instructional strategies to teach problem solving

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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Teaching problem solving

Strategies for teaching problem solving apply across disciplines and instructional contexts. First, introduce the problem and explain how people in your discipline generally make sense of the given information. Then, explain how to apply these approaches to solve the problem.

Introducing the problem

Explaining how people in your discipline understand and interpret these types of problems can help students develop the skills they need to understand the problem (and find a solution). After introducing how you would go about solving a problem, you could then ask students to:

• frame the problem in their own words
• define key terms and concepts
• determine statements that accurately represent the givens of a problem
• identify analogous problems
• determine what information is needed to solve the problem

Working on solutions

In the solution phase, one develops and then implements a coherent plan for solving the problem. As you help students with this phase, you might ask them to:

• identify the general model or procedure they have in mind for solving the problem
• set sub-goals for solving the problem
• identify necessary operations and steps
• draw conclusions
• carry out necessary operations

You can help students tackle a problem effectively by asking them to:

• systematically explain each step and its rationale
• explain how they would approach solving the problem
• help you solve the problem by posing questions at key points in the process
• work together in small groups (3 to 5 students) to solve the problem and then have the solution presented to the rest of the class (either by you or by a student in the group)

In all cases, the more you get the students to articulate their own understandings of the problem and potential solutions, the more you can help them develop their expertise in approaching problems in your discipline.

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Teaching Students About the Basilisk: Exploring a Mythical Creature

Teaching students about the history of taiwan, teaching students about the definition of brahman in hinduism, teaching students about the definition of spheres of influence, teaching students about the definition of vaporization, teaching students about speed in physics, teaching students about invertebrates, teaching students about god of the sea in greek mythology, from ‘the holler’ to higher ed: james russell’s first-gen journey, i-dream grant implemented for first american students pursuing careers in education, strategies and methods to teach students problem solving and critical thinking skills.

The ability to problem solve and think critically are two of the most important skills that PreK-12 students can learn. Why? Because students need these skills to succeed in their academics and in life in general. It allows them to find a solution to issues and complex situations that are thrown there way, even if this is the first time they are faced with the predicament.

Okay, we know that these are essential skills that are also difficult to master. So how can we teach our students problem solve and think critically? I am glad you asked. In this piece will list and discuss strategies and methods that you can use to teach your students to do just that.

• Direct Analogy Method

A method of problem-solving in which a problem is compared to similar problems in nature or other settings, providing solutions that could potentially be applied.

• Attribute Listing

A technique used to encourage creative thinking in which the parts of a subject, problem, or task are listed, and then ways to change those component parts are examined.

• Attribute Modifying

A technique used to encourage creative thinking in which the parts of a subject, problem, or task are listed, and then options for changing or improving each part are considered.

• Attribute Transferring

A technique used to encourage creative thinking in which the parts of a subject, problem or task listed and then the problem solver uses analogies to other contexts to generate and consider potential solutions.

• Morphological Synthesis

A technique used to encourage creative problem solving which extends on attribute transferring. A matrix is created, listing concrete attributes along the x-axis, and the ideas from a second attribute along with the y-axis, yielding a long list of idea combinations.

SCAMPER stands for Substitute, Combine, Adapt, Modify-Magnify-Minify, Put to other uses, and Reverse or Rearrange. It is an idea checklist for solving design problems.

• Direct Analogy

A problem-solving technique in which an individual is asked to consider the ways problems of this type are solved in nature.

• Personal Analogy

A problem-solving technique in which an individual is challenged to become part of the problem to view it from a new perspective and identify possible solutions.

• Fantasy Analogy

A problem-solving process in which participants are asked to consider outlandish, fantastic or bizarre solutions which may lead to original and ground-breaking ideas.

• Symbolic Analogy

A problem-solving technique in which participants are challenged to generate a two-word phrase related to the design problem being considered and that appears self-contradictory. The process of brainstorming this phrase can stimulate design ideas.

• Implementation Charting

An activity in which problem solvers are asked to identify the next steps to implement their creative ideas. This step follows the idea generation stage and the narrowing of ideas to one or more feasible solutions. The process helps participants to view implementation as a viable next step.

• Thinking Skills

Skills aimed at aiding students to be critical, logical, and evaluative thinkers. They include analysis, comparison, classification, synthesis, generalization, discrimination, inference, planning, predicting, and identifying cause-effect relationships.

Can you think of any additional problems solving techniques that teachers use to improve their student’s problem-solving skills?

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Matthew Lynch

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8 Strategies for Teaching Problem-Solving Skills in Elementary Education

Elementary education refers to the foundational years of schooling, typically from classes 1 to 5. During this stage, children develop key cognitive and social skills, making it the perfect time to introduce problem-solving techniques. For parents, understanding how these skills are nurtured in the classroom helps them reinforce these practices at home, ensuring children are better prepared to navigate academic and personal challenges.

Here are 8 innovative ways or proven strategies for parents to support their child’s journey:

1. Encourage Open-Ended Questions – Children benefit greatly when encouraged to think critically by answering open-ended questions. Parents can ask questions like, “What do you think we should do to solve this?” or “Can you come up with more than one solution to this problem?” These discussions at home build confidence, enhance critical thinking skills in elementary education , and foster curiosity.

2. Relate to Real-World Scenarios – Connecting learning to everyday situations helps children see the relevance of their problem-solving skills. For instance, involve them in decisions like planning a family outing or managing their weekly allowance. This approach mirrors what they learn in school, where real-world problems make lessons more relatable and engaging.

3. Integrate Interactive Activities – Encourage the child to participate in interactive activities like solving puzzles, playing strategy-based games, or engaging in creative group tasks. These activities develop adaptability and allow children to explore multiple solutions in a fun, low-pressure environment, aligning with hands-on learning techniques used in classrooms.

4. Promote Teamwork at Home – Collaborative problem-solving isn’t limited to school. Encourage the child to work with siblings or friends on small projects like building a Lego structure or baking a cake. Team activities teach communication, compromise, and teamwork—skills integral to collaborative learning in elementary education .

5. Demonstrate Problem-Solving – Parents can adopt the “think-aloud” method to model effective problem-solving. For example, when facing a household issue like fixing a leaky tap, explain the steps one is taking to address the problem. This strategy mirrors what teachers do in classrooms and helps children internalise logical approaches to challenges.

6. Encourage Trial and Error – Create an environment where it’s okay for the child to make mistakes and try again. This approach fosters resilience and teaches them that failure is part of the learning process. For instance, if a craft project doesn’t turn out as planned, guide them to make improvements, reinforcing the concept of trial-and-error problem-solving . At Narayana Schools, we integrate trial-and-error analysis into our curriculum, encouraging students to experiment with solutions, learn from their mistakes, and build resilience. This approach ensures that students not only solve problems effectively but also develop the confidence to tackle challenges independently.

7. Use Visual Aids – Introduce tools like charts, diagrams, or even drawing mind maps to help your child break down complex problems. These techniques not only make challenges more tangible but also reflect the visual learning methods used in schools to organise thoughts and structure solutions.

8. Instil a Growth Mindset – A growth mindset encourages children to embrace challenges and see effort as a path to mastery. Praise their perseverance and highlight how their hard work pays off, helping them develop optimism and confidence in tackling future obstacles.

Narayana’s age appropriate programme for Overall Growth

At Narayana Schools, age-appropriate and tailor-made programmes ensure that students receive the guidance needed to grow into well-rounded individuals, with a special emphasis on developing problem-solving skills. Recognising that every child learns differently, these personalised programmes provide individualised attention, effectively nurturing students from a young age to create a lasting impact on their academic success and overall development. By fostering creativity, resilience, and adaptability, Narayana equips students with essential life skills, empowering them to become confident problem-solvers.

Teaching problem-solving skills during elementary education builds a solid foundation for lifelong success. For parents, understanding and reinforcing strategies like teamwork, real-world problem-solving, and fostering resilience can make a significant difference. At Narayana, we are committed to nurturing these abilities early on, helping your child grow into a confident, adaptable individual because, at Narayana, your dreams are our dreams.

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Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

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Problem-based Instruction

This tool explores approaching curriculum design and classroom instruction from the perspective of learning through solving problems.

# DESCRIPTION

Effective learning often exists within the context of a problem. These problems define both the purpose and motivation for learning. All problems, however, are not created equal, and some provide richer ground for learning than others. Sometimes that problem is “How do I get a good grade?” or “What does the teacher want?” (rocky ground). Other times, it’s “I’m curious about…” (sandy ground). Ideally, the problem sounds like, “I need to build a structurally sound building,” or “I want to deepen my relationship with God,” or “What should be our policy in the Middle East?” These problems provide fertile ground for deep and meaningful learning.

As educator John Dewey has suggested:

A large part of the art of instruction lies in making the difficulty of new problems large enough to challenge thought, and small enough so that, in addition to the confusion naturally attending the novel elements, there shall be luminous familiar spots from which helpful suggestions may spring.

(Democracy and Education, 1916; MW 9:164)

Defining a problem that becomes an effective springboard for deep learning is not easy. A process to help is detailed below.

# Developing a Problem

• Define Outcomes. If the problem is authentic or real-life, one of the learning outcomes is clearly to solve it or attempt to do so. Other learning outcomes include the skills and knowledge needed in that process. The problem can define the required outcomes, or the desired outcomes can define the problem.
• Content. Once outcomes are determined, you define what resources are available to be used.
• Developmentally appropriate (not too difficult), yet complex enough to benefit from group work
• Grounded in a student reality (authentic, real-world, personal)
• Reflective of learning outcomes, often targeted at a common misconception or difficulty 
• Ill-structured—meaning that the problem might have multiple possible or seemingly-possible solutions, that it is couched in the complexities of real life, and that it doesn’t contain all the information for its own resolution (not a story problem)

The problem statement may be as short as a question or as detailed as a multi-page case study. A good problem statement will provide enough information to define the boundaries of the issue without leading the student toward an answer. It will challenge students to research, discuss, analyze, and interpret. Students should be able to break it down in ways that indicate starting points or directions. 

The final problem statement is often framed in terms of a specific situation in a specific context along with a role the student is to assume ( Imagine that you’ve been asked to…)

• Motivation. Although problems are often intrinsically motivating, sometimes you need to spark initial interest. Allowing students to experience the authenticity, the reality or the personal impact of the problem can help.
• Support. Once students are interested, you can often help them launch their investigation with focus questions, a tutorial guide, or suggestions.
• Work collaboratively. Students should work collaboratively in small groups or teams towards a solution. Physics instructors use iClickers and Concept Tests to give group quizzes. Business uses Case Methods. Different pedagogies work in different settings, but all require the students to draw from and contribute to group learning.

4.     Assessment: Lastly, you need to consider ways to evaluate student work. 

# Project  

An education instructor finds it difficult to get her students to see past their own biases and to understand the complexities involved when thinking about educational reform. She chooses to put them in charge of the management of failing Chicago schools. In the problem description, she gives some background, establishes a time frame and resource list. The students are excited and begin collaborative research immediately after determining the relevant issues. She supports them in their work with lists of helpful websites and a handbook on educational design. Finally, she develops a rubric for assessing each team’s final proposal based on their abilities to articulate and defend the positions that they took.

# Concept Test  

An instructor chooses several problems with multiple or counter-intuitive solutions as the framework for a curricular unit. She then uses concept tests as a way to assess the individual and group work used to approach the problems.

# Case Study 

An instructor uses a mixture of pre-written and self-generated case studies to emphasize key understandings. He has students work together in teams to discuss and resolve the issues and then present their solutions to the rest of the class.

Sequence carefully.  Careful sequencing of the problems is crucial if the course is to use a number of problem-based activities. The most  important problem is often not appropriate as the first problem. Rather, early problems should model the process and be supported by the instructor.

Pair with collaborative strategies ( Teach One Another ) for the most effective problem-solving. Consider paired discussion, Socratic Method, projects, learning teams, and other approaches.

Use appropriately.  Use this strategy only when a recall is not the primary task of the learning.

Find context. Threshold concepts, concepts that underlie new ways of thinking, are often effective settings for good problem-based activities.

Find the appropriate  level . Many effective problems are messy at first glance. They are complex and ill-structured, offering no easy answer and many potential solutions, which allows for students to find solutions to problems that are not a single-solution scenario.

Not a hands-off instructional strategy. The instructor needs to be deeply involved in structuring, training, guiding, and evaluating student performance.

Time. Problem-based instruction takes time and is less-directly controlled than other approaches.

Newness . Problem-based instruction often requires new skills for both instructor and students. Introducing it for the first time should be done with due preparation and deliberation. 

Difficult . Instructors often tend to under-estimate the difficulties students face when confronted with problems and diminished guidance.

Not content coverage. Although it’s tempting to do so, a problem shouldn’t be designed around a given block of content, but rather around learning outcomes for the content.

# KEY ARTICLES

Merrill, M.D. (2007). A task-centered instructional strategy. Journal of Research on Technology in Education , 40(1), 33-50.

Wilkerson, LuAnn & Gijselaers W.H. (Eds.). (1996). Bringing problem-based learning to higher education. New Directions for Teaching and Learning , San Fransisco: Jossey-Bass, 68. 

# OTHER RESOURCES

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Using professional literature to create problems

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