teaching of heuristic problem solving strategies

Heuristic Method Of Teaching: A Guide for Teachers

The heuristic method is a student-centered approach that actively encourages learners to explore and discover knowledge through problem-solving and inquiry-based learning.

In this article, I will delve into the origin and development of the heuristic method, explain its principles and steps, discuss its advantages and disadvantages, provide examples of successful implementation, and explore ways to incorporate it into different subjects.

Table of Contents

The origin and development of the heuristic method of teaching

The renowned mathematician George Pólya developed the heuristic teaching method in the early 20th century . Pólya believed students should be taught how to think rather than what to think.

He recognized the importance of problem-solving and inquiry as effective ways to deepen understanding and foster creativity.

Pólya’s groundbreaking book, “How to Solve It,” outlined a four-step problem-solving process that became the foundation of the heuristic method.

Understanding the heuristic method of teaching

What exactly is the heuristic method of teaching? At its core, it is an approach that encourages students to actively engage in problem-solving, critical thinking, and self-directed learning.

Unlike traditional teaching methods focusing on rote memorization and passive learning, the heuristic method empowers students to take ownership of their learning journey .

Teachers can guide students toward discovering solutions and constructing their knowledge by posing open-ended questions, encouraging exploration, and promoting independent thinking.

Applying the heuristic method of teaching in mathematics

Mathematics is an ideal subject for implementing the heuristic teaching method due to its inherent problem-solving nature. When teaching mathematics using the heuristic method, teachers present students with challenging problems that require them to think critically and apply mathematical concepts and principles.

Instead of providing step-by-step solutions, teachers guide students through problem-solving, encouraging them to explore different strategies, make connections, and justify their reasoning.

This approach enhances students’ mathematical skills and develops their problem-solving abilities, critical thinking, and perseverance.

Steps involved in the heuristic method of teaching

There are several steps that teachers should follow to implement the heuristic method of teaching effectively. Firstly, teachers must present students with open-ended problems that stimulate their curiosity and require them to think critically.

Secondly, teachers should guide students in exploring different problem-solving strategies, encouraging them to brainstorm ideas and consider multiple approaches.

Thirdly, students should be free to experiment, make mistakes, and learn from errors. Fourthly, teachers should facilitate discussions and provide guidance, asking probing questions to deepen students’ understanding and prompt reflection.

Advantages of using the heuristic method of teaching

The heuristic method of teaching offers several advantages over traditional teaching methods. Firstly, it promotes active engagement and student-centered learning, fostering a sense of ownership and autonomy.

Students participate actively in their learning journey, developing problem-solving skills, critical thinking abilities, and creativity.

Secondly, the heuristic method encourages students to think outside the box and explore different perspectives, enhancing their ability to tackle complex problems in various domains.

Thirdly, by focusing on the process rather than the final answer, the heuristic method cultivates a growth mindset and resilience in students, instilling the belief that mistakes are opportunities for learning and growth.

Disadvantages and challenges of the heuristic method of teaching

While the heuristic teaching method has numerous advantages, it has challenges. One of the main difficulties teachers may face is the time-consuming nature of the approach.

Guiding students through the problem-solving process and facilitating discussions can be time-intensive, making it challenging to cover a wide range of topics within a limited timeframe.

Additionally, implementing the heuristic method requires a shift in the traditional teacher-student dynamic, which may require additional training and support for educators.

Finally, assessing students’ understanding and progress can be more complex in a heuristic classroom, as the focus is on the process rather than the final answer.

Examples of successful implementation of the heuristic method of teaching

Numerous educators have successfully implemented the heuristic method of teaching across different subjects.

For example, teachers have used open-ended problems to engage students in authentic mathematical thinking. Students are encouraged to explore multiple strategies, justify their reasoning, and communicate their thought processes.

Similarly, in science, the heuristic method can be applied by posing real-world problems that require students to apply scientific concepts and conduct investigations.

Incorporating the heuristic method of teaching different subjects

While the heuristic method of teaching has been commonly associated with mathematics and science, it can be adapted and incorporated into various subjects.

In literature, for instance, students can explore different interpretations of texts, engage in discussions, and analyze complex themes and characters. In history, students can investigate primary sources, critically evaluate historical events, and draw connections to contemporary issues.

By applying the principles of the heuristic method, teachers can create dynamic and interactive learning experiences that transcend traditional subject boundaries.

Conclusion: Embracing the power of the heuristic method in education

In conclusion, the heuristic method of teaching is a powerful approach that empowers students to become active learners, critical thinkers, and problem solvers.

By embracing this student-centered approach, educators can foster a love for learning, develop essential skills, and cultivate a growth mindset in their students.

While implementing the heuristic method may present challenges, the benefits far outweigh the difficulties. We can unleash their full potential and prepare them for success in an ever-evolving world by providing students with opportunities to explore, discover, and construct knowledge.

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Research in the area of computer simulation of human thought processes indicates that the solution of every problem involves the element of search in a space of many alternatives (Newell, Shaw, & Simon, 1958). For human problem solving, the space may conceivably include infinitely many alternatives; however, humans appear to exhibit more efficient performance than exhaustive scanning or purely random trial and error. Human problem solving is characterized by heuristic strategies . These higher-order processes (heuristics) guide the search, enabling the problem solver to select from a reduced set of alternatives and to order his solution process in a sequence of steps; they are tentative rules of thumb that are based on experience or plausible assumptions and that apply generally to problems (Pylyshyn, 1963).

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What Are Heuristics?

These mental shortcuts can help people make decisions more efficiently

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

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

Verywell / Cindy Chung 

• History and Origins
• Heuristics vs. Algorithms
• Heuristics and Bias

How to Make Better Decisions

Heuristics are mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. These rule-of-thumb strategies shorten decision-making time and allow people to function without constantly stopping to think about their next course of action.

However, there are both benefits and drawbacks of heuristics. While heuristics are helpful in many situations, they can also lead to  cognitive biases . Becoming aware of this might help you make better and more accurate decisions.

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The History and Origins of Heuristics

Nobel-prize winning economist and cognitive psychologist Herbert Simon originally introduced the concept of heuristics in psychology in the 1950s. He suggested that while people strive to make rational choices, human judgment is subject to cognitive limitations. Purely rational decisions would involve weighing all the potential costs and possible benefits of every alternative.

But people are limited by the amount of time they have to make a choice as well as the amount of information they have at their disposal. Other factors such as overall intelligence and accuracy of perceptions also influence the decision-making process.

During the 1970s, psychologists Amos Tversky and Daniel Kahneman presented their research on cognitive biases. They proposed that these biases influence how people think and the judgments people make.

As a result of these limitations, we are forced to rely on mental shortcuts to help us make sense of the world. Simon's research demonstrated that humans were limited in their ability to make rational decisions, but it was Tversky and Kahneman's work that introduced the study of heuristics and the specific ways of thinking that people rely on to simplify the decision-making process.

How Heuristics Are Used

Heuristics play important roles in both  problem-solving  and  decision-making , as we often turn to these mental shortcuts when we need a quick solution.

Here are a few different theories from psychologists about why we rely on heuristics.

• Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
• Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
• Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

In order to cope with the tremendous amount of information we encounter and to speed up the decision-making process, our brains rely on these mental strategies to simplify things so we don't have to spend endless amounts of time analyzing every detail.

You probably make hundreds or even thousands of decisions every day. What should you have for breakfast? What should you wear today? Should you drive or take the bus? Fortunately, heuristics allow you to make such decisions with relative ease and without a great deal of agonizing.

There are many heuristics examples in everyday life. When trying to decide if you should drive or ride the bus to work, for instance, you might remember that there is road construction along the bus route. You realize that this might slow the bus and cause you to be late for work. So you leave earlier and drive to work on an alternate route.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

Are Heuristics Good or Bad?

Heuristics aren't inherently good or bad, but there are pros and cons to using them to make decisions. While they can help us figure out a solution to a problem faster, they can also lead to inaccurate judgments about other people or situations.

Types of Heuristics

There are many different kinds of heuristics. While each type plays a role in decision-making, they occur during different contexts. Understanding the types can help you better understand which one you are using and when.

Availability

The availability heuristic  involves making decisions based upon how easy it is to bring something to mind. When you are trying to make a decision, you might quickly remember a number of relevant examples. Since these are more readily available in your memory, you will likely judge these outcomes as being more common or frequently occurring.

For example, if you are thinking of flying and suddenly think of a number of recent airline accidents, you might feel like air travel is too dangerous and decide to travel by car instead. Because those examples of air disasters came to mind so easily, the availability heuristic leads you to think that plane crashes are more common than they really are.

Familiarity

The familiarity heuristic refers to how people tend to have more favorable opinions of things, people, or places they've experienced before as opposed to new ones. In fact, given two options, people may choose something they're more familiar with even if the new option provides more benefits.

Representativeness

The representativeness heuristic  involves making a decision by comparing the present situation to the most representative mental prototype. When you are trying to decide if someone is trustworthy, you might compare aspects of the individual to other mental examples you hold.

A soft-spoken older woman might remind you of your grandmother, so you might immediately assume that she is kind, gentle, and trustworthy. However, this is an example of a heuristic bias, as you can't know someone trustworthy based on their age alone.

The affect heuristic involves making choices that are influenced by the emotions that an individual is experiencing at that moment. For example, research has shown that people are more likely to see decisions as having benefits and lower risks when they are in a positive mood. Negative emotions, on the other hand, lead people to focus on the potential downsides of a decision rather than the possible benefits.

The anchoring bias involves the tendency to be overly influenced by the first bit of information we hear or learn. This can make it more difficult to consider other factors and lead to poor choices. For example, anchoring bias can influence how much you are willing to pay for something, causing you to jump at the first offer without shopping around for a better deal.

Scarcity is a principle in heuristics in which we view things that are scarce or less available to us as inherently more valuable. The scarcity heuristic is one often used by marketers to influence people to buy certain products. This is why you'll often see signs that advertise "limited time only" or that tell you to "get yours while supplies last."

Trial and Error

Trial and error is another type of heuristic in which people use a number of different strategies to solve something until they find what works. Examples of this type of heuristic are evident in everyday life. People use trial and error when they're playing video games, finding the fastest driving route to work, and learning to ride a bike (or learning any new skill).

Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

Algorithms are step-by-step instructions that lead to predictable, reliable outcomes; whereas heuristics are mental shortcuts that are basically best guesses. Algorithms always lead to accurate outcomes, whereas, heuristics do not.

Examples of algorithms include instructions for how to put together a piece of furniture or a recipe for cooking a certain dish. Health professionals also create algorithms or processes to follow in order to determine what type of treatment to use on a patient.

How Heuristics Can Lead to Bias

While heuristics can help us solve problems and speed up our decision-making process, they can introduce errors. As in the examples above, heuristics can lead to inaccurate judgments about how commonly things occur and about how representative certain things may be.

Just because something has worked in the past does not mean that it will work again, and relying on a heuristic can make it difficult to see alternative solutions or come up with new ideas.

Heuristics can also contribute to stereotypes and  prejudice . Because people use mental shortcuts to classify and categorize people, they often overlook more relevant information and create stereotyped categorizations that are not in tune with reality.

While heuristics can be a useful tool, there are ways you can improve your decision-making and avoid cognitive bias at the same time.

We are more likely to make an error in judgment if we are trying to make a decision quickly or are under pressure to do so. Whenever possible, take a few deep breaths . Do something to distract yourself from the decision at hand. When you return to it, you may find you have a fresh perspective, or notice something you didn't before.

Identify the Goal

We tend to focus automatically on what works for us and make decisions that serve our best interest. But take a moment to know what you're trying to achieve. Are there other people who will be affected by this decision? What's best for them? Is there a common goal that can be achieved that will serve all parties?

Process Your Emotions

Fast decision-making is often influenced by emotions from past experiences that bubble to the surface. Is your decision based on facts or emotions? While emotions can be helpful, they may affect decisions in a negative way if they prevent us from seeing the full picture.

Recognize All-or-Nothing Thinking

When making a decision, it's a common tendency to believe you have to pick a single, well-defined path, and there's no going back. In reality, this often isn't the case.

Sometimes there are compromises involving two choices, or a third or fourth option that we didn't even think of at first. Try to recognize the nuances and possibilities of all choices involved, instead of using all-or-nothing thinking .

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Shah AK, Oppenheimer DM. Heuristics made easy: An effort-reduction framework . Psychol Bull. 2008;134(2):207-22. doi:10.1037/0033-2909.134.2.207

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77–89. PMID: 22577307

Schwikert SR, Curran T. Familiarity and recollection in heuristic decision making .  J Exp Psychol Gen . 2014;143(6):2341-2365. doi:10.1037/xge0000024

Finucane M, Alhakami A, Slovic P, Johnson S. The affect heuristic in judgments of risks and benefits . J Behav Decis Mak . 2000; 13(1):1-17. doi:10.1002/(SICI)1099-0771(200001/03)13:1<1::AID-BDM333>3.0.CO;2-S

Cheung TT, Kroese FM, Fennis BM, De Ridder DT. Put a limit on it: The protective effects of scarcity heuristics when self-control is low . Health Psychol Open . 2015;2(2):2055102915615046. doi:10.1177/2055102915615046

Mohr H, Zwosta K, Markovic D, Bitzer S, Wolfensteller U, Ruge H. Deterministic response strategies in a trial-and-error learning task . Inman C, ed. PLoS Comput Biol. 2018;14(11):e1006621. doi:10.1371/journal.pcbi.1006621

Lang JM, Ford JD, Fitzgerald MM.  An algorithm for determining use of trauma-focused cognitive-behavioral therapy .  Psychotherapy   (Chic) . 2010;47(4):554-69. doi:10.1037/a0021184

Bigler RS, Clark C. The inherence heuristic: A key theoretical addition to understanding social stereotyping and prejudice. Behav Brain Sci . 2014;37(5):483-4. doi:10.1017/S0140525X1300366X

del Campo C, Pauser S, Steiner E, et al.  Decision making styles and the use of heuristics in decision making .  J Bus Econ.  2016;86:389–412. doi:10.1007/s11573-016-0811-y

Marewski JN, Gigerenzer G. Heuristic decision making in medicine .  Dialogues Clin Neurosci . 2012;14(1):77-89. doi:10.31887/DCNS.2012.14.1/jmarewski

Zheng Y, Yang Z, Jin C, Qi Y, Liu X. The influence of emotion on fairness-related decision making: A critical review of theories and evidence .  Front Psychol . 2017;8:1592. doi:10.3389/fpsyg.2017.01592

Bazerman MH. Judgment and decision making. In: Biswas-Diener R, Diener E, eds.,  Noba Textbook Series: Psychology.  DEF Publishers.

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

Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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Center for Teaching

Teaching problem solving.

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Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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Heuristic Method

Heuristic Method: this article explains the concept of the Heuristic Method , developed by George Pólya in a practical way. After reading it, you will understand the basics of this powerful Problem Solving tool.

What is the Heuristic Method?

A heuristic method is an approach to finding a solution to a problem that originates from the ancient Greek word ‘eurisko’, meaning to ‘find’, ‘search’ or ‘discover’. It is about using a practical method that doesn’t necessarily need to be perfect. Heuristic methods speed up the process of reaching a satisfactory solution.

Previous experiences with comparable problems are used that can concern problem situations for people, machines or abstract issues. One of the founders of heuristics is the Hungarian mathematician György (George) Pólya , who published a book about the subject in 1945 called ‘How to Solve It’. He used four principles that form the basis for problem solving.

Heuristic method: Four principles

Pólya describes the following four principles in his book:

• try to understand the problem
• make a plan
• carry out this plan
• evaluate and adapt

If this sequence doesn’t lead to the right solution, Pólya advises to first look for a simpler problem.

A solution may potentially be found by first looking at a similar problem that was possible to solve. With this experience, it’s possible to look at the current problem in another way.

First principle of the heuristic method: understand the problem

It’s more difficult than it seems, because it seems obvious. In truth, people are hindered when it comes to finding an initially suitable approach to the problem.

It can help to draw the problem and to look at it from another angle. What is the problem, what is happening, can the problem be explained in other words, is there enough information available, etc. Such questions can help with the first evaluation of a problem issue.

Second principle of the heuristic method: make a plan

There are many ways to solve problems. This section is about choosing the right strategy that best fits the problem at hand. The reversed ‘working backwards’ can help with this; people assume to have a solution and use this as a starting point to work towards the problem.

It can also be useful to make an overview of the possibilities, delete some of them immediately, work with comparisons, or to apply symmetry. Creativity comes into play here and will improve the ability to judge.

Third principle of the heuristic method: carry out the plan

Once a strategy has been chosen, the plan can quickly be implemented. However, it is important to pay attention to time and be patient, because the solution will not simply appear.

If the plan doesn’t go anywhere, the advice is to throw it overboard and find a new way.

Fourth principle of the heuristic method: evaluate and adapt

Take the time to carefully consider and reflect upon the work that’s already been done. The things that are going well should be maintained, those leading to a lesser solution, should be adjusted. Some things simply work, while others simply don’t.

There are many different heuristic methods, which Pólya also used. The most well-known heuristics are found below:

1. Dividing technique

The original problem is divided into smaller sub-problems that can be solved more easily. These sub-problems can be linked to each other and combined, which will eventually lead to the solving of the original problem.

2. Inductive method

This involves a problem that has already been solved, but is smaller than the original problem. Generalisation can be derived from the previously solved problem, which can help in solving the bigger, original problem.

3. Reduction method

Because problems are often larger than assumed and deal with different causes and factors, this method sets limits for the problem in advance. This reduces the leeway of the original problem, making it easier to solve.

4. Constructive method

This is about working on the problem step by step. The smallest solution is seen as a victory and from that point consecutive steps are taken. This way, the best choices keep being made, which will eventually lead to a successful end result.

5. Local search method

This is about the search for the most attainable solution to the problem. This solution is improved along the way. This method ends when improvement is no longer possible.

Exact solutions versus the heuristic method

The heuristic approach is a mathmatical method with which proof of a good solution to a problem is delivered. There is a large number of different problems that could use good solutions. When the processing speed is equally as important as the obtained solution, we speak of a heuristic method.

The Heuristic Method only tries to find a good, but not necessarily optimal, solution. This is what differentiates heuristics from exact solution methods, which are about finding the optimal solution to a problem. However, that’s very time consuming, which is why a heuristic method may prove preferable. This is much quicker and more flexible than an exact method, but does have to satisfy a number of criteria.

It’s Your Turn

What do you think? Is the Heuristic Method applicable in your personal or professional environment? Do you recognize the practical explanation or do you have more suggestions? What are your success factors for solving problems

Share your experience and knowledge in the comments box below.

More information

• Groner, R., Groner, M., & Bischof, W. F. (2014). Methods of heuristics . Routledge .
• Newell, A. (1983). The heuristic of George Polya and its relation to artificial intelligence . Methods of heuristics, 195-243.
• Polya, G. (2014, 1945). How to solve it: A new aspect of mathematical method . Princeton university press .

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Published on: 29/05/2018 | Last update: 04/03/2022

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Patty Mulder

Patty Mulder is an Dutch expert on Management Skills, Personal Effectiveness and Business Communication. She is also a Content writer, Business Coach and Company Trainer and lives in the Netherlands (Europe). Note: all her articles are written in Dutch and we translated her articles to English!

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The Effect of Heuristic Training When Solving a Fermi Problem at Primary School

• First Online: 04 June 2024

Cite this chapter

• Marta Pla-Castells 13 ,
• Maria-Emilia Garcia-Marques 13 &
• Carmen Melchor-Borja 13  

Part of the book series: International Perspectives on the Teaching and Learning of Mathematical Modelling ((IPTL))

The use of heuristic strategies to solve problems, and as a part of the modelling problem-solving process, has been traditionally studied. This chapter aims to analyse, by means of an exploratory and qualitative study, how an instruction in different heuristics effects elementary school students’ performance when they solve a Fermi problem. We have determined a performance rate defined in terms of progress through the modelling cycle, and of the absence of mistakes made in solving the problem. Also, this rate is complemented with an analysis of the different strategies that appear in the resolution. The results indicate that heuristics training could have a beneficial effect on mathematical and modelling competences in the context of the resolution of a Fermi problem.

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Acknowledgements

This research is supported by R+D+I project PID2020-117395RB-I00 and the project UV-INV-AE-1557785 funded by Universitat de València-Estudi General.

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Pla-Castells, M., Garcia-Marques, ME., Melchor-Borja, C. (2024). The Effect of Heuristic Training When Solving a Fermi Problem at Primary School. In: Siller, HS., Geiger, V., Kaiser, G. (eds) Researching Mathematical Modelling Education in Disruptive Times. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-031-53322-8_36

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8.2 Problem-Solving: Heuristics and Algorithms

Learning objectives.

• Describe the differences between heuristics and algorithms in information processing.

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when looking for a library book, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in the table below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the table below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads” five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neibour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991).

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment does not just happen when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

Key Takeaways

• We use a variety of shortcuts in our information processing, such as the representativeness, availability, and anchoring and adjustment heuristics. These help us to make fast judgments but may lead to errors.
• Algorithms are problem-solving strategies that are based on rules rather than guesses. Algorithms, if applied correctly, are far less likely to result in errors or incorrect solutions than heuristics. Algorithms are based on logic.

Bennett, M. W. (2014). Confronting cognitive ‘anchoring effect’ and ‘blind spot’ biases in federal sentencing: A modest solution for reforming and fundamental flaw. Journal of Criminal Law and Criminology , 104 (3), 489-534.

Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.

MacLeod, C., & Campbell, L. (1992). Memory accessibility and probability judgments: An experimental evaluation of the availability heuristic.  Journal of Personality and Social Psychology, 63 (6), 890–902.

Poses, R. M., & Anthony, M. (1991). Availability, wishful thinking, and physicians’ diagnostic judgments for patients with suspected bacteremia.  Medical Decision Making,  11 , 159-68.

Rutledge, R. W. (1993). The effects of group decisions and group-shifts on use of the anchoring and adjustment heuristic. Social Behavior and Personality, 21 (3), 215-226.

Statistics Canada. (2018). Ho micide in Canada, 2017 . Retrieved from https://www150.statcan.gc.ca/n1/en/daily-quotidien/181121/dq181121a-eng.pdf

Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability.  Cognitive Psychology, 5 , 207–232.

Psychology - 1st Canadian Edition Copyright © 2020 by Sally Walters is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Heuristic Method of Teaching: How Is It Helpful For Teachers?

• June 12, 2023

Table of Content

Students have multiple interests and it can be anything from economics to artificial intelligence, anything. Teachers must help students to explore what they are truly passionate about on their own. Heuristic method of teaching is one of the best ways for experience based learning.

Using the heuristic teaching technique students can learn problem solving skills and they can discover their passions and learn more towards their interests. Heuristic method makes it easier for teachers to help their students identify their interests and then they can focus on improving their skills as per their interests. Let us clearly understand the heuristic method of teaching. 

What Is Heuristic Method of  Teaching?

A heuristic method of teaching is an instructional approach that emphasizes the use of problem-solving and discovery-based learning as well as experience-based learning  to facilitate student learning. Heuristic basically means any method or process that helps in problem-solving, self learning, and discovery.

Heuristic teaching approach means the teacher acts as more than an instructor  and encourages students to explore concepts, ideas, and problems. Teacher poses open-ended questions, encourages student participation, and guides students towards the results.

Objective of Heuristic Method of Teaching

• Objective: Encourage students to become independent learners and critical thinkers in life.
• Focus: Emphasize the learning process rather than just gaining knowledge.
• Applicability: Suitable for various subject areas.
• Effectiveness: Particularly effective in fields requiring problem-solving, critical thinking, and creativity.

Examples of heuristic methods include inquiry-based learning, problem-based learning, and project-based learning. Each of these methods encourage students to explore, discover, and develop solutions to real-world problems, rather than just learning  information. Heuristic method of teaching is a student-centered approach. 

Principles of Heuristic Methods of Teaching

There are some principles of heuristic teaching and it is important for teachers to know them. Let us understand the principles:

1. The Principle of Activity

The principle of activity means that self activity is the main component of this method. Students can learn by discovering on their own and this drives the self learning experience as well. 

2. The Principle of Laws of Learning

The laws of learning say that the problem should be as per the learner’s age and capabilities. It is based on the law of readiness. With this principle students learn a lot of things as they discover and face the consequences on their own they learn the law of cause and effect. 

3. The Principle of Logical Thinking

The principle of logical thinking or the heuristic method combines both inductive and deductive logical reasoning approaches, where students learn the fundamentals through various examples and experiments.

4. The Principle of Purposeful Experience

The principle of purposeful experience means  purposeful self-exploration, where students are encouraged to develop an understanding of the activities they engage in. With the help of such activities students can enhance their ability to reflect on their actions and gain a deeper understanding of the world around them. 

A coaching app enhances heuristic teaching by promoting active learning, critical thinking, collaboration, and individualized support. Through interactive features, real-time assessments, and personalized feedback, it engages students, identifies knowledge gaps, and guides them towards alternative solutions.

The Role of Teacher In Heuristic Teaching  

The role of the teacher in heuristic approach is to act as a facilitator, guiding students towards discovering knowledge and understanding through inquiry and self-exploration and experiences.

Some specific ways in which the teacher can play a role in heuristic teaching are as follows:

• Supportive Learning Environment: Teachers can create a classroom atmosphere that encourages open communication and active engagement, where students feel comfortable asking questions, sharing their ideas, and exploring new concepts on their own.
• Creating Activities That Promote Exploration: Teachers can design activities that encourage students to explore and experiment with new concepts, rather than simply absorbing the information being provided to them. it might involve hands-on activities, simulations, or group discussions as well as Q&A sessions.
• Providing Guidance and Feedback: Teachers can offer guidance and feedback throughout the learning process, helping students to reflect on their experiences. This might involve asking probing questions, providing additional resources, or offering criticism  to help students.
• Encouraging independent thinking: The teacher can encourage students to think independently and critically, rather than simply accepting information at face value. This might involve challenging assumptions, questioning authority, and fostering a spirit of intellectual curiosity.

Overall, the role of the teacher in a heuristic method of teaching is to act as a facilitator, creating a supportive learning environment and guiding students towards discovering knowledge and understanding through inquiry and exploration.

Benefits of Heuristic Method Of Teaching 

There are several benefits associated with the heuristic method of teaching . Some of the advantages of this teaching approach  are as follows :

1. Active Learning

The Heuristic teaching encourages students to engage with the material, rather than simply passively absorbing information. This will help students to develop a deeper understanding of the concepts being taught and their ability to question things will be raised.

2. Improving Critical Thinking Skills

With exploring new concepts and ideas, students are encouraged to think critically, question assumptions, and challenge their own beliefs and thoughts. This will help them develop critical thinking skills, which are valuable both in and outside of the classroom.

3. Enhances Creativity 

Heuristic method encourages students to approach problems and challenges in creative ways, which can help to enhance creativity. It is particularly important in fields that require creative thinking. 

4. Develops Problem-Solving Skills 

The Heuristic teaching focuses on problem-solving and discovery, which can help students to develop strong problem-solving skills. It is particularly valuable in fields that require complex problem-solving abilities, such as medicine, and law.

5. Promotes independent learning 

By encouraging students to explore and discover new concepts, the heuristic method helps to promote independent learning. This can help students to develop the skills they need to learn on their own, which is particularly important in today’s fast-paced, rapidly changing world.

Overall, the heuristic method of teaching has many benefits, from enhancing critical thinking skills and fostering creativity to developing problem-solving skills and promoting independent learning.

So, overall we can say that heuristic method of teaching is a very helpful and fun teaching approach that can help students to easily identify their interests and then work on learning more about them. This teaching approach has many benefits and teachers have vital roles to play as to help their students grow and succeed. 

Heuristic Method of Teaching FAQs

A1. Heuristic method of teaching is an approach that emphasizes active learning, problem-solving, and discovery. It encourages students to explore new concepts and ideas, rather than simply memorizing information.

A2. The traditional teaching methods involve lectures and presentations where the teacher provides information for students to memorize. On the other hand the heuristic method emphasizes active engagement, critical thinking, and problem-solving in the students.

A3. The Heuristic teaching strategies might include project-based learning, inquiry-based learning, case studies, simulations, and problem-based learning and many more.

A4. This teaching method  can benefit students in a number of ways, including by enhancing critical thinking skills, promoting creativity, developing problem-solving skills, as well as independent learning.

A5. Teachers can incorporate heuristic teaching into their classroom by designing activities and assignments that encourage exploration and experimentation. This might involve hands-on activities, group discussions, simulations, and other approaches that emphasize active engagement and problem-solving.

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Problem solving part b.

About the Training

Description.

In part two of Unpacking the Pyramid Model: Problem Solving, we will continue digging in to the instructional strategies for teaching social problem-solving skills. We will explore a variety of resources, ideas, videos, and photo examples. The session will conclude with a moment for reflection and planning for application.

Kymberly Horth began in education as a preschool and kindergarten teacher, laying the foundation for a career dedicated to fostering high-quality early childhood learning environments. Currently serving as a consultant with Pyramid Model Consortium, Kym brings a variety of experiences garnered over nearly a decade as a trainer, coach, and "coach of coaches." Specializing in Pyramid Model practices and Practice-Based Coaching, Kym is deeply passionate about equipping educators with the tools to create inclusive and nurturing spaces where every child feels a sense of belonging.

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