the trial and error approach to problem solving is most effective when

Trial and Error

Trial and Error is a fundamental method of problem-solving, which involves attempting different solutions until the correct one is found. As a strategy frequently used in multiple fields, including psychology, science, and computer programming, its significance is profound and multifaceted.

Understanding the term

To fully appreciate the trial and error method’s value, let’s delve into its characteristics, process, and theoretical underpinnings.

Characteristics of the Trial and Error Method

The trial and error method is defined by two key elements: making attempts (trials) and learning from failures (errors). The process continues until a solution is found.

The Trial and Error Process

The process of trial and error consists of generating possible solutions, applying them, assessing their effectiveness, and revising the approach based on the results.

Theoretical Background

Trial and error has roots in behavioral psychology, where it’s often associated with Edward Thorndike’s Law of Effect. This law suggests that responses followed by satisfaction will be repeated, while those followed by discomfort will be discontinued.

Trial and Error in Everyday Life

The application of the trial and error method is ubiquitous, extending from our daily activities to complex scientific research.

Learning New Skills

When we learn to ride a bicycle, cook a new dish, or play a musical instrument, we use trial and error to master the skills.

Technological Advancements

In the tech industry, trial and error play a crucial role in software development and debugging, hardware design, and algorithm optimization.

Advantages and Disadvantages

The trial and error method, despite its universal application, comes with its pros and cons.

H3: Advantages

Trial and error encourages creativity and fosters resilience. It allows for the discovery of all possible solutions and can lead to unexpected yet effective outcomes.

H3: Disadvantages

However, trial and error can be time-consuming and resource-intensive. It may not be feasible when there’s a need for immediate solutions or when the risks of failure are high.

To better illustrate the concept of trial and error, let’s consider a couple of examples.

Example 1: Learning to Code

When learning to code, students often write a program, run it to see if it works, and if it doesn’t, they debug and modify their code. This is an example of trial and error.

Example 2: Medicinal Drug Discovery

In medicinal chemistry, scientists often synthesize and test numerous compounds before finding one that effectively treats a disease. This process embodies the trial and error method.

Enhancing the Trial and Error Process

While trial and error inherently involve some degree of uncertainty, some strategies can enhance its efficiency.

Learn from Each Attempt

Each trial, whether successful or unsuccessful, provides valuable information. Reflecting on each attempt can improve future trials and hasten the problem-solving process.

Embrace Failure

Viewing errors as learning opportunities rather than failures can foster resilience and creativity, essential traits for effective problem-solving.

In essence, trial and error is an indispensable problem-solving strategy that encourages creativity, resilience, and comprehensive solution discovery. By understanding its characteristics, benefits, and limitations, we can harness its potential more effectively in various domains of life. Remember, each trial brings you one step closer to a solution, and each error is a stepping stone to success.

Psychology Discussion

Thorndike’s trial and error theory | learning | psychology.

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In this article we will discuss about:- 1. Meaning of Thorndike’s Trial and Error Theory 2. Experimental Evidences of Thorndike’s Trial and Error Theory 3. Educational Implications 4. Some Objections.

Meaning of Thorndike’s Trial and Error Theory:

Edward Lee Thorndike (1874-1949) is generally considered to have been the foremost educational psychologist not only of the United States but of the world. He contributed to research and theory in the field of learning and genetic psychology, testing and social psychology, testing and social psychology.

Thorndike first stated the elements of his theory of learning in 1913 that connections are formed in the nervous system between stimuli and response. These connections formed are illustrated by the symbols S-R. Another word used to describe these connections is the word ‘bond’ and hence,’ this theory is sometimes called a ‘Bond Theory of learning’. Thorndike has written- “Learning is connecting. The mind is man’s connection system.”

According to Thorndike learning takes place by trial and error. Some people call it, “Learning by selection of the successful variant,” accordingly when no ready-made solution of a problem is available to the learner, he adopts the method of trial and error. He first, tries one solution. If it does not help him, he rejects it, then, he tries another and so on. In this way he eliminates errors or irrelevant responses which do not serve the purpose and finally discovers the correct solution.

Thus, in trial and error method, the learner makes random activities and finally reaches the goal accidently. Here, one thing should be remembered that in trial and error also, there are often systematic and relevant responses. Activities are not wholly random. All these activities, though apparently random are suggested to him by the situation and the learner proceeds on accordingly. The stages through which the learner has to pass are Goal, Block (hinderances), Random Movements or multiple response, chance success, selection and Fixation.

When and how the connection is accomplished was stated first in the following three laws:

1. Law or Readiness:

First primary law of learning, according to him, is the ‘Law or Readiness’ or the ‘Law of Action Tendency’, which means that learning takes place when an action tendency’ is aroused through preparatory adjustment, set or attitude. Readiness means a preparation for action. If one is not prepared to learn, learning cannot be automatically instilled in him, for example, unless the typist, in order to learn typing prepares himself to start, he would not make much progress in a lethargic and unprepared manner.

2. Law of Exercise:

The second law of learning is the ‘Law of Exercise’, which means that drill, or practice helps in increasing efficiency and durability of learning and according to Thorndike’s S-R Bond Theory, the connections are strengthened with trail or practice and the connections are weakened when trial or practice is discontinued.

The ‘law of exercise’, therefore, is also understood as the ‘law of use and disuse’ in which case connections or bonds made in the brain cortex are weakened or loosened. Many examples of this are found in case of human learning. Learning to drive a motor-car, typewriting, singing or memorizing a poem or a mathematical table, and music etc. need exercise and repetition of various movements and actions May times.

3. Law of Effect:

The third law is the ‘Law of Effect’, according to which the trial or steps leading to satisfaction stamps in the bond or connection. Satisfying states lead to consolidation and strengthening of the connection, whereas dis-satisfaction, annoyance or pain leads to the weakening or stamping out of the connections.

In fact, the ‘law or effect’ signifies that if the responses satisfy the subject, they are learnt and selected. While those which are not satisfying are eliminated. Teaching, therefore, must be pleasing. The educator must obey the tastes and interests of his pupils. In other words, greater the satisfaction stronger will be the motive to learn. Thus, intensity is an important condition of the ‘law of effect’.

Besides these three basic laws, Thorndike also refers to five sub-ordinate laws which further help to explain the learning process.

1. Law of Multiple-Response:

According to it the organism varies or changes its responses till an appropriate behaviour is hit upon. Without varying the responses, the correct response for the solution might never be elicited. If the individual wants to solve a puzzle, he is trying in different ways rather than mechanically persisting in the same way. Thorndike’s cat in the puzzle box moved about and tried many ways to come out till finally it hit the latch with her paw which opened the door and it jumped out.

2. The Law of Set or Attitude:

Learning is guided by a total set or attitude of the organism, which determines not only what the person will do but what will satisfy or annoy him. For instance, unless the cricketer sets himself to make a century, he will not be able to score more runs. A student, similarly, unless he sets to get first position and has the attitude of being at the top, would while away the time and would not learn much. Hence, learning is affected more in the individual if he is set to learn more or to excel.

3. Pre-Potency of Elements:

According to this law, the learner reacts selectively to the important or essential element in the situation and neglects the other features or elements which may be irrelevant or non-essential. The ability to deal with the essential or the relevant part of the situation makes analytical and insightful learning possible. In this law of pre-potency of elements, Thorndike is really anticipating insight in learning which was more emphasised by the Gestations.

4. Law of Response by Analogy:

According to this law, the individual makes use of old experiences or acquisitions while learning a new situation. There is a tendency to utilize common elements in the new situation as existed in a similar past situation. The learning of driving a car, for instance, is facilitated by the earlier acquired skill of driving a motor-cycle or even riding a bicycle, because the perspective or maintaining a balance and controlling the handle helps in steering the car.

5. The Law of Associative Shifting:

According to this law we may get any response, of which a learner is capable, associated with any other situation to which he is sensitive. Thorndike illustrated this by the act of teaching a cat to stand up at a command. A fish was dangled before the vat while he said ‘stand up’. After a number of trials by presenting the fish after uttering the command ‘stand up’, he later ousted the fish and the overall command of ‘stand up’ was found sufficient to evoke the response to the cat by standing up on her hind legs.

Experimental Evidences of Thorndike’s Trial and Error Theory:

Various experiments have been performed on men as well as animals to study this method. Thorndike made several experiments on rats and cats. Two important experiments are mentioned here.

Thorndike’s most widely quoted experiment was with the cat placed in a puzzle box. The hungry cat was put in the puzzle box and a fish, as an incentive, was put out-side the cage a little beyond its reach. The box was designed in such a way that the door of the cage can be released by some simple act like depressing a lever inside the cage.

At first, the cat made a great deal of varied attempts to reach the food in a trial and error fashion such as jumping up and down, clawing at the bars, scratching the cage, whaling around trying to push the bars, pawing and shaking movable parts of the cage etc., but all attempts proved to vain.

Ultimately by chance her paw fell on the loop of the rope and the door opened. The cat jumped out immediately and ate the fish. When next day, the cat was put in the box again, this time she took less time in coming out and in the subsequent trials the time decreased further so much so that the stage reached when the cat came out soon after being put inside by directly striking the latch with her paw without any random movement. This is how she learnt to reach its goal.

Expt. 2 (Experiment with Human Subjects):

Gopalaswamy demonstrated trial and error in human beings through Mirror-Drawing Experiment. This is a classical experiment in the psychology of learning. In this experiment the subject is asked to trace a star-shaped drawing, not looking at it directly, but as it is reflected in a mirror, the subject’s hand movements are visible in the mirror only and not directly. The experimenter observes the movements of the hands and thus, records the time of tracing in successive trials and the number of errors committed in each trial.

In first six trials the subject traces the star with the right hand and then in the next six trials he traces it by the left hand. Two graphs-the Time Curve and the Error Curve are then drawn, which show the general characteristics of trial and error learning. In the original experiment Gopalaswamy arranged his apparatus so that a record was automatically made of all the movements of the styles of the subject as it traced out the pattern. In this way the successive times of tracings and a record of errors was obtained.

Gopalaswamy analyzed the errors into two groups-lower level errors and higher level errors. Those errors which do not involve any noble process on the part of the subject in tracing the star are lower-level errors and those which involve higher process of mind on the perceptual and conceptual level are higher-level errors.

He discovered that improvement in the higher-level responses correlated highly with intelligence and that the improvement in the responses of the lower-level errors did not show much correlation with intelligence. This clears the respective share of trial and error and of higher learning.

For Fundulus fishes Thorndike got a glass tub with a dividing wall of glass in the middle. In the dividing wall there was a hole through which the fish could go from one part to another. By nature Fundulus fish like to remain in shade. The glass tub was filled with water and it was put under such a situation that half of its part remained under shade and the other half was in the sunshine. The fishes were kept in the sunny portion.

They began to try to coming over to the shady portion. By trying again and again the fishes succeeded in tracing the hole of the dividing wall and reached the shady portion one by one. But, at first the fishes took more time in reaching the shady portion, then in the second attempt they took less time and in the third attempt they took the least time. Trying it again finally a stage came when the fishes happened to come one after another in a row to the shady portion immediately in the very first attempt i.e., the number of errors of their wandering here and there amounted to a zero.

Educational Implications of Thorndike’s Trial and Error Theory:

Thorndike’s theory of Trial and Error and his three basic laws of learning have direct educational implications. The ‘Law of Readiness’ lays emphasis on motivation while the ‘Law of Exercise’ compels us to accept a well-known fact ‘Practice makes a man perfect’, and the third one i.e., ‘Law of Effect’ opens fairly a large scope to discuss the role of reward and punishment as an incentive in the child’s learning.

Actually, motivation and learning are inter-related concepts. No motivation; No learning. Here we can remember a proverb, ‘the one man can take horse to the pool of water but twenty cannot make him drink’. This statement clearly shows the impact of motivation on learning. Clearly speaking motive is a force that compels an individual to act or to behave in a particular direction. And, hence the success of a teacher lies in motivating the roomfuls of energy. His prime duty is to produce ‘thirst’ (a motive to drink water) in the horses. Then and only then he may succeed in making the process of learning easier and interesting.

To quote with the experiment to Tolman and Honzik (1930) which they performed in rats will be of interest and situational here. In this experiment the rats were taught to follow a complex pattern of runs and turns through a maze to reach the food. The rats were divided in three groups. First group of rats was neither hungry nor given any food at the end or trial. The second group was hungry but was not given food. The third one was hungry and given food at the end of a trial.

It was concluded that only the third group learned appreciably i.e., the number of errors went on decreasing in each attempt. The logic is simple. To be motivated and unrewarded leaves to you only frustration instead a notable amount of learning. Also nor is it worthwhile to work for a prize you do not want. Thus, it is the motive that gives the reward its value and the satisfaction of reward that fixes the learning of which it is the effect.

Briefly speaking, without motivation or drive learning is impossible, as firstly, it prods the learner into action and secondly, it introduces light and shadow into an otherwise different field. So, teacher’s concern primarily shall be the motivating of goals and releasing tensions which signalise success. Above all he should have a psychological involvement in reaching and has to be charged with values and therefore, naturally motivated himself. The advice of an old principal of a school is very pertinent here.

“Teachers, you are going to be emulated in your talk and walk by your students, but a little less. If you run, your students will walk. If you walk, your students will stand. If you stand, your students will lie down. If you lie down, your students will sleep. And if you sleep in the class, your students will die”. But, one has to admit here that the organism’s level of performance can’t be beyond a physiological limit, whatever incentive we provide to him. For instance, higher bonus to factory workers, more praise to students may lead to a better performance, but no athlete can jump over the Chinese wall, whatever the intensity of motivation is provided.

Another significant aspect of this theory is that to master a complex situation or to elaborate task, practice is must. It is not possible to handle each difficult situation in a single trial, no matter what the degree of motivation or reward is. One cannot blame the entire constitution of India in one reading even if the reward is a crore of Rupees or the threat is to be shot dead otherwise. Each task initially seems to be difficult and fatiguing but as practice continues, it becomes smoother and requires less effort.

Finally, we say that habit or S-R is established. An expert driver, for instance, goes on driving, listening to the radio and taking to his friend sitting by. In the light of class room teaching blundering is a natural phenomenon associated with student learning. But, the teacher should not regard this as a symptom of inefficient teaching, because this is the way the pupils learn. He should not be at all worried when blundering appears.

Insights will emerge as the blundering progresses from simpler associations to higher units. There is not royal road to success. Kennedy-Fraser, the Psychologist concludes, “The teachers who are responsible for the beginning of any new subject should be the best available, since at the point, the pupils have no defensive system of properly formed habits to protect them from the evil effects of bad teaching.”

Actually, we learn by doing. The teachers’ duty should be to arrange situations in which the student has chance to discover for himself what is significant. The blundering must be directed and methods that are wholly futile must be eliminated. But at the same time the teacher must exercise, constant restraint in his supervision.

Further, both punishment and reward may play a significant role in the process of learning. But, experiments go to show that motivation is successfully handled when it is kept in the positive phase. Drastic forms of inhibition tend to spread their effects over the whole learning situation. Sometimes, the teachers impress upon the negative processes. The false response is effectively inhibited when the correct reaction is fixated and the emphasis should be on the latter process. The fixating rewards are most effective when they afford immediate and complete release.

A delay introduced between the successful performance and the releasing reward has a considerable effect on their rate of learning and co-ordination. In school, the satisfactions should be closely coupled with the activity itself otherwise the likelihood of permanent effects is small. Another aspect of motivating problem is simpler than the manipulations of tensions and releases and can be mastered by all. This is that the learner should be kept informed of his progress and promptly.

Finally, though the theory is not widely accepted for its educational significance, yet, there are certain subjects such as mathematics, tables of mathematics, memorising poetry, rules of grammar etc. in which learning by Trial and Error cannot be avoided. All reasoning subjects afford the greatest opportunity for the application of the Trial and Error method.

In Brief, the implications of the theory are:

1. According to his theory the task can be started from the easier aspect towards its difficult side. This approach will benefit the weaker and backward children.

2. A small child learns some skills through trial and error method only such as sitting, standing, walking, running etc. In teaching also the child rectifies the writing after committing mistakes.

3. In this theory more emphasis has been laid on motivation. Thus, before starting teaching in the classroom the students should be properly motivated.

4. Practice leads a man towards maturity. Practice is the main feature of trial and error method. Practice helps in reducing the errors committed by the child in learning any concept.

5. Habits are formed as a result of repetition. With the help of this theory the wrong habits of the children can be modified and the good habits strengthened.

6. The effects of rewards and punishment also affect the learning of the child. Thus, the theory lays emphasis on the use of reward and punishment in the class by the teacher.

7. The theory may be found quite helpful in changing the behaviour of the delinquent children. The teacher should cure such children making use of this theory.

8. With the help of this theory the teacher can control the negative emotions of the children such as anger, jealousy etc.

9. The teacher can improve his teaching methods making use of this theory. He must observe the effects of his teaching methods on the students and should not hesitate to make necessary changes in them, if required.

10. The theory pays more emphasis on oral drill work. Thus, a teacher should conduct oral drill of the taught contents. This helps in strengthening the learning more.

Some Objections to Thorndike’s Trial and Error Theory:

The theory has been criticised by various psychologists on the following grounds. Firstly, the theory is mechanical, for it leaves no room for an end or purpose in any sense whatsoever. On the contrary psychologist Mc Dougall maintained that even the behaviour of the amoeba or the paramecia consists in learning to face novel conditions to serve some unknown purpose Even repeated trials are of no avail if the tendency to learn is not there.

Again, if the tendency is there, even one trial may be fruitful. Mc Dougall and Woodworth insist on readiness for reaching a goal in learning and Lloyd Morgan lays stress on persistency with varied efforts till the goal of learning is achieved. The hungry cat confined in the puzzle-box with food in front of it goes on persistently trying various means until it gets out of it and has food. So, its trials are not blind and mechanical. In fact, they are guided by perceptual attention and feelings of pleasure and pain. Yet, Thorndike pays no attention to these higher order mental processes.

Secondly, in course or repeated trials the numbers of errors are not corrected of themselves or mechanically. The effects of Trial and Error depend to a great extent upon the psycho-physical state of the animal or man. In the absence of any purpose in view the animal is so puzzled, rather than enlightened by the errors committed that it goes on blindly repeating them without end.

Thirdly, Thorndike assumes that learning consists only in the association of several separate movements. But, learning is a whole process related to a whole situation. The hungry cat confined in a puzzle-box with food placed near it does not perceive the situation in a piece-meal fashion but as a whole of hunger food-puzzle box-confinement.

Finally, the laws of learning formulated by Thorndike appear to be unjustified. For instance, the ‘law of effect’ seems to be in consistent with his mechanical point of view. Satisfaction in or the sense of being rewarded by success and dissatisfaction in or the sense of being punished by failure seen to ascribe higher mental processes to animals like cats and rats than are psychologically ascribable to them. Or, it violates Lloyd Morgans’s law.

Similarly, the ‘Law of Exercise’ has been severely criticised on the grounds that it does not regard other factors like motives, interests, special training etc. Mechanical repetition without motive, interest, significance or understanding does not make anyone learn anything and remember it. One rupee-currency note passes hundred times through the hand of a person, but hardly anyone is able to tell the size, the colour and other details of it.

A boy was asked to write hundred times ‘I have gone’ after school. He wrote it mechanically and correctly all the times. But, when he left the school in the absence of the teacher, he wrote “I have written,” ‘I have gone’ correctly one hundred times and since you are not here “I have went home”. After repeating one correct thing so many times he again committed the same mistake. This shows that repetition without motive, interest or understanding is of no avail.

Thus, learning by Trial and Error is not of very much use and should not be resorted to by the teacher as it lays a stress on cramming. Also, there is much wastage of time and energy by this method.

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means-ends analysis

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means-ends analysis , heuristic , or trial-and-error, problem-solving strategy in which an end goal is identified and then fulfilled via the generation of subgoals and action plans that help overcome obstacles encountered along the way. Solving a problem with means-ends analysis typically begins by examining the end goal and breaking it down into subgoals. Actions needed to achieve each subgoal are then developed. In some cases, subgoals are further broken down into sub-subgoals. When all of the subgoals have been achieved (or obstacles eliminated), the end goal has been met.

The idea of problem solving by means-ends analysis was introduced in 1972 by American computer scientists Allen Newell and Herbert A. Simon in their book Human Problem Solving . They developed the theory in the late 1950s and early ’60s while generating a computer model capable of simulating human problem solving, working with John Clifford Shaw, a scientist and computer expert at the RAND Corporation , where beginning in 1950 Newell also worked as a researcher. The scientists called their model the General Problem Solver (GPS). GPS would recursively apply heuristic techniques in solving a given problem and conduct a means-ends assessment after each subproblem was solved to determine whether it was closer to the intended solution. Through this process, GPS could find solutions to mathematical theorems, logical proofs, word problems, and a wide variety of other well-defined problems. (Newell and Simon received the 1975 Turing Award for their research pertaining to human cognition and artificial intelligence .)

Means-ends analysis is unique among problem-solving algorithms in that it emphasizes the generation of subgoals that directly contribute to reaching the end goal. The subgoals are not necessarily of the same type. In other approaches, namely divide-and-conquer, subproblems are created that are then solved recursively and are finally combined to solve the end problem; with divide-and-conquer, the subproblems are always of the same type.

An example of the process of carrying out means-ends analysis can be illustrated by using the end goal of having a well-designed, well-functioning website. Possible subgoals and sub-subgoals include:

technical setup, such as choosing a web hosting service, registering a domain name , and setting up the hosting environment and linking the domain;

design, involving the creation of a layout for the homepage, the creation of landing pages and interior pages, the selection of a colour scheme and typography, and the design of menus, buttons, and other interactive elements;

coding, with a need to learn coding languages and the coding and implementation of interactive elements;

content development, such as writing content and gathering images and videos;

testing browser compatibility, with testing of the website on different browsers and on different devices; and

testing and debugging to make sure the website functions properly, test interactive elements, and fix formatting issues, bugs, or inconsistencies.

Means-ends analysis is frequently used in artificial intelligence (AI) systems. As a goal-based problem-solving technique, it plays a significant role in creating AI systems that exhibit humanlike behaviour, because the algorithmic steps involved in the analysis simulate aspects of human cognition and problem-solving skills. AI systems also use means-ends analysis for limiting searches in programs by evaluating the difference between the current state of a problem and the goal state, while using a combination of backward and forward search techniques.

Businesses and organizations use means-ends analysis for planning, project management, and transformation projects. In project management, for example, means-end analysis can be used to break down complex projects into subprojects and then to track the progress of those subprojects. It is used in transformation projects to implement changes to business processes by splitting new processes into subprocesses.

Research has been conducted on applying means-ends analysis to product marketing campaigns for brand persuasion purposes. For example, in the 1990s, researchers applied means-ends analysis to study how consumers link a product’s attributes with the consequences (benefits) of using the product and how the attributes and consequences align with personal values. Such studies supported the effectiveness of means-ends analysis in brand persuasion. Later research confirmed the effectiveness of means-ends analysis and its suitability for a wide range of marketing applications and suggested the development of additional methodologies for analyzing observations.

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Problem-Solving Strategies and Obstacles

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

7.3 Problem Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving and decision making

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

Problem-Solving Strategies

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( Table 7.2 ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Everyday Connection

Solving puzzles.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( Figure 7.7 ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

Here is another popular type of puzzle ( Figure 7.8 ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Take a look at the “Puzzling Scales” logic puzzle below ( Figure 7.9 ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

Pitfalls to Problem Solving

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but they just need to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. Duncker (1945) conducted foundational research on functional fixedness. He created an experiment in which participants were given a candle, a book of matches, and a box of thumbtacks. They were instructed to use those items to attach the candle to the wall so that it did not drip wax onto the table below. Participants had to use functional fixedness to overcome the problem ( Figure 7.10 ). During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

Check out this Apollo 13 scene about NASA engineers overcoming functional fixedness to learn more.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in Table 7.3 .

Watch this teacher-made music video about cognitive biases to learn more.

Were you able to determine how many marbles are needed to balance the scales in Figure 7.9 ? You need nine. Were you able to solve the problems in Figure 7.7 and Figure 7.8 ? Here are the answers ( Figure 7.11 ).

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4 Main problem-solving strategies

In Psychology, you get to read about a ton of therapies. It’s mind-boggling how different theorists have looked at human nature differently and have come up with different, often somewhat contradictory, theoretical approaches.

Yet, you can’t deny the kernel of truth that’s there in all of them. All therapies, despite being different, have one thing in common- they all aim to solve people’s problems. They all aim to equip people with problem-solving strategies to help them deal with their life problems.

Problem-solving is really at the core of everything we do. Throughout our lives, we’re constantly trying to solve one problem or another. When we can’t, all sorts of psychological problems take hold. Getting good at solving problems is a fundamental life skill.

Problem-solving stages

What problem-solving does is take you from an initial state (A) where a problem exists to a final or goal state (B), where the problem no longer exists.

To move from A to B, you need to perform some actions called operators. Engaging in the right operators moves you from A to B. So, the stages of problem-solving are:

• Initial state

The problem itself can either be well-defined or ill-defined. A well-defined problem is one where you can clearly see where you are (A), where you want to go (B), and what you need to do to get there (engaging the right operators).

For example, feeling hungry and wanting to eat can be seen as a problem, albeit a simple one for many. Your initial state is hunger (A) and your final state is satisfaction or no hunger (B). Going to the kitchen and finding something to eat is using the right operator.

In contrast, ill-defined or complex problems are those where one or more of the three problem solving stages aren’t clear. For example, if your goal is to bring about world peace, what is it exactly that you want to do?

It’s been rightly said that a problem well-defined is a problem half-solved. Whenever you face an ill-defined problem, the first thing you need to do is get clear about all the three stages.

Often, people will have a decent idea of where they are (A) and where they want to be (B). What they usually get stuck on is finding the right operators.

Initial theory in problem-solving

When people first attempt to solve a problem, i.e. when they first engage their operators, they often have an initial theory of solving the problem. As I mentioned in my article on overcoming challenges for complex problems, this initial theory is often wrong.

But, at the time, it’s usually the result of the best information the individual can gather about the problem. When this initial theory fails, the problem-solver gets more data, and he refines the theory. Eventually, he finds an actual theory i.e. a theory that works. This finally allows him to engage the right operators to move from A to B.

Problem-solving strategies

These are operators that a problem solver tries to move from A to B. There are several problem-solving strategies but the main ones are:

• Trial and error

1. Algorithms

When you follow a step-by-step procedure to solve a problem or reach a goal, you’re using an algorithm. If you follow the steps exactly, you’re guaranteed to find the solution. The drawback of this strategy is that it can get cumbersome and time-consuming for large problems.

Say I hand you a 200-page book and ask you to read out to me what’s written on page 100. If you start from page 1 and keep turning the pages, you’ll eventually reach page 100. There’s no question about it. But the process is time-consuming. So instead you use what’s called a heuristic.

2. Heuristics

Heuristics are rules of thumb that people use to simplify problems. They’re often based on memories from past experiences. They cut down the number of steps needed to solve a problem, but they don’t always guarantee a solution. Heuristics save us time and effort if they work.

You know that page 100 lies in the middle of the book. Instead of starting from page one, you try to open the book in the middle. Of course, you may not hit page 100, but you can get really close with just a couple of tries.

If you open page 90, for instance, you can then algorithmically move from 90 to 100. Thus, you can use a combination of heuristics and algorithms to solve the problem. In real life, we often solve problems like this.

When police are looking for suspects in an investigation, they try to narrow down the problem similarly. Knowing the suspect is 6 feet tall isn’t enough, as there could be thousands of people out there with that height.

Knowing the suspect is 6 feet tall, male, wears glasses, and has blond hair narrows down the problem significantly.

3. Trial and error

When you have an initial theory to solve a problem, you try it out. If you fail, you refine or change your theory and try again. This is the trial-and-error process of solving problems. Behavioral and cognitive trial and error often go hand in hand, but for many problems, we start with behavioural trial and error until we’re forced to think.

Say you’re in a maze, trying to find your way out. You try one route without giving it much thought and you find it leads to nowhere. Then you try another route and fail again. This is behavioural trial and error because you aren’t putting any thought into your trials. You’re just throwing things at the wall to see what sticks.

This isn’t an ideal strategy but can be useful in situations where it’s impossible to get any information about the problem without doing some trials.

Then, when you have enough information about the problem, you shuffle that information in your mind to find a solution. This is cognitive trial and error or analytical thinking. Behavioral trial and error can take a lot of time, so using cognitive trial and error as much as possible is advisable. You got to sharpen your axe before you cut the tree.

When solving complex problems, people get frustrated after having tried several operators that didn’t work. They abandon their problem and go on with their routine activities. Suddenly, they get a flash of insight that makes them confident they can now solve the problem.

I’ve done an entire article on the underlying mechanics of insight . Long story short, when you take a step back from your problem, it helps you see things in a new light. You make use of associations that were previously unavailable to you.

You get more puzzle pieces to work with and this increases the odds of you finding a path from A to B, i.e. finding operators that work.

Pilot problem-solving

No matter what problem-solving strategy you employ, it’s all about finding out what works. Your actual theory tells you what operators will take you from A to B. Complex problems don’t reveal their actual theories easily solely because they are complex.

Therefore, the first step to solving a complex problem is getting as clear as you can about what you’re trying to accomplish- collecting as much information as you can about the problem.

This gives you enough raw materials to formulate an initial theory. We want our initial theory to be as close to an actual theory as possible. This saves time and resources.

Solving a complex problem can mean investing a lot of resources. Therefore, it is recommended you verify your initial theory if you can. I call this pilot problem-solving.

Before businesses invest in making a product, they sometimes distribute free versions to a small sample of potential customers to ensure their target audience will be receptive to the product.

Before making a series of TV episodes, TV show producers often release pilot episodes to figure out whether the show can take off.

Before conducting a large study, researchers do a pilot study to survey a small sample of the population to determine if the study is worth carrying out.

The same ‘testing the waters’ approach needs to be applied to solving any complex problem you might be facing. Is your problem worth investing a lot of resources in? In management, we’re constantly taught about Return On Investment (ROI). The ROI should justify the investment.

If the answer is yes, go ahead and formulate your initial theory based on extensive research. Find a way to verify your initial theory. You need this reassurance that you’re going in the right direction, especially for complex problems that take a long time to solve.

Getting your causal thinking right

Problem solving boils down to getting your causal thinking right. Finding solutions is all about finding out what works, i.e. finding operators that take you from A to B. To succeed, you need to be confident in your initial theory (If I do X and Y, they’ll lead me to B). You need to be sure that doing X and Y will lead you to B- doing X and Y will cause B.

All obstacles to problem-solving or goal-accomplishing are rooted in faulty causal thinking leading to not engaging the right operators. When your causal thinking is on point, you’ll have no problem engaging the right operators.

As you can imagine, for complex problems, getting our causal thinking right isn’t easy. That’s why we need to formulate an initial theory and refine it over time.

I like to think of problem-solving as the ability to project the present into the past or into the future. When you’re solving problems, you’re basically looking at your present situation and asking yourself two questions:

“What caused this?” (Projecting present into the past)

“What will this cause?” (Projecting present into the future)

The first question is more relevant to problem-solving and the second to goal-accomplishing.

If you find yourself in a mess , you need to answer the “What caused this?” question correctly. For the operators you’re currently engaging to reach your goal, ask yourself, “What will this cause?” If you think they cannot cause B, it’s time to refine your initial theory.

Hi, I’m Hanan Parvez (MA Psychology). I’ve published over 500 articles and authored one book. My work has been featured in Forbes , Business Insider , Reader’s Digest , and Entrepreneur .

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Trial and error

Imagine that you wake up in the morning, turn on your computer to do some study, and then discover your Wi-Fi isn’t working. First, you run a diagnostic test on your computer, but it doesn’t uncover anything. Next, you restart your computer, and still no luck. Lastly, you reboot your modem router, and… success!

The process you have just used is called trial and error, and it can be used to solve small problems like the one you had with your Wi-Fi. It can also be a powerful method in controlled situations for scientific breakthroughs, inventions, and developing new products. The idea is that you keep trying different approaches until you find one that works. The benefit of trial and error is that it allows you to test certain ideas (or hypotheses) to see if they are an effective solution to a problem. You can then take what you’ve learnt from your trials (and errors) and use it to make adjustments and to guide your next moves.

The downsides are that it can take time to conduct these trials, and this technique can’t be used in all situations. In some cases, a simple error could lead to disaster. For example, if you work as a bomb disposal expert and you need to disarm an explosive, cutting wires until you find the right one probably wouldn’t be a good idea!

• Can you think of another example of a situation in which it would not be a good idea to use trial and error?
• What about a situation in which trial and error would be a good strategy to use?

Answer the following questions to identify in which situations trial and error would be a good problem-solving technique to use.

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7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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8 Effective Problem-Solving Strategies

Categories Cognition

If you need to solve a problem, there are a number of different problem-solving strategies that can help you come up with an accurate decision. Sometimes the best choice is to use a step-by-step approach that leads to the right solution, but other problems may require a trial-and-error approach. 

Some helpful problem-solving strategies include: Brainstorming Step-by-step algorithms Trial-and-error Working backward Heuristics Insight Writing it down Getting some sleep

Table of Contents

Why Use Problem-Solving Strategies

While you can always make a wild guess or pick at random, that certainly isn’t the most accurate way to come up with a solution. Using a more structured approach allows you to:

• Understand the nature of the problem
• Determine how you will solve it
• Research different options
• Take steps to solve the problem and resolve the issue

There are many tools and strategies that can be used to solve problems, and some problems may require more than one of these methods in order to come up with a solution.

Problem-Solving Strategies

The problem-solving strategy that works best depends on the nature of the problem and how much time you have available to make a choice. Here are eight different techniques that can help you solve whatever type of problem you might face.

Brainstorming

Coming up with a lot of potential solutions can be beneficial, particularly early on in the process. You might brainstorm on your own, or enlist the help of others to get input that you might not have otherwise considered.

Step-by-Step

Also known as an algorithm, this approach involves following a predetermined formula that is guaranteed to produce the correct result. While this can be useful in some situations—such as solving a math problem—it is not always practical in every situation.

On the plus side, algorithms can be very accurate and reliable. Unfortunately, they can also be time-consuming.

And in some situations, you cannot follow this approach because you simply don’t have access to all of the information you would need to do so.

Trial-and-Error

This problem-solving strategy involves trying a number of different solutions in order to figure out which one works best. This requires testing steps or more options to solve the problem or pick the right solution. 

For example, if you are trying to perfect a recipe, you might have to experiment with varying amounts of a certain ingredient before you figure out which one you prefer.

On the plus side, trial-and-error can be a great problem-solving strategy in situations that require an individualized solution. However, this approach can be very time-consuming and costly.

Working Backward

This problem-solving strategy involves looking at the end result and working your way back through the chain of events. It can be a useful tool when you are trying to figure out what might have led to a particular outcome.

It can also be a beneficial way to play out how you will complete a task. For example, if you know you need to have a project done by a certain date, working backward can help you figure out the steps you’ll need to complete in order to successfully finish the project.

Heuristics are mental shortcuts that allow you to come up with solutions quite quickly. They are often based on past experiences that are then applied to other situations. They are, essentially, a handy rule of thumb.

For example, imagine a student is trying to pick classes for the next term. While they aren’t sure which classes they’ll enjoy the most, they know that they tend to prefer subjects that involve a lot of creativity. They utilize this heuristic to pick classes that involve art and creative writing.

The benefit of a heuristic is that it is a fast way to make fairly accurate decisions. The trade-off is that you give up some accuracy in order to gain speed and efficiency.

Sometimes, the solution to a problem seems to come out of nowhere. You might suddenly envision a solution after struggling with the problem for a while. Or you might abruptly recognize the correct solution that you hadn’t seen before. 

No matter the source, insight-based problem-solving relies on following your gut instincts. While this may not be as objective or accurate as some other problem-solving strategies, it can be a great way to come up with creative, novel solutions.

Write It Down

Sometimes putting the problem and possible solutions down in paper can be a useful way to visualize solutions. Jot down whatever might help you envision your options. Draw a picture, create a mind map, or just write some notes to clarify your thoughts.

Get Some Sleep

If you’re facing a big problem or trying to make an important decision, try getting a good night’s sleep before making a choice. Sleep plays an essential role in memory consolidation, so getting some rest may help you access the information or insight you need to make the best choice.

Other Considerations

Even with an arsenal of problem-solving strategies at your disposal, coming up with solutions isn’t always easy. Certain challenges can make the process more difficult. A few issues that might emerge include:

• Mental set : When people form a mental set, they only rely on things that have worked in the last. Sometimes this can be useful, but in other cases, it can severely hinder the problem-solving process.
• Cognitive biases : Unconscious cognitive biases can make it difficult to see situations clearly and objectively. As a result, you may not consider all of your options or ignore relevant information.
• Misinformation : Poorly sourced clues and irrelevant details can add more complications. Being able to sort out what’s relevant and what’s not is essential for solving problems accurately.
• Functional fixedness : Functional fixedness happens when people only think of customary solutions to problems. It can hinder out-of-the-box thinking and prevents insightful, creative solutions.

Important Problem-Solving Skills

Becoming a good problem solver can be useful in a variety of domains, from school to work to interpersonal relationships. Important problem-solving skills encompass being able to identify problems, coming up with effective solutions, and then implementing these solutions.

According to a 2023 survey by the National Association of Colleges and Employers, 61.4% of employers look for problem-solving skills on applicant resumes.

Some essential problem-solving skills include:

• Research skills
• Analytical abilities
• Decision-making skills
• Critical thinking
• Communication
• Time management 
• Emotional intelligence

Solving a problem is complex and requires the ability to recognize the issue, collect and analyze relevant data, and make decisions about the best course of action. It can also involve asking others for input, communicating goals, and providing direction to others.

How to Become a Better Problem-Solver

If you’re ready to strengthen your problem-solving abilities, here are some steps you can take:

Identify the Problem

Before you can practice your problem-solving skills, you need to be able to recognize that there is a problem. When you spot a potential issue, ask questions about when it started and what caused it.

Do Your Research

Instead of jumping right in to finding solutions, do research to make sure you fully understand the problem and have all the background information you need. This helps ensure you don’t miss important details.

Hone Your Skills

Consider signing up for a class or workshop focused on problem-solving skill development. There are also books that focus on different methods and approaches.

The best way to strengthen problem-solving strategies is to give yourself plenty of opportunities to practice. Look for new challenges that allow you to think critically, analytically, and creatively.

Final Thoughts

If you have a problem to solve, there are plenty of strategies that can help you make the right choice. The key is to pick the right one, but also stay flexible and willing to shift gears.

In many cases, you might find that you need more than one strategy to make the choices that are right for your life.

Brunet, J. F., McNeil, J., Doucet, É., & Forest, G. (2020). The association between REM sleep and decision-making: Supporting evidences. Physiology & Behavior , 225, 113109. https://doi.org/10.1016/j.physbeh.2020.113109

Chrysikou, E. G, Motyka, K., Nigro, C., Yang, S. I. , & Thompson-Schill, S. L. (2016). Functional fixedness in creative thinking tasks depends on stimulus modality. Psychol Aesthet Creat Arts , 10(4):425‐435. https://doi.org/10.1037/aca0000050

Sarathy, V. (2018). Real world problem-solving. Front Hum Neurosci , 12:261. https://doi.org/10.3389/fnhum.2018.00261

Chapter 7: Thinking and Intelligence

Problem solving, learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

PROBLEM-SOLVING STRATEGIES

When you are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them ( [link] ). For example, a well-known strategy is trial and error . The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below ( [link] ) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

Here is another popular type of puzzle ( [link] ) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

Take a look at the “Puzzling Scales” logic puzzle below ( [link] ). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

PITFALLS TO PROBLEM SOLVING

Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

Link to Learning

Check out this Apollo 13 scene where the group of NASA engineers are given the task of overcoming functional fixedness.

Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in [link] .

Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students.

Were you able to determine how many marbles are needed to balance the scales in [link] ? You need nine. Were you able to solve the problems in [link] and [link] ? Here are the answers ( [link] ).

Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

Self Check Questions

Critical thinking questions.

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question

3. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

1. Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

2. An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel.

• Psychology. Authored by : OpenStax College. Located at : http://cnx.org/contents/[email protected]:1/Psychology . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/content/col11629/latest/.

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Trial and Error

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• Andrew Hayes

Trial and error refers to the process of verifying that a certain choice is right (or wrong). We simply substitute that choice into the problem and check. Some questions can only be solved by trial and error; for others we must first decide if there isn't a faster way to arrive at the answer. In the examples to follow, we test all choices for your benefit. Once you have the right answer, there is no need to check the rest of the choices.

\[(2, 3), (3, 5), (4, 4), (6, 3), (10, 0)\] How many of the above pairs of integers are solutions to \( 2x + 3y = 20 ?\) (A) \(\ \ 1\) (B) \(\ \ 2\) (C) \(\ \ 3\) (D) \(\ \ 4\) (E) \(\ \ 5\) Show Answer Correct Answer: B Solution: We try each of the pairs of integers: For \((2, 3)\), we have \( 2 \times 2 + 3 \times 3 = 4 + 9 = 13 \neq 20 \). For \((3, 5)\), we have \( 2 \times 3 + 3 \times 5 = 6 + 15 = 21 \neq 20 \). For \((4, 4)\), we have \( 2 \times 4 + 3 \times 4 = 8 + 12 = 20 \). This is a solution. For \((6, 3)\), we have \( 2 \times 6 + 3 \times 3 = 12 + 9 = 21 \neq 20 \). For \((10, 0)\), we have \( 2 \times 10 + 3 \times 0 = 20 + 0 = 20 \). This is a solution. Thus, 2 of the pairs are solutions. Incorrect Choices: (A) , (C) , (D) , and (E) See the solution for why these choices are wrong.

\[ ab - 2a - 2b - 2 = 0 \]

Which of the following pairs of numbers \( (a, b) \) is a solution to the equation above?

• \( (3, 8) \)
• \( (4, 5 ) \)
• \( (4.5, 4.5) \)

(A)\(\ \ \) I only (B)\(\ \ \) II only (C)\(\ \ \) I and II only (D)\(\ \ \) I and III only (E)\(\ \ \) I, II and III

When the wind blows, half of the leaves on a tree fall, and then 5 more. When the wind blows a second time, again half of the leaves fall and then 5 more. If there are no leaves remaining on the tree, how many leaves are there at the start? (A) \(\ \ 5\) (B) \(\ \ 10\) (C) \(\ \ 15\) (D) \(\ \ 30\) (E) \(\ \ 50\) Show Answer Correct Answer: D Solution 1: Let's analyze each answer using the trial and error approach. (A) If there are 5 leaves at the start, when the wind blows the first time, half of the leaves fall, which is 2.5, and then 5 more, so there are \( 5 - 2.5 - 5 = - 2.5 \) leaves left. This does not make sense, so we eliminate this choice. (B) If there are 10 leaves at the start, when the wind blows the first time, half of the leaves fall, which is 5, and then 5 more, so there are \( 10 - 5 - 5 = 0 \) leaves left. When the wind blows the second time, half of the remaining leaves fall, which is 0, and then 5 more. Thus there are \( 0 - 0 - 5 = - 5 \) leaves left. This does not make sense, so we eliminate this choice. (C) If there are 15 leaves at the start, when the wind blows the first time, half of the leaves fall, which is 7.5, and then 5 more. Thus there are \( 15 - 7.5 - 5 = 2.5 \) leaves left. When the wind blows the second time, it blows down half of the remaining leaves, which is 1.25, and then 5 more. Thus there are \( 2.5 - 1.25 - 5 = -3.75 \) leaves left. Wrong choice. (D) If there are 30 leaves at the start, when the wind blows the first time, half of the leaves fall, which is 5, and then 5 more. Thus there are \( 30 - 15 - 5 = 10 \) leaves left. When the wind blows the second time, half of the remaining leaves fall, which is 5, and then 5 more. Thus there are \( 10 - 5 - 5 = 0 \) leaves left. This is the correct answer. (E) If there are 50 leaves at the start, when the wind blows the first time, half of the leaves fall, which is 25, and then 5 more. Thus there are \( 50- 25 - 5 = 20 \) leaves left. When the wind blows the second time, it blows down half of the remaining leaves, which is 10, and then 5 more. Thus there are \( 20 - 10 - 5 = 5 \) leaves left. But we are told that no leaves remain on the tree. Wrong choice. Thus, the answer is (D). Solution 2: We can solve this problem by working backwards. At the end, we are left with 0 leaves. Just before that, 5 leaves fall, so there were 5 leaves on the tree. Just before that, half of the leaves fall, so there are \(2\cdot 5=10\) leaves on the tree. Just before that, 5 leaves fall, so there are \(10+5=15\) leaves on the tree. And just before that, half of the leaves fall, so there are \(2\cdot 15=30\) leaves on the tree. Incorrect Choices: (A) This is the number of leaves that are blown down right at the end. (B) This is the number of leaves that are on the tree before the second wind. (C) This is the number of leaves that are on the tree just after the first wind blows half of the leaves down. (E) This choice is offered to confused you.

There are several people in a meeting, and each pair of them shake hands. If there are a total of 210 handshakes, how many people are in the meeting? (A)\(\ \ \) 14 (B)\(\ \ \) 15 (C)\(\ \ \) 18 (D)\(\ \ \) 20 (E)\(\ \ \) 21 Show Answer Correct Answer: E Solution: If there are \(n\) people at the meeting, each person will shake hands with \(n-1\) other people (a person cannot shake hands with himself). So, there are \(n\cdot (n-1)\) ways we can pair the people at the meeting. But, the number of handshakes isn't equal to the number of ways we can pair the people. Since the handshake between person A and person B is the same as the handshake between person B and person A, we must divide \(n\cdot (n-1)\) by 2 so as to not count each handshake twice. Let's analyze each answer choice. (A) If there are 14 people, there will be \( \frac{14 \times 13 } { 2} = 91 \) handshakes. Wrong choice. (B) If there are 15 people, there will be \( \frac{15 \times 14 } { 2} = 105 \) handshakes. Wrong choice. (C) If there are 18 people, there will be \( \frac{18 \times 17 } { 2} = 153 \) handshakes. Wrong choice. (D) If there are 20 people, there will be \( \frac{20 \times 19 } { 2} = 190 \) handshakes. Wrong choice. (E) If there are 21 people, there will be \( \frac{21 \times 20 } { 2} = 210 \) handshakes. Correct answer. Incorrect Choices: (A) , (B) , (C) , and (D) The solution explains how to eliminate these choices.

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