We already mentioned some problems where a branch and bound can be an efficient choice over the other algorithms. In this section, we’ll list all such cases where a branch and bound algorithm is a good choice.

If the given problem is a discrete optimization problem, a branch and bound is a good choice. Discrete optimization is a subsection of optimization where the variables in the problem should belong to the discrete set. Examples of such problems are 0-1 Integer Programming  or  Network Flow problem .

Branch and bound work efficiently on the combinatory optimization problems. Given an objective function for an optimization problem, combinatory optimization is a process to find the maxima or minima for the objective function. The domain of the objective function should be discrete and large. Boolean Satisfiability , Integer Linear Programming are examples of the combinatory optimization problems.

4. Branch and Bound Algorithm Example

In this section, we’ll discuss how the job assignment problem can be solved using a branch and bound algorithm.

4.1. Problem Statement

We can assign any of the available jobs to any worker with the condition that if a job is assigned to a worker, the other workers can’t take that particular job. We should also notice that each job has some cost associated with it, and it differs from one worker to another.

Here the main aim is to complete all the jobs by assigning one job to each worker in such a way that the sum of the cost of all the jobs should be minimized.

4.2. Branch and Bound Algorithm Pseudocode

Now let’s discuss how to solve the job assignment problem using a branch and bound algorithm.

Let’s see the pseudocode first:

In the search space tree, each node contains some information, such as cost, a total number of jobs, as well as a total number of workers.

Now let’s run the algorithm on the sample example we’ve created:

4. Advantages

In a branch and bound algorithm, we don’t explore all the nodes in the tree. That’s why the time complexity of the branch and bound algorithm is less when compared with other algorithms.

If the problem is not large and if we can do the branching in a reasonable amount of time, it finds an optimal solution for a given problem.

The branch and bound algorithm find a minimal path to reach the optimal solution for a given problem. It doesn’t repeat nodes while exploring the tree.

5. Disadvantages

The branch and bound algorithm are time-consuming. Depending on the size of the given problem, the number of nodes in the tree can be too large in the worst case.

Also, parallelization is extremely difficult in the branch and bound algorithm.

6. Conclusion

One of the most popular algorithms used in the optimization problem is the branch and bound algorithm. We’ve discussed it thoroughly in this tutorial.

We’ve explained when a branch and bound algorithm would be the right choice for a user to use. Furthermore, we’ve presented a branch and bound based algorithm for solving the job assignment problem.

Finally, we mentioned some advantages and disadvantages of the branch and bound algorithm.

Hungarian Method

The Hungarian method is a computational optimization technique that addresses the assignment problem in polynomial time and foreshadows following primal-dual alternatives. In 1955, Harold Kuhn used the term “Hungarian method” to honour two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry. Let’s go through the steps of the Hungarian method with the help of a solved example.

Hungarian Method to Solve Assignment Problems

The Hungarian method is a simple way to solve assignment problems. Let us first discuss the assignment problems before moving on to learning the Hungarian method.

What is an Assignment Problem?

A transportation problem is a type of assignment problem. The goal is to allocate an equal amount of resources to the same number of activities. As a result, the overall cost of allocation is minimised or the total profit is maximised.

Because available resources such as workers, machines, and other resources have varying degrees of efficiency for executing different activities, and hence the cost, profit, or loss of conducting such activities varies.

Assume we have ‘n’ jobs to do on ‘m’ machines (i.e., one job to one machine). Our goal is to assign jobs to machines for the least amount of money possible (or maximum profit). Based on the notion that each machine can accomplish each task, but at variable levels of efficiency.

Hungarian Method Steps

Check to see if the number of rows and columns are equal; if they are, the assignment problem is considered to be balanced. Then go to step 1. If it is not balanced, it should be balanced before the algorithm is applied.

Step 1 – In the given cost matrix, subtract the least cost element of each row from all the entries in that row. Make sure that each row has at least one zero.

Step 2 – In the resultant cost matrix produced in step 1, subtract the least cost element in each column from all the components in that column, ensuring that each column contains at least one zero.

Step 3 – Assign zeros

• Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.
• Examine the columns one by one until you find one with precisely one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.

Step 4 – Perform the Optimal Test

• The present assignment is optimal if each row and column has exactly one encircled zero.
• The present assignment is not optimal if at least one row or column is missing an assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and ensure that each column has at least one zero.

Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:

(a) Highlight the rows that aren’t assigned.

(b) Label the columns with zeros in marked rows (if they haven’t already been marked).

(c) Highlight the rows that have assignments in indicated columns (if they haven’t previously been marked).

(d) Continue with (b) and (c) until no further marking is needed.

(f) Simply draw the lines through all rows and columns that are not marked. If the number of these lines equals the order of the matrix, then the solution is optimal; otherwise, it is not.

Step 6 – Find the lowest cost factor that is not covered by the straight lines. Subtract this least-cost component from all the uncovered elements and add it to all the elements that are at the intersection of these straight lines, but leave the rest of the elements alone.

Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment.

Hungarian Method Example

Use the Hungarian method to solve the given assignment problem stated in the table. The entries in the matrix represent each man’s processing time in hours.

\(\begin{array}{l}\begin{bmatrix} & I & II & III & IV & V \\1 & 20 & 15 & 18 & 20 & 25 \\2 & 18 & 20 & 12 & 14 & 15 \\3 & 21 & 23 & 25 & 27 & 25 \\4 & 17 & 18 & 21 & 23 & 20 \\5 & 18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)

With 5 jobs and 5 men, the stated problem is balanced.

\(\begin{array}{l}A = \begin{bmatrix}20 & 15 & 18 & 20 & 25 \\18 & 20 & 12 & 14 & 15 \\21 & 23 & 25 & 27 & 25 \\17 & 18 & 21 & 23 & 20 \\18 & 18 & 16 & 19 & 20 \\\end{bmatrix}\end{array} \)

Subtract the lowest cost element in each row from all of the elements in the given cost matrix’s row. Make sure that each row has at least one zero.

\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 5 & 10 \\6 & 8 & 0 & 2 & 3 \\0 & 2 & 4 & 6 & 4 \\0 & 1 & 4 & 6 & 3 \\2 & 2 & 0 & 3 & 4 \\\end{bmatrix}\end{array} \)

Subtract the least cost element in each Column from all of the components in the given cost matrix’s Column. Check to see if each column has at least one zero.

\(\begin{array}{l}A = \begin{bmatrix}5 & 0 & 3 & 3 & 7 \\6 & 8 & 0 & 0 & 0 \\0 & 2 & 4 & 4 & 1 \\0 & 1 & 4 & 4 & 0 \\2 & 2 & 0 & 1 & 1 \\\end{bmatrix}\end{array} \)

When the zeros are assigned, we get the following:

The present assignment is optimal because each row and column contain precisely one encircled zero.

Where 1 to II, 2 to IV, 3 to I, 4 to V, and 5 to III are the best assignments.

Hence, z = 15 + 14 + 21 + 20 + 16 = 86 hours is the optimal time.

Practice Question on Hungarian Method

Use the Hungarian method to solve the following assignment problem shown in table. The matrix entries represent the time it takes for each job to be processed by each machine in hours.

\(\begin{array}{l}\begin{bmatrix}J/M & I & II & III & IV & V \\1 & 9 & 22 & 58 & 11 & 19 \\2 & 43 & 78 & 72 & 50 & 63 \\3 & 41 & 28 & 91 & 37 & 45 \\4 & 74 & 42 & 27 & 49 & 39 \\5 & 36 & 11 & 57 & 22 & 25 \\\end{bmatrix}\end{array} \)

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Frequently Asked Questions on Hungarian Method

What is hungarian method.

The Hungarian method is defined as a combinatorial optimization technique that solves the assignment problems in polynomial time and foreshadowed subsequent primal–dual approaches.

What are the steps involved in Hungarian method?

The following is a quick overview of the Hungarian method: Step 1: Subtract the row minima. Step 2: Subtract the column minimums. Step 3: Use a limited number of lines to cover all zeros. Step 4: Add some more zeros to the equation.

What is the purpose of the Hungarian method?

When workers are assigned to certain activities based on cost, the Hungarian method is beneficial for identifying minimum costs.

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• v.17(3); Fall 2018

When Group Work Doesn’t Work: Insights from Students

Yunjeong chang.

† Department of Instructional Technology, University of Georgia, Athens, GA 30602

Peggy Brickman

§ Department of Plant Biology, University of Georgia, Athens, GA 30602

Associated Data

Introducing group work in college science classrooms can lead to noticeable gains in student achievement, reasoning ability, and motivation. To realize these gains, students must all contribute. Strategies like assigning roles, group contracts, anonymous peer evaluations, and peer ratings all encourage student participation. In a class using these strategies, we conducted in-depth interviews to uncover student perceptions of group work in general and the utility of these support strategies. Students in both high- and low-performance groups still complained of unequal contributions while praising the social support provided by groups. Students who scored highly on tests were more likely to recognize the benefits of group work, regardless of their groups’ overall performance levels, while lower-scoring students perceived group work as time-consuming “busy work” with little cognitive benefit. Comments from anonymous peer evaluations differed only subtly between high- and low-performance groups. Numerical ratings on these evaluations did correlate with overall group performance. However, students in lower-performance groups assigned harsh ratings to their low-scoring members, while students in higher-performance groups were more generous in their ratings for low-scoring members. We discuss implications of relying on support strategies for promoting productive group work.

INTRODUCTION

Science education policy ( Handelsman et al. , 2004 ; American Association for the Advancement of Science, 2010 ; Couch et al. , 2015 ; National Research Council, 2015 ) advocates for including peer interactions (referred to as “group work” hereafter) in college courses because they provide opportunities for students to practice scientific reasoning, critical-thinking, communication, and problem-solving skills that have been shown to result in greater gains in achievement ( Slavin, 1991 ; Springer et al. , 1999 ; Johnson et al. , 2000 ; Armstrong et al. , 2007 ; Preszler, 2009 ; Freeman et al. , 2014 ; Batz et al. , 2015 ). Group-work pedagogies with demonstrated evidence of effectiveness include collaborative learning ( Phelps and Damon, 1989 ), cooperative learning ( Slavin, 1991 ), team-based learning ( Michaelsen et al. , 2014 ), peer instruction ( Crouch and Mazur, 2001 ), SCALE-UP (Student-Centered Activities for Large Enrollment Undergraduate Programs project) in physics ( Beichner et al. , 2007 ), and POGIL (process-oriented guided-inquiry learning) in chemistry ( Moog and Spencer, 2008 ). All of these group-work pedagogies encourage students to construct their own understanding of scientific concepts through a process of negotiation and consensus building with their peers ( Solomon, 1987 ; Latour and Woolgar, 2013 ). Group work also provides a basis for social comparison, social learning, and social cognition ( Solomon et al. , 2010 ), and students working in small groups may make gains in terms of achievement, motivation, and self-efficacy as a result of this comparison ( Bandura, 2000 ; Hernandez et al. , 2013 ).

Several integrated theoretical frameworks have been espoused within educational psychology to explain the different constructs (motivational, social, and cognitive) that influence the achievement effects of group work ( Sweet and Michaelsen, 2007 ; Slavin, 2014 ). Social interdependence theory ( Johnson and Johnson, 2009 ) is a particularly helpful theoretical framework, because it describes five major variables that mediate the effects of cooperation, including motivational, social, and cognitive aspects. The first variable described in social interdependence theory is positive interdependence: individuals’ perception that they can reach their goals if and only if the other individuals with whom they cooperate also reach their goals and, therefore, promote one another’s efforts to achieve the goals. The second variable is individual accountability: the responsibility to complete one’s own share of the work and also facilitate others’ work. The third variable is promotive interactions: individuals motivating and facilitating the work of others through sharing resources, providing help to one another, challenging reasoning and conclusions provided by group members, and taking varying points of view into account. The fourth variable is the appropriate use of social skills: skills in which individuals get to know and trust one another, communicate, support one another, and resolve conflicts that arise. Finally, group work should provide a mechanism for group processing and reflection: encouraging students to set collective goals, assess positive and negative group interactions, and provide feedback to group members. Instructors play a major role in promoting the variables required for these aspects of social interdependence during group work, and students express greater satisfaction with group work when their instructors include support strategies to assess and foster group collaboration ( Chapman and Van Auken, 2001 ).

Recommended support strategies to foster effective collaboration include assigning roles, group contracts, peer evaluations, and peer ratings that measure differences in contributions.

Role Assignment

Assigning tasks or roles for students to assume while completing tasks is recommended as a way to promote individual accountability and ensure that instructors can monitor contributions ( Chapman and Van Auken, 2001 ; Davies, 2009 ). Group work pedagogies like POGIL ( Moog and Spencer, 2008 ) and SCALE-UP ( Beichner et al. , 2007 ) recommend assigning specific roles to promote critical discussion and to prevent students from either dominating discussions or avoiding conflict by accepting the quickest answer during problem-solving tasks ( Heller and Hollabaugh, 1992 ). Role assignment has been shown to promote greater learning gains ( Bailey et al. , 2012 ) and student satisfaction ( Brown, 2010 ). The caveat remains that supervision is required so that students cycle through the cognitive acts of listening and recalling that are necessary for greater exchange of ideas and thus learning ( O’Donnell, 2006 ).

Group Contracts

Groups that discuss expectations before group work begins and draft group contracts that spell out consequences for failure to meet expectations foster appropriate use of social skills ( Chapman and Van Auken, 2001 ; Oakley et al. , 2004 ). Feelings of interdependence, cohesion, psychological safety, and confidence all strengthen the belief that investment in group activities will pay off and thus encourage students to engage in cognitive processes key to learning ( Van den Bossche et al. , 2006 ).

Peer Evaluations

Anonymous peer evaluations in which students reflect on their own and others’ contributions and group dynamics and have the ability to inform the instructor of problems within the group help promote reflection, group processing, and individual accountability ( Harkins and Jackson, 1985 ; Strong and Anderson, 1990 ; Brooks and Ammons, 2003 ; Oakley et al. , 2004 ; Aggarwal and O’Brien, 2008 ). Evaluations also help reduce social loafing, a situation in which students in a group commit less effort to a group project, because they believe their lack of effort will not be identified, and free riding, a situation in which students knowingly allow others to complete their work for them ( Aggarwal and O’Brien, 2008 ). In Strong and Anderson’s (1990) study of student opinions about group work, students indicated that they believed that peer evaluations do reduce free riding, but they rated other factors—including group cohesiveness, small team size, the option to “divorce” a team member, or the option to leave a team—as having a stronger effect on reducing free riding. Students also rated the divorcing option as more effective at motivating team members than end-of-semester evaluations, which have been shown to be negatively associated with good team experiences ( Bacon et al. , 1999 ). This suggests that peer evaluations may encourage students to tolerate bad behavior, knowing they can exact retribution at the end of the semester. In addition, researchers have found that students may be unlikely to provide honest evaluations of their peers and are unlikely to directly confront free riders ( Strong and Anderson, 1990 ).

Peer Ratings

There are challenges to determining the effort and achievement level of individual students during group tasks. On typical group tasks, all group members work together without being evaluated individually on the final product by the instructor, and all group members receive the same grade for the final product. If the level of contribution differs among group members, then the single group grade may not accurately reflect individual effort or performance. One solution is to collect information on the contributions of each group member using quantitative ratings and to adjust the final scores to reflect lack of effort ( Latane et al. , 1979 ; Bartlett, 1995 ). Students should be aware of the contributions of each member, and if they can be trusted to provide accurate ratings, the ratings could be used to derive a numerical weighting factor to adjust group grades accordingly. Researchers have recommended administering both holistic rubrics in which students are given points that they must divide between the group members to gauge contributions ( Lejk and Wyvill, 2001 ; Johnston and Miles, 2004 ) and analytical rubrics with multiple indicators such as attendance, cooperativeness, and academic contributions to gauge contributions ( Kaufman et al. , 2000 ; Stefanou et al. , 2001 ; Kilic and Cakan, 2006 ). Holistic rubrics have been found to be more effective at identifying very good and very weak contributors to the group, whereas analytic assessments are able to identify small differences in group contributions and may be more effective for providing formative feedback ( Falchikov and Goldfinch, 2000 ; Lejk and Wyvill, 2001 ). Holistic rubrics, however, need to be adjusted by calculating an individual’s contribution to maximize the correlation between actual group scores and true levels of a student’s contribution ( Zhang and Ohland, 2009 ).

Faculty members have reported concern about providing sufficient support to ensure that students are interacting productively during group work in large-enrollment classes ( Pundak and Rozner, 2008 ; Freeman and Greenacre, 2011 ; Barkley et al. , 2014 ). And many faculty attest to difficulties they have encountered implementing group work in their classes and have reported frustration with dysfunctional groups that require a great deal of supervision to ensure equitable student participation and reward productive social interactions ( Kreijns et al. , 2003 ; Davies, 2009 ; Svinicki and Schallert, 2016 ).

In an attempt to improve student learning through group work, we implemented many of these recommended strategies for supporting group dynamics in a very large enrollment introductory biology course that was often linked to poor student learning, attitudes, and retention ( Seymour and Hewitt, 1997 ; Barr et al. , 2008 ; Chang et al. , 2011 ; National Academies of Sciences, Engineering, and Medicine, 2016 ). In a preliminary study, we were able to demonstrate that group activities benefited students at diverse performance levels, but the students also reported persistent social loafing ( Chang and Hannafin, 2015 ).

Managing group dynamics for successful implementation of group work is time intensive for instructors. We hypothesized that exploring students’ perceptions of group work might provide insights into which time-consuming support strategies (e.g., role assignment, group contracts, peer evaluations at the midpoint and endpoint of the semester, and summative peer ratings) students were using effectively. We also hoped that the perceptions of students in high-performance groups could provide insight into critical features to be nurtured and enhanced in all groups. Because this was a primarily observational study aimed at characterizing student perceptions of group work and use of support strategies designed to monitor and improve group interactions in a large-enrollment college classroom, we employed a concurrent mixed-methods design ( Creswell, 2009 ). We characterized student perceptions of group work using qualitative interviews and written comments submitted on peer-evaluation surveys. We also compared the interviews, comments, and numeric peer-evaluation ratings given by and from students at different achievement levels, which we determined using quantitative data from course assessments ( Teddlie and Tashakkori, 2003 ). Table 1 outlines our major research questions and the data sources used to address each question.

Overview of research questions and data sources

Instructional Setting

We examined learning performance and group work for 246 students enrolled in an introductory biology course for non–­science majors at a large public university in the southeastern United States. The course included two 75-minute classes per week and comprised five different content units. Class time was devoted to providing core content through instructor minilectures and daily individual and group activities that required students to apply the content to specific situations ( Brickman et al. , 2012 ). Individual assignments included clicker questions, preclass written assignments to prepare for group work, practice tests, and a final unit test composed of multiple-choice questions. Group work included completing in-class worksheets to structure or organize content knowledge (e.g., drawing a diagram, finding relevant resources from websites) as well as outside-class group projects that required students to apply their knowledge ( Brickman et al. , 2012 ). In addition, after completing unit tests individually, group members collaboratively answered the same test items again to earn a group test score. Group activities were designed to build social interaction and interdependence through deadlines that required individual work be submitted before beginning group work, initial activities that built rapport, and grading that emphasized attaining common goals ( Deutsch, 1949 ). All group members received the same score for work from their group. All activities and test scores were weighted to compute each student’s final course grade: individual test scores: 36%; clicker questioning: 12%; individual assignments to prepare for group work: 12%; group assignments and projects: 28%; and group tests: 12%.

Group Formation and Support Strategies

During the second week of the semester, the instructor asked students to organize themselves into groups of four or five members, resulting in 65 groups that completed group assignments and tests together throughout the rest of the semester. Owing to a 5% withdrawal rate, no five-member groups were present at the midpoint. The instructor did not dictate group composition because of a lack of clear consensus from the literature on the most effective characteristics to use when forming groups and because autonomous group composition minimized logistical and practical problems in course administration (i.e., tackling individual group requests) and students’ resistance (i.e., request for changing groups or sitting near the front of the auditorium). Individuals assigned themselves to different roles within their groups for daily activities: manager/spokesperson, researcher, recorder, and whiteboard writer. The manager/spokesperson supported group processes during discussions (i.e., time management, soliciting ideas from all, speaking for the group); researchers gathered additional ideas for the group from class notes and the Internet; recorders summarized discussions and submitted group worksheets; and whiteboard writers created diagrams and figures on worksheets. At the beginning and during the semester, the instructor gave mini-lessons to remind groups to rotate roles in an attempt to balance participation by each group member ( Johnson et al. , 1998 ). The instructor also created a section in the group worksheets where the assigned roles of each student in the group could be recorded.

Throughout the semester, groups were given opportunities to promote productive interactions and mediate conflict. At the beginning of the semester, groups created a contract in which they established expectations, set ground rules (e.g., penalties for failure to participate), and established communication channels. At the midpoint of the semester, groups were encouraged to revise and resubmit their contracts if necessary and to complete an anonymous online peer-evaluation survey to provide midcourse feedback to one another. Students also completed an online, end-of-course peer-evaluation survey to assess each group member’s contribution. These surveys included eight numeric questions that asked students to evaluate individual group members’ preparation, participation, collaboration, attitude, and performance during group work. For example, “Did this person participate in group discussions during class? This could include sitting with the group during class, attending regularly, etc.” Students ranked each team member on a four-point scale for each question (1 = unacceptable performance, I would fire this person; 2 = improvement needed; 3 = good, met or exceeded all expectations; 4 = outstanding, a rare individual). Text for each question in the survey can be viewed in Appendix A in the Supplemental Material. Each group member was finally asked to respond to one open-ended question: “Please provide written comments about each of your team members so they can learn how you viewed their contributions to the team. After all evaluations are submitted they will be able to read these comments but not tell who they came from. You and they can use this feedback to improve your future performance.” Students were also asked to rate the quality of each group mate’s contributions to the group on a scale of 0–100, similar to earning a grade in a class. Students were told that their group scores would be adjusted based on the average rating that they received. The Opensource online platform that we used (Simple Team Experience Assessment Measure—STEAM) used the expected-contribution method ( Lejk et al. , 1996 ), which is based on adjusting the group grade by adding a deviance from the expected contribution. If you have a group of four members, each member is expected to contribute 25% of the work. If a group member’s average score indicates that he or she completed only 20% of the work, then the assigned group score is adjusted by subtracting 5% of the group score. Group members were able to view the scores and comments from their peers after all group members had submitted their responses.

Quantitative Data Collection and Analysis

Three different measures were used to compare individual students and groups. First, we calculated group performance levels based on the rank-ordered group assignment scores and averaged group scores on a series of group tests. We were interested in how groups performed relative to one another, so we rank ordered assignments within each unique unit, because topics differed and the variance of scores differed between units ( Kruskal and Wallis, 1952 ). To have an adequate number of groups for statistical analysis, we ranked groups based on the median group score. Groups ranked above the median score were classified as high-performance groups ( n = 32), while groups that scored lower than the median were categorized as lower-performance groups ( n = 33). Categorizing groups into high-performance groups and low-performance groups allowed us to select balanced numbers of interviewees and compare the perceptions of students within those groups (more details about the distribution of the interviewers are described in the Qualitative Data Collection and Analysis section).

Second, we used final course grades to divide students into higher-, mid-, and lower-scorer categories. Students ranked in the highest 33% using ranked final course grades were categorized as higher scorers ( n = 82), those in the middle 33% as midscorers ( n = 79), and those in the lowest 33% as lower scorers ( n = 84). This allowed us to quickly identify students to interview to address question 1, which compared perceptions of higher- and lower-scoring students within groups, and question 2, which addressed the use of group-based support strategies before the end of the course. A breakdown of the distribution of students at high-, mid-, and low-scoring levels is outlined in Figure 1 . Eighty-seven percent of the groups contained a mixture of students of different scoring levels (heterogeneous), rather than containing students of similar scoring levels (homogeneous). All of the high-performance groups included at least one higher-scoring student, while only 10 of the 33 low-performance groups included at least one or two more higher-scoring students in their groups.

Most student groups, either high-performance (A) or low-performance (B), were composed of a mixture of high-, mid-, and low-scoring members and classified as heterogeneous (top row), 57/65 total groups. A much smaller number of groups (8/57) were homogeneous (bottom row) and were composed of either all high- (three groups), all mid- (one group), or all low-scoring students (four groups).

To test our research question 4, whether numeric peer-evaluation ratings served as a quantitative measure of students’ perceptions of their group members, we used the average ratings that students received to compare average ratings between high- and low-performance groups as well as high- and low-scoring students within those groups. To investigate the effects of group performance, we used a random effects model that can control for the variance associated with random factors that may occur during the interaction between students and groups ( Judd et al. , 2012 ). By using random effects for students in different groups, we controlled for the influence of different student interactions associated with group variables. In our model, we used the score gap between group and individual scores as a dependent variable and group performance levels as the fixed effects. To determine whether a relationship existed between peer-evaluation scores and individual test scores, we used a paired t test. A student’s peer-evaluation rating score was used as an independent variable, and individual test scores as a dependent variable.

Qualitative Data Collection and Analysis

We conducted in-depth interviews ( Esterberg, 2002 ) to explore the range of students’ perceptions, attitudes, and participation in group work in order to gain better insight into the briefer comments made on the peer evaluations. Appendix B in the Supplemental Material contains our interview protocol and question items. We recruited interviewees at the beginning of the last unit (unit 5). The first author (Y.C.) verbally recruited interviewees by announcing the interview in front of the class and sending out an email. The verbal and email announcements included information of the purposes and the foci of the study and the interview. From among 27 volunteers, the authors purposefully selected 15 interviewees to ensure that we had seven higher-scoring students and eight lower-scoring students based on their test scores. Among the seven higher scorers whom we interviewed, five were from high-performance groups and two were from low-performance groups. Among the eight lower scorers whom we interviewed, three were from high-performance groups and five were from low-performance groups. The number of high and low scorers selected for interviews was related to the proportion of these students in the respective groups (see Figure 2 for the group score distribution of the interviewers and Figure 1 for breakdown of student distribution in groups). Thirteen groups were represented in our student interviewees; three were homogeneous groups (composed of all lower scorers), while 10 were heterogeneous groups (with a mix of high, mid-, and low scorers). Interviewee profiles with pseudonyms to maintain students’ confidentiality are provided in Table 2 . Emerged themes and quotes are summarized in Table 3 .

Performance levels of high- and low-performance groups. To select a balanced numbers of high- and low-performance groups, we divided groups into higher (> 175) and low-performance groups (< 175) using the median (175). Equal numbers of interviewees were selected (dark blue) from both types of groups.

Interviewee profiles

H = Higher scorer, L = Lower scorer, HG = Higher-performing group, LG = Lower-performing group.

Excerpts per theme from in-depth interviews

Interview data were recorded, transcribed verbatim, and coded through multiple transcript readings by both authors. Specifically, we employed thematic analysis of the student interviews using ATLAS.ti v. 7.1 software. One researcher created a codebook related to how students perceived the group work and how it influenced their learning. Then the researchers worked together to refine the codebook and identify and characterize themes represented by the codes ( Braun and Clarke, 2006 ).

We were interested in determining how statements made during interviews might be represented in comments on student evaluations of their peers, and we also believed these comments could provide insight into how students gave feedback to their group members to answer research question 3. Triangulating data from various sources provided a mechanism to verify and support the breadth and overall representation of our understanding of what students meant in their comments ( Morse et al. , 2002 ). Students from 65 groups provided a total of 1341 entries on the midsemester and end-of-semester peer evaluations. We excluded 120 blank entries without text from further analysis. Of 26 students who failed to leave comments, seven were high-scoring students, nine were lower-scoring students, and 10 were midscorers. Most of the students (20) were from high-performance groups, and only three were from low-performance groups. We analyzed the remaining 1221 comments to provide insight into what students told their peers to help them improve group dynamics.

Because these comments could help determine whether or not students were taking advantage of this as a vehicle to express positive as well as negative perceptions, we began with categorizing a priori codes into three categories: positive, neutral, and negative indicators/experiences. We then added more a priori codes elicited from theoretical models of collaborative or cooperative learning that focused on explaining student motivation and engagement. For example, social interdependence theory ( Johnson and Johnson, 2009 ) was considered, because the analysis aimed to examine how student perceptions of group work could derive from both interactions between individual students and group-level attributes that support effective group work. A priori codes that reflected students’ perceptions of group work in peer-evaluation comments and interviews are represented in Appendix C in the Supplemental Material. We initiated the coding of peer-evaluation comments by using these codes and added emerging codes as necessary. The first author (Y.C.) initiated the analysis and then the second author (P.B.) reviewed the analysis. Initially, 21 codes, including 11 codes for positive perspectives and 10 codes for negative perspectives on collaborative learning, were used to analyze peer-evaluation comments. After the second author (P.B.) reviewed the codes, the codebook was modified and clarified through discussion. Two codes were merged in both the positive and negative perspectives, and three more codes were added. Finally, both authors reviewed the coding together, discussing and merging codes through consensus, and adding emergent codes as needed. Interrater reliability ( Cohen, 1968 ) between the two authors was achieved at 0.85, considered as very good strength of agreement ( Altman, 1991 ). Among all codes, 18 codes (10 positive, six negative, and two neutral) finally emerged from the analysis of peer-evaluation comments (Appendix C in the Supplemental Material).

Students in Both High- and Low-Performance Groups Valued the Social and Cognitive Support Provided by Groups.

Seven interviewees (four from high-performance groups and three from low-performance groups) mentioned the social and cognitive benefits of group work. Among four students in higher-performance groups, two were higher scorers and the other two were lower scorers. Ruth, like other students (even those in lower-performance groups), exhibited positive perceptions about the benefits of group work, saying, “Our group got along a lot better with just interacting with each other. I’ve definitely learned better in a group because I had the opportunity to kind of answer some of their questions which helps me understand it more.” Amy, a lower scorer in a higher-performance group, also described group work as “a nice little support system” that helped her to feel like she was “not alone in the class.” Ethan, another lower scorer in a higher-performance group, mentioned that having group members helped him to understand course concepts, as they “elaborated on the concept and went into a little deeper context with me and tried to explain in it my terms in a way that the teacher couldn’t because there is just so many people.” Higher scorers in higher-performance groups also acknowledged benefits of group work, as it allowed them to “have friends in the class who can discuss things with typical lectures” (Beth) and “study together to prepare for the exam” (Chen). (See Table 3 for additional interview excerpts for each theme.)

Students Assigned Roles Depending on Circumstances and Ignored Group Contracts.

We were interested in determining students’ perceptions of the support strategies (e.g., role assignment and creating and revising group contracts) used to increase individual accountability and appropriate use of social skills. In general, students did not perceive the support strategies as beneficial. Regarding assigning or rotating roles, roles were naturally assigned “with respect and making it fair” (Amy) and rotated. One interviewee mentioned, “ We always rotated who would actually compile all of the finished work and put it into a document and submit it to the class” (Jenn). None of the interviewees used role assignments consistently, citing a variety of reasons. Some groups felt they were unnecessary. “Our group didn’t really do the role assignments, it was just kind of ‘You get it this time, I’ll get it next time’” (Jenn). Others reported grappling with disorganized or absent students. “If you’re not communicating as well … you don’t get to do the part that you want to do” (Emma). “Even though we assign each other the role, not everybody follows it in a way and they usually forget about it, it’s not something they are used to having to do” (Min). Finally, some students expressed anxiety about assuming certain roles. “You were supposed to assign someone each of those jobs but I found it kind of limiting sometimes because … I got put as manager except I don’t like raising my hand and talking in front of people and this other guy in my group did and he knew a lot of the answers” (Beth). Another interviewee commented that with such a large class they “never really had to use that role because we weren’t really asked questions like in class about stuff” (Zoe).

In terms of the group contract, students described it as “another assignment that we had to do so we could leave” (Karen). Although some groups set punishment rules, such as “treat a coffee for all in the group if you missed a class without communication with group members” (Chen), group members reported that they rarely abided by the rules from their contracts. In fact, most of the groups (59 out of 65 groups) simply resubmitted their original contracts without revision at the midpoint of the semester, with only seven groups revising their contracts to provide better feedback to one another. One group revised their contract following discussion about lack of compliance with the initial contract. However, the group members still did not comply: “They all said, ‘Sure’ and then they don’t do it” (Min). We also found peer pressure was significant when it came to opting not to follow through on punishments or criticize group member’s behaviors. “I’d never tell these guys, because I didn’t want them to say something about me” (Ethan).

We did find that students perceived the group contract as useful when it came to setting up communication methods. For example, “we all got our phone numbers and everything” (Min) and “when missing a class, text to all” (Beth). However, in well-functioning groups, the group contract was not needed. Six interviewees, five from high-performance groups and one from a low-performance group, mentioned that their groups did not need to use the group contract, because they encountered few challenges. For example, members from high-performance groups agreed that “we know we would follow through when we had stuff and we never really had to use the group contract” (Brian). As one of the interviewees mentioned, “I think if there had been problems in our group, the contract would’ve been a bigger role” (Nora).

Students in Both High- and Low-Performance Groups Reported Social Loafing.

Regardless of group performance, most of the interviewees reported social loafing issues during group work that resulted in them having to assume responsibility for submitting work for others. Min, a higher-scoring student in a high-performance group, stated, “[My group members] just sent me all copy and paste. They didn’t do any research and follow any APA format. But they simply sent me the link of the resources and said, ‘here is the link.’ So I have to go back to the website that they’d found and had to summarize them.” Lower-scorer Ruth, who was in a low-performance group, commented that “it’s more difficult to get all the members to contribute equally especially if someone is … doing all the work and then other people feel like they can relax. You’re doing all the work and I can just sit back and get a hundred sort of like the prisoner effect.”

Student remarks differed when they described the same situation, one in which they had to take over and perform work to make up for noncontributing students. Min, a high-scoring student in a high-performance group, criticized other group members’ inadequate participation, even though her group achieved higher scores on group work. “Normally they don’t do the pre-quiz because it’s not for a grade. But like I do it just for my good, but they don’t. It feels like they don’t care and know I’ll do it anyway” (Min). While Ruth, a lower scorer in a lower-performance group described her experience as “getting sucked into all of the group work.” Hard-working students reported experiencing the “sucker effect,” in which they began to pull back on the amount of work they contributed to force noncontributing members to work: “We were like ‘We’ll say we don’t understand this part so she can do it’ and then she like didn’t know and just held it until the end of the class and was like, ‘I don’t get it’… and so my friend got kind of bothered and she snatched it from her and did it” (Monica).

Perceptions of the Value of Group Activities Differed between High- and Low-Scoring Students.

We found that three of the seven higher-scoring students interviewed, two from high-performance groups and one from a low-performance group, remarked that they found group activities were critical for their learning and that they provided an opportunity to apply what they learned from lecture to their real life. For example, Beth, who was a higher scorer, reported that group work was “more real-life situations which I found interesting because it was more relatable and like scientific theories that would apply to you … based on how it would affect something in real life.” Six of the seven lower scorers interviewed, in both high- and low-performance groups, tended to perceive group activities as time-consuming. For example, Jenn asked, “Why do that and spend an hour going through all of that stuff when I could just finish it in ten minutes?” She felt, “It was like a stumbling around so that didn’t really help with the learning.” Zoe, another lower scorer, echoed this sentiment, describing group work as “something [that] doesn’t seem very important and sound[s] silly,” and said, “I don’t see any relationship with my real life.”

High- and Low-Performance Groups Left Very Similar Comments on Peer Evaluations.

We compared patterns observed between the overall frequency of peer-evaluation comments (positive or negative, as well as those expressing specific ideas) between students in high- and low-performance groups. We calculated the frequency of the code by total number of submitted comments. We found that there was no statistically significant association between group performance levels and the trends on the positive or negative comments; x 2 (34) = 30.78, p = 0.626. In addition, regardless of group performance levels, three categories of ideas were commonly expressed (appearing in more than 10% of all comments) in both groups in both the first and second peer-evaluation surveys ( Figure 3 ). A fourth and fifth category did differ in its frequency between groups of different performance levels, which we will describe later. No distinctive patterns were found in the comments categorized as no responses or not applicable.

Frequency comparison for the top four ideas provided as anonymous comments on peer evaluations. Student groups were categorized as higher-performing ( n = 32) and lower-performing ( n = 33) based on the rank-ordered group assignment scores and averaged group test scores. A total of 1221 comments on peer evaluations were coded using 21 a priori categories. Each number (%) in the figure is calculated as the frequency of the code/total numbers of submitted comments.

The most common idea mentioned (>55% of all codes present) in peer evaluations involved individual accountability. Individual accountability involves students completing their own work (personal accountability) and facilitating other students completing their work (accountability to the group; Johnson et al. , 2014 ). Students mentioned aspects that reflected positively on their peers: “always doing her part,” “completing assigned works in a timely and efficient manner,” and “pulls his weight and helps with all group work.” See Appendix C in the Supplemental Material for additional codes, summaries of ideas represented in those codes, and example quotes. We found that comments about individual accountability were equally predominant in high- and low-performance groups and at the midpoint and endpoint of the semester (χ 2 = 4, p = 0.261).

The second most prevalent idea that emerged in peer-evaluation comments concerned the cognitive learning supports provided by peers (22–31% of comments contained this idea). Students seemed to appreciate aspects of the promotive interactions mentioned by Johnson et al. (2014) that enhanced social constructivism, such as engaging in a dialogue with their peers to ask and answer questions, share reasoning, and build upon each other’s understanding until they reach mutual agreement ( Phelps and Damon, 1989 ; Slavin, 1991 ). Student evaluation comments mentioned students “explaining difficult concepts” or a peer “helps us understand” or “takes the time to learn the material so she can teach others.” The degree to which students mentioned learning supports appeared to differ between higher- and low-performance groups when comparing the midpoint to endpoint survey, but these differences were not significant (χ 2 = 3, p = 0.223).

The third most frequent idea that emerged in the peer-evaluation comments concerned students providing procedural support. This idea was present in more than 17% of all comments. However, there was no statistical difference between high- and low-performance groups mentioning procedural support (χ 2 = 4, p = 0.261). Procedural support involved helping to complete steps to finalize a task that were not connected to cognitive activities but aided in making decisions and completing assignments in a timely manner. Examples of comments that were coded for procedural support mentioned their peers helping to “keep everyone focused and turn in our papers at the end of class” or being “very organized and keeps the group on track, schedules group meetings.”

The fourth most frequent idea that was mentioned differed depending on the time of the semester the evaluation was given and the performance level of the group. At the midpoint of the semester, the fourth most frequent idea mentioned in high-performance groups involved social/interpersonal communication skills (10.3% of comments). This idea included the ability to get along with group members and communicate effectively, for example, “displays a positive attitude and is very encouraging,” “easy to talk to and easy to get along,” and “very flexible and open to everyone’s contributions and a fun person to have in the group.” Social perceptiveness has emerged as a major factor in predicting group performance ( Woolley et al. , 2015 ). Interestingly, social/interpersonal communication was not a frequent idea mentioned in low-performance groups until the end of the semester. In those groups, the fourth most frequent type of comment left at the midpoint was to not leave any comment at all (13% of comments left in low-performance groups were left intentionally blank). By the end of the semester, social/interpersonal skills rose in its frequency to become the fourth most frequent code mentioned in evaluations from students in low-performance groups (10.3% in the end-of-semester peer evaluations).

Students in high- and low-performance groups also differed in the degree to which they mentioned that their peers provided positive interdependence, with promoting the group’s success by working together seen as a fifth frequent idea. Calculating the percentage of frequency of the positive interdependence code by the total number of submitted comments, students in high-performance groups mentioned positive interdependence in 12% of all comments on the final peer evaluation, up from only 6% on the midsemester evaluation. Lower-performance groups mentioned positive interdependence on the midsemester evaluations (7% of comments); however, this level dropped to less than 2% of the final evaluation.

When comparing comments between heterogeneous groups of either higher- or lower-performance levels, we found that students in heterogeneous groups leave more comments with a negative perspective (31.25% on midpoint evaluation and 28.57% on final evaluation) compared with homogeneous groups (nothing on mid and 18.18% on final), regardless of the timing of the evaluation.

Influence of Group Work on Individual Learning Achievement within Groups.

We compared the mean score differences between group and individual test scores in units 1 and 4 to understand the influence of group work on individual learning. The random intercepts model results show that group performance levels influenced score differences between individual and group tests from unit 1 and unit 4. As shown in Table 4 , both high- and low-performance groups actually decreased the mean score differences between group and individual test scores from unit 1, F (1, 122) = 19.83, p < 0.005, to unit 4, F (1, 100.72) = 20.29, p < 0.005. In unit 1, the main effect of group performance levels on mean score differences between individual and group test scores are significant ( p < 0.005), estimating that the mean score differences of high-performance groups are 12.92 (SE = 2.68) higher than those of low-performance groups. In unit 4, the estimated mean score differences of high-performance groups are 11.85 (SE = 2.9) higher than those of low-performance groups.

Estimates of fixed effects of score gap between group and individual scores in units 1 and 4

Within groups, high-performance group score differences decreased significantly from unit 1 (M = −12.04, SE = 1.83) to unit 4 (M = −6.78, SE = 1.70), p < 0.005. Low-performance groups also decreased from unit 1 (M = 24.96, SE = 2.26) to unit 4 (M = 18.63, SE = 2.10). However, high-performance groups demonstrated a greater reduction (43.7%) in the learning gap between group members compared with low-performance groups (25.3%).

Peer-Evaluation Ratings: Indicative of Performance but Possibly Biased

We found that, when students were asked to provide quantitative ratings of their peers, the ratings differed based on their groups’ level of performance, F (1, 164) = 12.97, p < 0.001. In groups ranked as higher performing, students gave higher mean peer ratings to group members (M = 102.63, SD = 5.83) than students in low-performance groups (M = 92.32, SD = 19.15). As shown in Figure 4 , in terms of individual differences between group members, t tests revealed statistically significant differences, t (166) = −20.21, p < 0.001, r = 0.32. Students who earned lower test scores received higher mean peer-evaluation ratings when they were in high-performance groups (M = 101.21, SD = 1.99) rather than in low-performance groups (M = 86.96, SD = 25.63). Higher scorers received relatively similar peer-evaluation ratings from both high-performance groups (M = 101.78, SD = 5.96) and low-performance groups (M = 97.35, SD = 7.04). This resulted in greater mean score differences between higher and lower scorers in low-performance groups (mean score differences = 14.25) than between higher and lower scorers in high-performance groups (mean score differences = 5.53). In other words, students in low-performance groups were holding lower-scoring students to a greater degree of accountability on peer ratings than lower scorers in high-performance groups.

Peer-evaluation ratings and group performance. The average numerical ratings (out of 100) that students wrote on peer evaluations differed for high- and low-performance groups. The average rating for all students in high-performance groups (M = 102.63, SD = 5.83) was higher than students in low-performance groups (M = 92.32, SD = 19.15). Lower-scoring students received higher mean peer-evaluation ratings when they were in high-performance groups (M = 101.21, SD = 1.99) than in low-performance groups (M = 86.96, SD = 25.63). Higher scorers received relatively similar peer-evaluation ratings from both high-performance groups (M = 101.78, SD = 5.96) and low-performance groups (M = 97.35, SD = 7.04), t (166) = −20.21, p < 0.001, r = 0.32).

To understand group work in a real-world classroom setting, we conducted our study in a classroom that allowed students to self-assemble into groups. We conducted a mixed-methods analysis to investigate how students’ personal scoring in the course and their groups’ levels of performance on group tasks affected their perception of group activities. Much of a student’s individual performance was calculated after group work occurred. Group and individual performance, though, may not be completely independent of each other, because students who score highly on individual tests could have an increased effect on their groups’ scores on assignments and tests, and groups that worked well together could have had a positive effect on individual grades. Collection of an initial independent measure of a student’s abilities (e.g., grade point average [GPA] or pretest scores) or analysis of discourse practices during group work would be needed to further elucidate the relationship between individual ability on group performance. We also interviewed students on their use of strategies such as role assignment and group contracts, and we compared the comments and ratings from anonymous peer evaluations to determine what differences could be observed between high- and low-performance groups. We found that, regardless of group performance levels, salient elements that might affect students’ perceptions of the group work emerged. We did find differences in perceptions of group work, some comments on peer evaluations, and ratings between individuals. Our hope was to uncover factors that could explain why groups might not be working effectively and to provide faculty with a better mechanism to identify and solve group problems. However, we did not conduct empirical tests for these observations, so we will use our results to suggest future research to expand on our findings.

Without Supervision, Students Fail to Use Role Assignment and Group Contracts to Their Fullest

In our study, students were asked to self-assign to specific roles and rotate the roles within the group activities in a very large classroom without supervision (either from undergraduate peers or graduate students). It has been reported that structured discussion with role assignment enhances students’ engagement in interactive information sharing ( Mesmer-Magnus and DeChurch, 2009 ), knowledge construction, knowledge transfer ( Kane et al. , 2002 ), and equitable participation ( Savadori et al. , 2001 ). In the in-depth interviews, however, students did not report engaging in what Chan (2001) described as detailed “problem-centered” discourse that involved recognition of the problem, formulation of questions, and construction of explanations. Instead, they reported that they felt that they did not need official roles. Some students struggled assigning roles to absent or inactive members, and other students commented that certain roles were never used because of the number of groups and the difficulty hearing ideas from all groups during class discussion. Instead, they reported using roles to subdivide labor, merging individual contributions to a final document without critically evaluating members’ submissions, failing to communicate, and completing a task at the very last minute so that it could not be reviewed by all group members (see comments in Students in Both High- and Low-Performance Groups Reported Social Loafing ). All these obstructions to the collaboration process erode the sense of trust needed for the social interactions required for social interdependence. Students in our groups were only provided with brief descriptions of what group roles entailed and were not explicitly trained to use roles effectively. Several research groups have attempted to test the effect of providing scripts to enhance students’ use of cognitive prompts during group work ( O’Donnell, 1996 ; Gillies, 2003 ; Brewer and Klein, 2006 ). It would be interesting to determine whether these scripts can be useful in the very large lecture settings we encountered.

Group contracts provide a mechanism to initiate discussion of expectations and reservations, to strengthen social skills, and to build interpersonal relationships critical to effective group work ( Oakley et al. , 2004 ; Davies, 2009 ; Shimazoe and Aldrich, 2010 ). It is clear from our interviews, however, that students did not view the completion of a group contract as a significant vehicle to strengthening interdependence or other key social skills. They felt the assignment was cursory, just something to be completed without depth of thought. Student teams become progressively more collaborative and productive over time ( Hong et al. , 2014 ), with successful teams demonstrating constant levels of socioemotional and procedural support ( Kwon et al. , 2014 ). So, rather than assigning a simple contract at the beginning of the course, instructors may need to provide more opportunities for deeper interactions that build trust and a sense of belonging ( Kreijns et al. , 2003 ), to be conscious of the fact that trust can be easily eroded when members lower their individual participation and commitment toward quality work ( Kreijns et al. , 2003 ), and to provide greater opportunities for identifying and resolving conflict ( Brooks and Ammons, 2003 ). We found that students were not relying on group contracts to set punishments for lack of participation and that other mechanisms need to be employed to help groups resolve conflicts (see Peer Ratings May Be Biased against Low-Scoring Students in Low-Performance Groups ). An alternative assignment with more utility might be to engage in an initial team-building activity in which students share contact information to begin to build socioemotional interactions like getting to know one another by sharing hobbies, interests, and experiences ( Oakley et al. , 2004 ). Researchers could test the efficacy of such an assignment using measures like the Team Interdependence ( Van der Vegt et al. , 2001 ), Team Cohesiveness ( Carless and De Paola, 2000 ), or Psychological Safety ( Edmondson, 1999 ) surveys.

Peer-Evaluation Comments Are Not Useful for Identifying Group Dysfunction

Anonymous peer evaluations have been suggested as a method for identifying inequity and other problematic group issues ( Wenzel, 2007 ; Aggarwal and O’Brien, 2008 ). Peer evaluations have been shown to reduce the incidence of free riding and to improve student attitudes toward groups and group projects if they are done early and frequently ( Feichtner and Davis, 1984 ; Brooks and Ammons, 2003 ). Using performance on group assessments to identify high- and low-performance groups, we asked whether performance could be differentiated using responses to students’ peer-evaluation comments and numerical ratings. We also used students’ responses to in-depth interviews to provide context and explanations for our observations. Several assumptions may limit our findings: We must assume that students were willing to communicate honestly about problems that were occurring during group work. We also must rely on students’ ability to recognize what constitutes effective group functioning. Also, we assume that, because a group is performing well on assignments, they are functioning better than a group that is not earning high scores on group assignments and tests. It is possible that high-performance groups do better on assignments because one high-scoring student has taken on more of the responsibility. However, it is clear from our analysis of how the score gap between individual and group tests is minimized in high-performance groups ( Table 4 ) that learning as measured by the level of scoring on individual tests improves for low-scoring members of these groups. This study does not clarify the reason for this improvement, but high-performance groups had a higher percentage of high-scoring students, so access to these students could be one important variable. With this in mind, we were surprised that comments on anonymous peer evaluations do not adequately distinguish between high- and low-performance groups, considering that the major comment codes were similar in both these groups at the middle and end of the semester, with only a few subtle differences. The data did, however, spur us to hypothesize that one of the major differences between high- and low-performance groups may derive from student attitudes and appreciation of the value of group work to their learning overall.

We found that all groups, regardless of their success, clearly viewed individual accountability as their basic responsibility as a group member. This constituted the most frequent comment in peer evaluations from both high- and low-performance groups at both the midpoint and end of the semester. Individual accountability, although critical and mentioned as the primary comment in peer-evaluation comments, should be seen as a minimal requirement for effective group work. In well-designed group work, task assessments and grading for individual contribution play a greater role in promoting and enforcing individual accountability than self-regulation from group members. From a cognitive learning perspective, consensus building and coconstruction of knowledge ( Solomon, 1987 ; Latour and Woolgar, 2013 ) constitute a more effective method for enhancing learning during group work than promoting completion of tasks by divvying up the work. Students bring misconceptions about their fellow students’ attitudes and abilities to group work that prevent them from distinguishing peers who were deliberately failing to contribute from peers who were struggling academically and contributing to the best of their abilities ( Freeman and Greenacre, 2011 ). Without some clarity, peer evaluations can reinforce these attitudes. Providing students with a more careful evaluation of cognitive behaviors (e.g., asking to list individual efforts toward completing group activities such as editing, writing portions, finding references) and creating task structures that ensure that students provide explanations or elaborations could help produce more turn-taking, productive discourse, and appreciation that students bring varying levels of expertise and contributions to understanding. Student groups that exhibit networks of communication with frequent interpersonal interactions exhibit higher cognitive complexity and performance overall ( Curs¸eu et al. , 2012 ).

It is interesting that peer-evaluation comments related to communicating effectively were less frequently observed in lower-performance groups. Students in lower-performance groups do eventually mention this, but not until later in the semester. In addition to communication, students in high- and low-performance groups expressed an appreciation for the value and importance of positive interdependence in comments on midsemester evaluations. However, students in low-performance groups were less likely to mention positive interdependence in the end-of-semester evaluations. Reliance on group members to achieve common goals has been consistently identified as a critical factor in increasing collaboration, and its effect on achievement ( Slavin, 1991 ; Webb and Palincsar, 1996 ; Johnson et al. , 2007 ; Scager et al. , 2016 ). High-performance groups may work better because they perceive the value of group work from the beginning of the course and recognize their group members for providing features of learning support, communication, and positive interdependence ( Kwon et al. , 2014 ). The absence of comments about positive interdependence in low-performance groups at the end-of-semester evaluations is not unexpected: they were not performing effectively on assignments. However, in considering the implications for instructors, these are not the comments that are showing up most frequently, so it would be hard to identify dysfunctional groups using this feature.

There are several limitations to our findings, and additional research is needed to corroborate the correlations we observed between these self-report measures and academic performance. Our finding that lower-scoring students are critical of group work comes from interview data. It would be interesting to extend our work by surveying an entire course with a group-work satisfaction survey to determine whether our findings extend to all students within the course. We did not ask students to provide detailed self-reports on their own contributions to each assignment. These may prove useful for further studies that could compare individual self-reports (self-evaluations) with anonymous peer evaluations to correlate with individual and group performance measures. Interview and reflection journals may also prove important in determining the extent to which self-report indicators can be employed with either individual or consensus self-assessment measures. Instructors could then provide adaptive scaffolding to support students’ monitoring and reflection on their learning depending on the progress of group work. For example, when groups perform poorly, instructors would be able to provide extra procedural support (e.g., providing a checklist, suggesting using track-changes options to record individual contributions) or strategic support (e.g., providing summary notes or extra review sessions).

In addition to their ineffectiveness at identifying group dysfunction, peer evaluations may negatively impact how students interact with one another. During the interviews, students reported that they were concerned about the possibility of their identities being revealed in their peer-evaluation comments and that this would negatively affect their group relationships. It is obvious that students experienced peer pressure even with an online peer-evaluation system designed with a confidential log-in system to ensure anonymity.

As Bacon et al. ’s (1999) study indicated, use of evaluations can be negatively associated with good team experiences. Strong and Anderson (1990) observed that students preferred other factors—including group cohesiveness, small team size, the option to divorce a team member, or the option to leave a team—as stronger countermeasures for reducing free riding.

Peer Ratings May Be Biased against Low-Scoring Students in Low-Performance Groups

We also examined the numerical ratings that students provided for one another as a summative assessment of their effort on group work throughout the semester. This reward or punishment system is designed to deter social loafing, to motivate individual students to enhance their performances, and to account for inequities in students’ contributions. Students’ most common complaints about group work involve uneven contributions from group members ( Livingstone and Lynch, 2000 ; Aggarwal and O’Brien, 2008 ; Pauli et al. , 2008 ; Shimazoe and Aldrich, 2010 ; Hall and Buzwell, 2012 ). However, there are several problems with using peer ratings to evaluate contributions. First, students have expressed discomfort using ratings that they view as criticizing their friends ( Williams, 1992 ). Student raters may not have the ability to distinguish between high and low contributions, and their ratings may be influenced by their own experiences and norms within their groups ( Loughry et al. , 2007 ). Underperforming students tend to over- or underrate their individual progress, need for support, and understanding ( Winne and Jamieson-Noel, 2002 ). Students often resort to giving all students equal marks on a holistic evaluation compared with a categorical evaluation that queries about individual skills ( Lejk and Wyvill, 2001 ), and unadjusted ratings that students receive from their peers do not correlate with course grades ( Zhang and Ohland, 2009 ). Finally, students within a group may intentionally inflate or reduce the contribution of members due to friendship ( Zhang et al. , 2008 ).

We found that the ratings students gave their peers did correlate with group performance: high-performance groups gave higher ratings to their members compared with low-performance groups. So, groups were clearly using ratings in a small way to indicate poor performance, but their use may only be accurate for high-scoring students who received high ratings in both higher- and low-performance groups. Ratings may not provide an unbiased measure of individual effort or accountability for lower-scoring students, who were more likely to receive lower peer ratings in low-performance groups relative to lower-scoring students in high-performance groups. In the successful student groups that Scager and colleagues (2016) interviewed, students expressed a sense of empathy for their peers who contributed less, noting that it may have been “beyond (their) capabilities at that point.” This may echo what we have seen in our analysis of peer ratings. High-scoring students in high-performance groups may recognize that their lower-scoring peers are simply contributing to the level of their ability. It was clear from their peer-evaluation comments that students in high-performance groups value communication and the sense of communal effort that is afforded by positive interdependence to a greater degree than students in low-performance groups. It is also possible that lower-scoring students in low-performance groups actually participate less than those in high-performance groups and actually earn those lower scores. Considering that students in both high- and low-performance groups complained of social loafing and free riding in interviews and that there are discrepancies within ratings for low-scoring students, there are clearly problems with using peer ratings to evaluate contributions to group work.

Alternative measures may be required to ensure equitable assignment of group contributions to account for biases in peer ratings. We used the expected contributions adjustment to modify group scores based on peer ratings. However, Zhang and Ohland (2009) found this to have higher absolute error and low correlation with true contribution to the team as measured by Monte Carlo simulations or actual class data. They recommend using a between-group difference adjustment that compares students to other students in matched performance groups, explaining that “as peer and self ratings are related to the quality of group work, ratings from groups with different group scores are not directly comparable” ( Zhang and Ohland, 2009, p. 295 ). This is only a partial solution to the problems mentioned earlier. It may also be useful to ask students to specify the cognitive and functional efforts contributed by each group member on each assignment (e.g., an acknowledgments section in which they select from a list of tasks, including conducting a literature search, writing, creating figures, and editing). This could be very effective if students are also asked to reflect qualitatively on the social support (motivation, response to criticism, adaptability, creativity, and attitude) provided by members of their group.

For instructors with extremely limited time, there are also several scales specifically developed to identify conflict ( Jehn and Mannix, 2001 ) or satisfaction ( Van der Vegt et al. , 2001 ) in student teams. These may be a quick way to identify problems in the early stages of group work. Organizations can provide resources for managing team conflict ( Manktelow et al. , 2017 ), and there is evidence that conflict management can improve team performance, even in student teams ( Tekleab et al. , 2009 ). Assigning group members descriptions of group dysfunction and asking students to identify strategies for solving the problem as a way to mediate their own conflicts ( Lerner, 1995 ) or training students in reflexivity ( O’Neill et al. , 2017 ) could provide mechanisms for groups to resolve conflicts before they result in dysfunction.

Are Time-Consuming Strategies That Facilitate Group Work Worth All the Effort?

In this study, we discovered that students of all abilities valued group work for various reasons in addition to how it benefited their learning. In student interviews, we observed that only about one out of seven lower-scoring students perceived group work and instructional facilitating activities to be beneficial for their learning performance (compared with three of seven high-scoring students). Lower-scoring students commented that they found group work to be beneficial primarily as a comfort zone or the incentive for them to go to class because they have friends to talk with. Motivation and social cognition are important mediators of group work ( Slavin, 2014 ). Researchers have suggested that the quality of interactions between group members may be more predictive of learning gains than ability grouping and have recommended that an individual student’s attitude, motivation, or personality traits may provide a better predictor of group success than cognitive ability alone ( Webb et al. , 2002 ; Woolley et al. , 2010 ). In laboratory simulations of group work in which students are tasked with solving visual puzzles, brainstorming, making collective moral judgments, and negotiating limited resources, Woolley and colleagues (2010) have identified a single latent factor they call general collective intelligence—supported by strong interitem correlation on different tasks—that strongly predicts the groups’ ability to solve tasks. Collective intelligence appears to depend both on the composition of the group (e.g., average member intelligence and, more importantly, social sensitivity) and how group members interact when they are assembled (e.g., their conversational turn-taking behavior). Groups in which a few people dominated the conversation were less collectively intelligent than those with a more equal distribution of conversational turn-taking ( Woolley et al. , 2010 ). This was substantiated recently in a study that demonstrated that students who indicate higher levels of comfort with their group members achieve higher learning gains, whereas lower learning gains occur in groups with a reported conversation dominator ( Theobald et al. , 2017 ). Because we allowed students to self-select in this study, it is possible that purposeful group composition may yield different results, as peer relationship can be used as a predictor of student performance within a group ( Klein and Mulvey, 1995 ; Chung et al. , 2018 ). It would be interesting to examine the role of social sensitivity, beliefs about learning, friendship, and social skills such as conversational turn-taking as predictors of group performance in the college science, technology, engineering, and mathematics classroom. Also, as one of the goals of this study is to understand the effectiveness of group work in an uncontrolled classroom, we did not measure students’ prior knowledge levels (e.g., Scholastic Aptitude Test scores, college GPA, pretest). To further investigate the influence of the specific group-based activity, we recommend administering pre- and posttests.

We found that, regardless of group composition or group performance level, students were likely to report positive experiences with group members. When group members function interdependently, collective efficacy beliefs have been shown to provide a greater impact on performance: groups with higher self-efficacy beliefs were more likely to encourage group members to use resources more effectively ( Bandura, 2001 ) and to engage in higher-quality discussions ( Wang and Lin, 2007 ). Thus, the establishment of collective group efficacy may be well worth the effort to promote group-learning performance ( Gully et al. , 2002 ).

Supplementary Material

Acknowledgments.

We acknowledge continuing support and feedback from the University of Georgia SEER (Scientists Engaged in Education Research) Center. Permission to survey and audio-record students was obtained from the University of Georgia Institutional Review Board (STUDY2013104060 and MOD00000647).

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Assignment Method

Published on :

21 Aug, 2024

Blog Author :

Edited by :

Reviewed by :

Dheeraj Vaidya

What Is The Assignment Method?

The assignment method is a strategic approach to allocating organizational resources, including tasks and jobs to various departments like people, machines, or teams. It aims to minimize total costs or completion time and gain maximum efficiency, by assigning resources to corresponding units.

The assignment procedure's importance stems from its capacity to optimize resource allocation procedures in a business. Organizations may guarantee that resources are used optimally, reducing waste and increasing productivity by implementing a systematic method. It facilitates the decision-making process for the efficient and economical use of resources by helping to make well-informed choices.

Table of contents

Assignment method explained, methodology, advantages & disadvantages, frequently asked questions (faqs), recommended articles.

• The assignment method strategically allocates resources to tasks, jobs or teams to minimize costs or completion time. It optimizes resource utilization, reduces waste, and improves operational efficiency.
• It involves using methods like complete enumeration, simplex, transportation, or the Hungarian method. It involves using the assignment method of linear programming .
• The   Hungarian assignment method efficiently solves assignment problems by determining optimal assignments using a cost matrix.
• Advantages include structured resource allocation, enhanced resource utilization, and improved operational effectiveness. Limitations include data accuracy requirements and limited flexibility for dynamic changes.

The assignment method in operation research is a strategy for allocating organizational resources to tasks to increase profit via efficiency gains, cost reductions , and improved handling of operations that might create bottlenecks . It is an operations management tool that, by allocating jobs to the appropriate individual, minimizes expenses , time, and effort.

The technique is an essential tool for project management and cost accounting . It assists in allocating indirect expenses , such as overhead, to objects or cost centers according to predetermined standards, such as direct labor hours or required machine hours. The method helps determine the overall cost of every good or service, which helps with pricing, output, and resource distribution decisions. It also guarantees effective work allocation, on-time project completion, and economical use of resources. In short, it solves assignment problems.

Assignment problems involve assigning workers to specific roles, such as office workers or trucks on delivery routes, or determining which machines or products should be used in a plant during a specific period. Transportation problems involve distributing empty freight cars or assigning orders to factories. Allocation problems also involve determining which machines or products should be used to produce a given product or set of products. Unit costs or returns can be independent or interdependent, and if allocations affect subsequent periods, the problem is dynamic, requiring consideration of time in its solution.

The assignment problem can be solved using four methods: The complete enumeration method, the simplex method, the transportation method, and the Hungarian method.

The complete enumeration approach generates a list of potential assignments between resources and activities, from which the best option is chosen based on factors like cost, distance, time, or optimum profit. If the minimum cost, time, or distance for two or more assignments is the same, then this approach offers numerous optimal solutions. However If there are a lot of assignments, it is no longer appropriate for manual calculations. Assignment method calculators, if reliable, can be used for the same.

The simplex method can be solved as a linear programming problem using the simplex algorithm. The transportation method is a special case of the assignment problem. The method is, however, computationally inefficient for solving the assignment problem due to the solution's degeneracy problem.

The Hungarian assignment method problem, developed by mathematician D. Konig, is a faster and more efficient approach to solving assignment problems. It involves determining the cost of making all possible assignments using a matrix. Each problem has a row representing the objects to be assigned and columns representing assigned tasks. The cost matrix is square, and the optimum solution is to have only one assignment in a row or column. This method is a variation of the transportation problem, with the cost matrix being square and the optimum solution being one assignment in a row or column of the cost matrix.

Let us look into a few examples to understand the concept better.

TechLogistics Solutions, an imaginary delivery company, employs the assignment method to optimize the distribution of its delivery trucks. They meticulously consider distance, traffic conditions, and delivery schedules. TechLogistics efficiently allocates trucks to routes through strategic assignments, effectively reducing fuel costs and ensuring punctual deliveries. This method significantly enhances the company's operational efficiency and optimizes the utilization of its delivery resources.

Suppose XYZ Inc., a manufacturing company, is challenged to efficiently assign tasks to its machines (A, B, and C). Using the assignment method, XYZ calculates the cost matrix, reflecting the cost associated with each task assigned to each machine. Leveraging advanced algorithms like the Hungarian method, the company identifies optimal task-machine assignments, minimizing overall costs. This approach enables XYZ to streamline its production processes and enhance cost-effectiveness in manufacturing operations .

Advantages of the assignment method include:

• Resource allocation is carried out in a structured and organized manner.
• Enhancement of resource utilization to achieve optimal outcomes.
• Facilitation of efficient distribution of tasks.
• Improvement in operational effectiveness and productivity.
• Economical allocation of resources.
• Reduction in project completion time.
• Consideration of multiple factors and constraints for informed decision-making.

The disadvantages of the assignment method are as follows:

• Dependence on accurate and up-to-date data for effective decision-making.
• Complexity when dealing with resource allocation on a large scale.
• Subjectivity is involved in assigning values to the resource-requirement matrix.
• Limited flexibility in accommodating dynamic changes or unforeseen circumstances.
• Applicable primarily to quantitative tasks, with limitations in addressing qualitative aspects.

Johnson's rule is an operations research method that aims to estimate the optimal sequence of jobs in two work centers to reduce makespan. It optimizes the overall efficiency of the process. In contrast, the assignment method is useful for resource allocation, matching resources to specific tasks or requirements to optimize efficiency.

The study assignment method refers to the process of allocating students to specific courses or study programs based on their preferences, skills etc. It involves matching students with appropriate courses or programs to ensure optimal utilization of educational resources and meet individual student needs.

The assignment method is frequently employed when there is a requirement to allocate restricted resources like personnel, equipment, or budget to particular tasks or projects. It aids in enhancing resource utilization operational efficiency, and enables informed decision-making regarding resource allocation considering various factors and constraints.

This article has been a guide to what is Assignment Method. Here, we explain its methodologies, examples, advantages, & disadvantages. You may also find some useful articles here -

• Cost Allocation Methods
• Propensity Score Matching
• Regression Discontinuity Design

5 Advantages and Disadvantages of Problem-Based Learning [+ Activity Design Steps]

Written by Marcus Guido

• Teaching Strategies

• Advantages of Problem-Based Learning
• Disadvantages of Problem-Based Learning
• Steps to Designing Problem-Based Learning Activities

Used since the 1960s, many teachers express concerns about the effectiveness of problem-based learning (PBL) in certain classroom settings.

Whether you introduce the student-centred pedagogy as a one-time activity or mainstay exercise, grouping students together to solve open-ended problems can present pros and cons.

Below are five advantages and disadvantages of problem-based learning to help you determine if it can work in your classroom.

If you decide to introduce an activity, there are also design creation steps and a downloadable guide to keep at your desk for easy reference.

1. Development of Long-Term Knowledge Retention

Students who participate in problem-based learning activities can improve their abilities to retain and recall information, according to a literature review of studies about the pedagogy .

The literature review states “elaboration of knowledge at the time of learning” -- by sharing facts and ideas through discussion and answering questions -- “enhances subsequent retrieval.” This form of elaborating reinforces understanding of subject matter , making it easier to remember.

Small-group discussion can be especially beneficial -- ideally, each student will get chances to participate.

But regardless of group size, problem-based learning promotes long-term knowledge retention by encouraging students to discuss -- and answer questions about -- new concepts as they’re learning them.

2. Use of Diverse Instruction Types

You can use problem-based learning activities to the meet the diverse learning needs and styles of your students, effectively engaging a diverse classroom in the process. In general, grouping students together for problem-based learning will allow them to:

• Address real-life issues that require real-life solutions, appealing to students who struggle to grasp abstract concepts
• Participate in small-group and large-group learning, helping students who don’t excel during solo work grasp new material
• Talk about their ideas and challenge each other in a constructive manner, giving participatory learners an avenue to excel
• Tackle a problem using a range of content you provide -- such as videos, audio recordings, news articles and other applicable material -- allowing the lesson to appeal to distinct learning styles

Since running a problem-based learning scenario will give you a way to use these differentiated instruction approaches , it can be especially worthwhile if your students don’t have similar learning preferences.

3. Continuous Engagement

Providing a problem-based learning challenge can engage students by acting as a break from normal lessons and common exercises.

It’s not hard to see the potential for engagement, as kids collaborate to solve real-world problems that directly affect or heavily interest them.

Although conducted with post-secondary students, a study published by the Association for the Study of Medical Education reported increased student attendance to -- and better attitudes towards -- courses that feature problem-based learning.

These activities may lose some inherent engagement if you repeat them too often, but can certainly inject excitement into class.

4. Development of Transferable Skills

Problem-based learning can help students develop skills they can transfer to real-world scenarios, according to a 2015 book that outlines theories and characteristics of the pedagogy .

The tangible contexts and consequences presented in a problem-based learning activity “allow learning to become more profound and durable.” As you present lessons through these real-life scenarios, students should be able to apply learnings if they eventually face similar issues.

For example, if they work together to address a dispute within the school, they may develop lifelong skills related to negotiation and communicating their thoughts with others.

As long as the problem’s context applies to out-of-class scenarios, students should be able to build skills they can use again.

5. Improvement of Teamwork and Interpersonal Skills

Successful completion of a problem-based learning challenge hinges on interaction and communication, meaning students should also build transferable skills based on teamwork and collaboration . Instead of memorizing facts, they get chances to present their ideas to a group, defending and revising them when needed.

What’s more, this should help them understand a group dynamic. Depending on a given student, this can involve developing listening skills and a sense of responsibility when completing one’s tasks. Such skills and knowledge should serve your students well when they enter higher education levels and, eventually, the working world.

1. Potentially Poorer Performance on Tests

Devoting too much time to problem-based learning can cause issues when students take standardized tests, as they may not have the breadth of knowledge needed to achieve high scores. Whereas problem-based learners develop skills related to collaboration and justifying their reasoning, many tests reward fact-based learning with multiple choice and short answer questions. Despite offering many advantages, you could spot this problem develop if you run problem-based learning activities too regularly.

2. Student Unpreparedness

Problem-based learning exercises can engage many of your kids, but others may feel disengaged as a result of not being ready to handle this type of exercise for a number of reasons. On a class-by-class and activity-by-activity basis, participation may be hindered due to:

• Immaturity  -- Some students may not display enough maturity to effectively work in a group, not fulfilling expectations and distracting other students.
• Unfamiliarity  -- Some kids may struggle to grasp the concept of an open problem, since they can’t rely on you for answers.
• Lack of Prerequisite Knowledge  -- Although the activity should address a relevant and tangible problem, students may require new or abstract information to create an effective solution.

You can partially mitigate these issues by actively monitoring the classroom and distributing helpful resources, such as guiding questions and articles to read. This should keep students focused and help them overcome knowledge gaps. But if you foresee facing these challenges too frequently, you may decide to avoid or seldom introduce problem-based learning exercises.

3. Teacher Unpreparedness

If supervising a problem-based learning activity is a new experience, you may have to prepare to adjust some teaching habits . For example, overtly correcting students who make flawed assumptions or statements can prevent them from thinking through difficult concepts and questions. Similarly, you shouldn’t teach to promote the fast recall of facts. Instead, you should concentrate on:

• Giving hints to help fix improper reasoning
• Questioning student logic and ideas in a constructive manner
• Distributing content for research and to reinforce new concepts
• Asking targeted questions to a group or the class, focusing their attention on a specific aspect of the problem

Depending on your teaching style, it may take time to prepare yourself to successfully run a problem-based learning lesson.

4. Time-Consuming Assessment

If you choose to give marks, assessing a student’s performance throughout a problem-based learning exercise demands constant monitoring and note-taking. You must take factors into account such as:

• Completed tasks
• The quality of those tasks
• The group’s overall work and solution
• Communication among team members
• Anything you outlined on the activity’s rubric

Monitoring these criteria is required for each student, making it time-consuming to give and justify a mark for everyone.

5. Varying Degrees of Relevancy and Applicability

It can be difficult to identify a tangible problem that students can solve with content they’re studying and skills they’re mastering. This introduces two clear issues. First, if it is easy for students to divert from the challenge’s objectives, they may miss pertinent information. Second, you could veer off the problem’s focus and purpose as students run into unanticipated obstacles. Overcoming obstacles has benefits, but may compromise the planning you did. It can also make it hard to get back on track once the activity is complete. Because of the difficulty associated with keeping activities relevant and applicable, you may see problem-based learning as too taxing.

If the advantages outweigh the disadvantages -- or you just want to give problem-based learning a shot -- follow these steps:

1. Identify an Applicable Real-Life Problem

Find a tangible problem that’s relevant to your students, allowing them to easily contextualize it and hopefully apply it to future challenges. To identify an appropriate real-world problem, look at issues related to your:

• Students’ shared interests

You must also ensure that students understand the problem and the information around it. So, not all problems are appropriate for all grade levels.

2. Determine the Overarching Purpose of the Activity

Depending on the problem you choose, determine what you want to accomplish by running the challenge. For example, you may intend to help your students improve skills related to:

• Collaboration
• Problem-solving
• Curriculum-aligned topics
• Processing diverse content

A more precise example, you may prioritize collaboration skills by assigning specific tasks to pairs of students within each team. In doing so, students will continuously develop communication and collaboration abilities by working as a couple and part of a small group. By defining a clear purpose, you’ll also have an easier time following the next step.

3. Create and Distribute Helpful Material

Handouts and other content not only act as a set of resources, but help students stay focused on the activity and its purpose. For example, if you want them to improve a certain math skill , you should make material that highlights the mathematical aspects of the problem. You may decide to provide items such as:

• Data that helps quantify and add context to the problem
• Videos, presentations and other audio-visual material
• A list of preliminary questions to investigate

Providing a range of resources can be especially important for elementary students and struggling students in higher grades, who may not have self-direction skills to work without them.

4. Set Goals and Expectations for Your Students

Along with the aforementioned materials, give students a guide or rubric that details goals and expectations. It will allow you to further highlight the purpose of the problem-based learning exercise, as you can explain what you’re looking for in terms of collaboration, the final product and anything else. It should also help students stay on track by acting as a reference throughout the activity.

5. Participate

Although explicitly correcting students may be discouraged, you can still help them and ask questions to dig into their thought processes. When you see an opportunity, consider if it’s worthwhile to:

• Fill gaps in knowledge
• Provide hints, not answers
• Question a student’s conclusion or logic regarding a certain point, helping them think through tough spots

By participating in these ways, you can provide insight when students need it most, encouraging them to effectively analyze the problem.

6. Have Students Present Ideas and Findings

If you divided them into small groups, requiring students to present their thoughts and results in front the class adds a large-group learning component to the lesson. Encourage other students to ask questions, allowing the presenting group to elaborate and provide evidence for their thoughts. This wraps up the activity and gives your class a final chance to find solutions to the problem.

Wrapping Up

The effectiveness of problem-based learning may differ between classrooms and individual students, depending on how significant specific advantages and disadvantages are to you. Evaluative research consistently shows value in giving students a question and letting them take control of their learning. But the extent of this value can depend on the difficulties you face.It may be wise to try a problem-based learning activity, and go forward based on results.

Create or log into your teacher account on Prodigy -- an adaptive math game that adjusts content to accommodate player trouble spots and learning speeds. Aligned to US and Canadian curricula, it’s used by more than 350,000 teachers and 10 million students. It may be wise to try a problem-based learning activity, and go forward based on results.

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A Critique of the Hungarian Method of Solving Assignment Problem to the Alternate Method of Assignment Problem by Mansi

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Education resources › Blog › 10 advantages and disadvantages of classroom group work

10 advantages and disadvantages of classroom group work

• Leadership & teamwork
• The science of learning

Written by the InnerDrive team | Edited by Bradley Busch

The use of group work in the classroom is one of the most widely researched and implemented teaching approaches in the world.  Numerous research studies  have shown the benefits of collaborative learning on academic performance, communication skills, and confidence. 

However, our understanding of how group work facilitates learning and why group work is only effective in certain situations is still limited. And like with all teaching strategies, the disadvantages need to be taken into consideration. 

Amongst educators, there is a growing debate surrounding the efficacy of group work due to the potential for laziness, unequal workload, conflict between students, and a loss of focus on the task at hand. So, we took a look at the pros and cons of implementing group work into the classroom to determine how effective it really is.

10 advantages and disadvantages of group work

5 advantages of group work, a new perspective .

The phrase “two heads are better than one” certainly has some merit. Researchers found that  if students are able to work together , for example on a problem-solving task, they are more likely to experiment with different techniques in order to try and solve it. They can also learn faster from positive and negative feedback.

Students also learn better by discussing and questioning each other’s opinions and reasoning as this allows them to develop different perspectives of how they can go about completing a task.  Research shows  this promotes  cognitive restructuring , enhancing academic,  social, and emotional learning  as a result.

Personal satisfaction

Working in a group can be tough. So, when students are able to overcome all the conflict, stress, and long hours that come with group assignments, the end result of getting a good grade can be extremely satisfying and motivating. 

Research shows  that students who contribute to group discussion and engage with the assigned problem-solving task are highly dedicated to figuring out a solution. When they find that solution, students report feeling extremely satisfied with their role in making that decision compared to students who weren’t as involved. This leads to a more positive depiction of their group learning experience.

Teamwork skills 

Teamwork is a staple part of academic life  and allows students to explore complex tasks that they otherwise wouldn’t have done if they had been alone, enhancing both their individual and collective learning. This is because working in a group exposes students to new perspectives, styles of thinking, and disagreement.

This provides students with an opportunity to improve their communication skills, collaboration and provides a larger capacity for brainstorming different ideas. This not only contributes to a more holistic approach to learning but can help group productivity as well.

Enhancing learning 

A survey showed  that 97% of students reported that working in a group environment has helped facilitate their learning and collaborative skills in some way. Some students suggested that group work served as a learning process in itself; that is, they learnt about groups by working in a group. 

Research also shows  that learning in a group leads to better memory recall and understanding. This is because students remember more from group discussions than if they listened to the same content in a more instructional format. 

However, these benefits are only felt if:

• Clear goals are set
• There is clear leadership
• Each member is assigned a specific role
• There’s equal participation from all group members
• The task is relevant to syllabus content

Although this study  was conducted with university students, these findings are still relevant to other educational levels.

Learning to overcome conflict 

Some teachers argue  that conflict during group work can actually be a good thing as it is representative of experiences students will have in their future workplaces. By experiencing it in a more controlled setting, students learn about communication skills and how to resolve interpersonal issues more safely. 

Group work also allows students to develop a better understanding of themselves and how their peers view them. By gaining  constructive feedback  from their peers about how well they did on a task and how well they worked as part of the group, students are better equipped to evaluate their social skills and behaviour.

5 disadvantages of group work

Anyone who has done group work knows that is can have its fair share of disadvantages. Let’s take a look at why. 

Presence of conflict 

When working with others, it’s natural that disagreement will arise due to differences in opinions. Some students find it difficult to accept  criticism from their peers  and struggle to get on board with ideas that aren’t their own.

Moreover, students who are quiet often have difficulty expressing their ideas in a group and may feel uncomfortable working with people they don’t normally speak to. As a result, they may be seen as lazy, creating conflict. 

Research shows  that the presence of conflict in group work can negatively impact the students’ enjoyment of that class, inhibit their individual learning, and increase stress levels. This is because students felt that compromising and coming to an agreement was an extremely difficult and draining process. This led to many students developing a fear of conflict.

Unequal participation

In group work, you’ll often observe a large discrepancy in participation between the different group members. With a lot of group projects, it’s common to find 1-2 students taking the bulk of the workload, whilst other members essentially freeload. This can lead to conflict and breed bitterness amongst the different group members – especially if the student feels others are being rewarded for their hard work. 

Research shows  that this is more evident in larger groups as individuals tend to diffuse the responsibility of tasks onto others as grades typically don’t consider individual contribution. Other times, a student may just give their peers the answer without explaining how they worked it out. Consequently, no real knowledge and understanding have been gained.

Avoiding the task

When working in a group, it’s quite common for students to go off-topic, especially if the task involves discussion. Some students may use that time to gossip, do other tasks, or loaf around. This results in the group work session being less  effective and productive . 

As a teacher, it’s difficult to make sure everyone is doing the task they’re supposed to for the entire session, not just as you approach their table to see how they’re doing. For some teachers, it feels that they have to  micromanage  the task in order for the task to be effective, diminishing the purpose of working in a group.

Time consuming 

Working in a team can be extremely time-consuming as a student. Not only do meetings have to be scheduled outside of class hours but they have to co-ordinate with everyone’s schedule. For sixth-form students in particular, this can be quite difficult due to  already being overscheduled . 

Researchers have even argued  whether the time-consuming nature of group work made the strategy ineffective. As a result, more research is emerging about when not to use group work in the classroom and suggest that for simpler tasks, students complete them individually.

Individual needs are dominated by the needs of the group 

Not all students learn at the same speed. Some may need more time to fully understand the task and process the information they’re being taught. On the flip side, some students may grasp the material very quickly.

Therefore, when working as a group, certain students are either forced to hurry up their learning to the extent that they either learn nothing or resort to copying. Alternatively, those who work faster may actually be going too fast, attempting to move onto the next task before everyone is ready. This can lead to conflict as students may get frustrated by the learning process.

Final thoughts

Group learning can be effective regardless of people’s socioeconomic status or whether they’re put into a group with the same people throughout the year. However, the advantages of this active learning environment are only observed when it is done right. 

Group size, how groups are assigned and how the teacher manages the groups can have both a positive and negative impact on learning. Due to the potential disadvantages, some  research suggests  that group work should only be used in moderation by allowing simpler tasks to be completed individually and more complex tasks to be completed in groups. 

For tips on how to engage your students in the classroom, take a look at our blogs on how to create a  psychologically smart classroom  and why you should  interleave your teaching .

About the editor

Bradley Busch

Bradley Busch is a Chartered Psychologist and a leading expert on illuminating Cognitive Science research in education. As Director at InnerDrive, his work focuses on translating complex psychological research in a way that is accessible and helpful. He has delivered thousands of workshops for educators and students, helping improve how they think, learn and perform. Bradley is also a prolific writer: he co-authored four books including Teaching & Learning Illuminated and The Science of Learning , as well as regularly featuring in publications such as The Guardian and The Telegraph.

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