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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.

## Center for Teaching

Teaching problem solving.

Print Version

## 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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## Speaking skills: Speaking matters

- 1 Speaking skills: Speaking matters
- 2 Speaking matters: Developing fluency
- 3 Speaking matters: Developing and dealing with accuracy
- 4 Speaking matters: Assessing speaking
- 5 Speaking matters: Personalization
- 6 Speaking matters: Problem-solving
- 7 Speaking matters: Role-play
- 8 Speaking matters: Pairwork

## Speaking matters: Problem-solving

By Adrian Tennant

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This article looks at problem-solving activities and what they are like. It covers how to set them up, why it's good to use them, the disadvantages and what you should do after the activity.

## Introduction

Students need a reason to speak in the classroom. Many speaking activities seem to have no aim other than to get students to talk to each other, but for what reason? By doing the activity what will they achieve? Some activities, like pairwork activities, try to create a purpose by creating an information gap - i.e. where one student has some of the information and another student the rest and, only by speaking to each other can they complete the task. However, this simple transference of information only replicates a small part of what speaking in real life is used for.

Role-plays are another favourite classroom activity designed to get students speaking, but these often focus on creating scenarios or situations where students practise functional language such as giving directions, asking for information, etc. Although this is realistic, it is still often on a level of one student having information that another student doesn't. In real life, we often speak about something when we both, or all, share a lot of the same information. This can take the form of a discussion or a debate where we have opinions, but it can also take the shape of a discussion based on having to solve a problem. In this article, we'll take a closer look at problem-solving speaking activities.

## What are problem-solving activities like?

There are a number of types of problem solving activities. For the sake of simplicity I'll split them into three types:

1. The opinion problem-solving activity.

In this type of activity students are given information to discuss where there is not necessarily one right or wrong answer. This type of activity differs from a normal discussion in that there is a built-in problem within the information.

You and three friends rowed out to a small island in the middle of a lake. When you landed you forgot to tie the boat up properly and it has drifted away. Night is now approaching. It is 3km back to the shore, but one of your friends can't swim. You do not have any food with you and you don't know if anyone knows where you are. What do you do?

Students are then expected to discuss the problem and come up with a solution. To help students you can provide a set of ideas/options for them to choose from. You can also make the activity more complicated by giving each student a 'role card' with an extra piece of information on it (that might be a problem) i.e.

There is no wood on the island so you can't build a fire. At night the temperature drops to freezing .

2. The logical thinking problem-solving activity.

In this type of problem-solving activity there is usually one correct solution. To arrive at the solution the students need to discuss information they are given and logically work out what the solution is. There are two ways in which the information can be given, either split between a number of students so that they don't have the same information and they must share it, or where they all have the same information and simply have to discuss things together. In the later version a set of questions can often help students work out the answer. (See activity 2 in the 'Practical ideas' section below for a logical thinking activity).

3.The information gap problem-solving activity.

How does this differ from a normal information gap (i.e. a pairwork information gap where one student has information that the other student doesn't)? Well, the main difference is that in a normal information gap activity it is simply a matter of transferring the information, i.e. two students have a profile of a person. Student A knows the person's age and nationality, etc. Student B then asks 'How old is he?' and fills in the missing information they obtain in the correct space, etc. In a problem-solving information gap, getting the missing information is not the ultimate aim, but merely a stepping stone on the way to solving a problem.

## Why use problem-solving activities?

Apart from the fact that these kinds of activities can be a lot of fun they are also very stimulating. They usually require students to communicate information to each other where the focus is on expressing ideas and opinions and not simply repeating phrases. In many ways, problem-solving activities replicate 'real' speaking in that people have a need to speak. Problem-solving activities can also be an effective way of practising language items that have been taught, i.e. both grammar and vocabulary. They are also a great way of developing students' cognitive abilities helping them to process language in a meaningful way.

## Are there any disadvantages to problem-solving activities?

Yes, there are. One of the major problems is that stronger students often dominate the discussions, taking over and giving the less able students little opportunity to contribute. Often, this is due to the need for one person to organize and collate information and ideas. One way around this is to give certain students specific tasks, i.e. someone to 'chair' the discussion, someone to make sure everyone has a turn, etc.

Another disadvantage of this type of activity is that students may become frustrated when trying to solve the problem and, especially if they don't have the language skills in English, will switch to their L1. To avoid this it is important that you, the teacher, consider what language they are likely to need in order to complete the task and to pre-teach any necessary phrases, expressions or vocabulary you think they do not possess. Remember, using a problem-solving activity is not the main focus of your lesson/teaching but simply a way in providing students with a forum for using the language they have learnt.

## How do you set up a problem-solving activity?

As with other speaking activities, how you set up the activity will often be the difference between a successful activity and one that doesn't work. The first thing to consider is whether the activity uses the language you want the students to practise. If not, then ask yourself why exactly you are using it. Then, it is important to look at the language that is needed and make sure that you pre-teach any new language before they start the activity. This will help the activity run smoothly with the focus being on solving the problem rather than working out the meaning of any new language. Finally, think about whether you want students to work alone to begin with and then discuss the problem with other students or whether you will start with pair or groupwork. Whenever you decide to use pair or groupwork think about who you get to work together so that there is a balance in each group.

## What should I do after the activity?

Just as with roleplays, don't just move onto a different activity. If you move on immediately after the activity and don't at least discuss what happened, then students will often lose interest in problem-solving activities, or at least won't benefit to the full. There needs to be an obvious outcome and a rounding-up of the activity. Opening up the activity to a class discussion where you compare solutions is an obvious follow-up. It is also important that during the activity you note down any mistakes students made with the language and think about how you will tackle these either after the activity or in a subsequent lesson.

## Some practical ideas

An opinion problem-solving activity

Here I am going to use the idea I mentioned earlier but give a few variations to show how it can be run in a number of different ways.

Variation 1

Put students in groups of 3-5 and give each group a copy (or copies) of the following handout:

Ask students to talk to each other and make a list of possible solutions. Ask them to also think about what problems they might face/encounter with each solution. i.e. If they stay on the island, where will they sleep and what will they eat? What if there is no food on the island? etc.

Variation 2

Give the students the same handout, but also give them the following options (either as part of the handout or written on the board).

- One of you swims to the shore to get help.
- Try and make a fire on the island to attract attention.
- Find somewhere to sleep for the night and then try and get off in the morning.
- Look for the boat and get one person to try and swim to it and bring it back.
- All swim back to the shore taking it in turns to help the person who can't swim.

Variation 3

Give the students the same handout, but also give each one a role card with extra information. i.e.

A logical thinking problem-solving activity

A new teacher starts working at school. In her class there are a set of triplets, Ana, Bryan and Carl. Unfortunately, the teacher can't remember which one is which, but she has some notes about the three kids.

She knows that two of the triplets are boys and one is a girl.

Carl, one of the boys, is always calm and patient.

- One of the triplets likes playing football and he has a tattoo on his arm.

One of the triplets has red hair, one brown and one blonde.

- The triplet who doesn't get angry easily has short blonde hair.

The triplet with red hair has an earring and she likes to sing.

The triplet who has a tattoo gets angry easily.

Can she work out who is who?

Students should be able to work out the answer simply with the information provided, but, if you want to help them you could also give them a set of questions to answer. e.g.

- Should the teacher have known which triplet was Ana? Why?
- Which triplet likes to sing? How do you know?
- What colour is Ana's hair?
- What else do you know about Ana?
- What kind of person is Carl?
- Does he have a tattoo?
- How do you know?
- What colour is Carl's hair?
- Does Carl like football?
- Which triplet likes football?

These questions guide students through step-by-step, enabling them to work out the answer.

An information gap problem-solving activity

A simple example of this would be to use the same worksheet as above but cut the information about the triplets into strips, put students in small groups and give each student one or two strips. Tell students they have the information between them but that they must not show their information to the other students in their group.

A new teacher starts working at school. In her class there are a set of triplets, Ana, Bryan and Carl. Unfortunately, the teacher can’t remember which one is which, but she has some notes about the three kids. Can she work out who is who?

One of the triplets likes playing football and he has a tattoo on his arm

The triplet who doesn’t get angry easily has short blonde hair.

- British English

## Speaking matters: Developing fluency

Speaking matters: developing and dealing with accuracy, speaking matters: assessing speaking, speaking matters: personalization, speaking matters: role-play.

## Speaking matters: Pairwork

Related articles.

Adrian Tennant gives an introduction to using pairwork for teaching speaking skills.

## Professional Communication Skills: Body Language

Use these interactive materials to deliver an online or face-to-face lesson on using our body language in a professional environment.

## Elementary Business: Keeping Customer Information Safe

What steps are businesses taking to protect customer data? Discuss this topic with your elementary-level students.

## No comments yet

Only registered users can comment on this article., more from support for teaching speaking.

## Pronunciation skills with Adrian Underhill: Overcoming common pronunciation challenges

In the last article in this series, ELT pronunciation expert Adrian Underhill looks at how to overcome common pronunciation problems.

## Pronunciation skills: Consonants – consciously rediscovering the ON and OFF voice buttons

In his latest article, ELT pronunciation expert Adrian Underhill looks at consonants and how consciously rediscoving the ON and OFF voice buttons can benefit both your teaching and your students’ learning.

## Pronunciation skills: Minimal pairs /θ/ and /ð/

In this video, Adrian looks at the minimal pair and and /θ/ and /ð/ and shows us how to make each sound in a simple and effective way while giving advice on how to gain control of the physicality needed to produce each sound.

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## Problem-Solving Method in Teaching

The problem-solving method is a highly effective teaching strategy that is designed to help students develop critical thinking skills and problem-solving abilities . It involves providing students with real-world problems and challenges that require them to apply their knowledge, skills, and creativity to find solutions. This method encourages active learning, promotes collaboration, and allows students to take ownership of their learning.

## Table of Contents

Definition of problem-solving method.

Problem-solving is a process of identifying, analyzing, and resolving problems. The problem-solving method in teaching involves providing students with real-world problems that they must solve through collaboration and critical thinking. This method encourages students to apply their knowledge and creativity to develop solutions that are effective and practical.

## Meaning of Problem-Solving Method

The meaning and Definition of problem-solving are given by different Scholars. These are-

Woodworth and Marquis(1948) : Problem-solving behavior occurs in novel or difficult situations in which a solution is not obtainable by the habitual methods of applying concepts and principles derived from past experience in very similar situations.

Skinner (1968): Problem-solving is a process of overcoming difficulties that appear to interfere with the attainment of a goal. It is the procedure of making adjustments in spite of interference

## Benefits of Problem-Solving Method

The problem-solving method has several benefits for both students and teachers. These benefits include:

- Encourages active learning: The problem-solving method encourages students to actively participate in their own learning by engaging them in real-world problems that require critical thinking and collaboration
- Promotes collaboration: Problem-solving requires students to work together to find solutions. This promotes teamwork, communication, and cooperation.
- Builds critical thinking skills: The problem-solving method helps students develop critical thinking skills by providing them with opportunities to analyze and evaluate problems
- Increases motivation: When students are engaged in solving real-world problems, they are more motivated to learn and apply their knowledge.
- Enhances creativity: The problem-solving method encourages students to be creative in finding solutions to problems.

## Steps in Problem-Solving Method

The problem-solving method involves several steps that teachers can use to guide their students. These steps include

- Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers can present students with a real-world problem or challenge that requires critical thinking and collaboration.
- Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying causes.
- Generating solutions: After analyzing the problem, students should generate possible solutions. This step requires creativity and critical thinking.
- Evaluating solutions: The next step is to evaluate each solution based on its effectiveness and practicality
- Selecting the best solution: The final step is to select the best solution and implement it.

## Verification of the concluded solution or Hypothesis

The solution arrived at or the conclusion drawn must be further verified by utilizing it in solving various other likewise problems. In case, the derived solution helps in solving these problems, then and only then if one is free to agree with his finding regarding the solution. The verified solution may then become a useful product of his problem-solving behavior that can be utilized in solving further problems. The above steps can be utilized in solving various problems thereby fostering creative thinking ability in an individual.

The problem-solving method is an effective teaching strategy that promotes critical thinking, creativity, and collaboration. It provides students with real-world problems that require them to apply their knowledge and skills to find solutions. By using the problem-solving method, teachers can help their students develop the skills they need to succeed in school and in life.

- Jonassen, D. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments. Routledge.
- Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.
- Mergendoller, J. R., Maxwell, N. L., & Bellisimo, Y. (2006). The effectiveness of problem-based instruction: A comparative study of instructional methods and student characteristics. Interdisciplinary Journal of Problem-based Learning, 1(2), 49-69.
- Richey, R. C., Klein, J. D., & Tracey, M. W. (2011). The instructional design knowledge base: Theory, research, and practice. Routledge.
- Savery, J. R., & Duffy, T. M. (2001). Problem-based learning: An instructional model and its constructivist framework. CRLT Technical Report No. 16-01, University of Michigan. Wojcikowski, J. (2013). Solving real-world problems through problem-based learning. College Teaching, 61(4), 153-156

## 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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## COMMENTS

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.

Speaking matters: Problem-solving. This article looks at problem-solving activities and what they are like. It covers how to set them up, why it's good to use them, the disadvantages and what you should do after the activity. Students need a reason to speak in the classroom.

Steps in Problem-Solving Method Identifying the problem: The first step in problem-solving is identifying the problem that needs to be solved. Teachers... Analyzing the problem: Once the problem is identified, students should analyze it to determine its scope and underlying... Generating solutions: ...

Principles for teaching problem solving Model a useful problem-solving method. Problem solving can be difficult and sometimes tedious. Show students how to be... Teach within a specific context. Teach problem-solving skills in the context in which they will be used by students (e.g. Help students ...