How to Teach Math Through Problem-solving


Teaching Problem solving isn’t an easy process. A teacher by nature is an expert; problem-solving is easy for them, and they are so fluent in their fields that they find it difficult to articulate the principles, strategies and the process of problem solving. To them, these have already become a second nature.

And that’s where the problem arises. Kids, especially the middle graders have no or little knowledge of these principles, strategies or the process.
And that’ where the difference between a teacher and a mathematician lies; teachers need to learn the art of putting himself in the student’s place, become aware of students’ pace of learning, understand their mindset. Although it is a necessary first step, it is just the beginning.


How to teach Math through problem-solving

Merely teaching students the ‘know about’ is not enough. It does not help create the knowledge base necessary to master problem-solving. What students need to be taught is the ‘knowing how to’ aspect of problem solving.

One of the ways of doing it is by deemphasizing the amount of information that students must commit to their memory and focus on problem-formulating and problem solving. An excellent instrument to that is solving plenty of ‘good problems.’

Teachers should concentrate on structuring situations where students are required to face a new question, define it in specific terms, and evaluate potential solutions to the given problem. This helps teach students to emphasize over the process rather than the answer.  Students learn to concentrate upon the sequence in which an event occurs.

Basically, it is teaching students mental skills, strategies, and attitudes that are basic to problem solving. Simply put it is moving towards an action-learning model.


Classroom culture

Nrich has written a post exploring the steps necessary to develop a classroom culture that supports problem-solving.  Jennie writes that a teacher’s role should primarily be to develop a classroom culture that supports problems solving. It needs to be one that promotes –questioning and deep-thinking; where making mistakes is seen as OK, being stuck is seen as awesome, and value is giving to the suggestions made by the students. A classroom culture that promotes collaboration among students. Students find it comfortable to share their discussions with their teachers and their peers.

They explicitly line up eight aspects that teachers need to consider for developing a problem-solving culture in their classrooms

  1. Who does most of the talking in whole-class parts of the lesson?

  2. What questions should I ask?

  3. Who answers the questions?

  4. How well do I listen to the students’ answers and seek to understand what they are saying?

  5. What do I do with the students’ answers?

  6. How do I facilitate the learning?

  7. How confident are the students to take a risk, to try out ideas, to make mistakes?

  8. What does my body language communicate?


The strength of routines

Routines are defined as the repetitive patterns of activities by students that help them organize and internalize the way problem-solving process works. They help address the issues of identifying the group that the problem belongs to, its status distribution, and the underlying relationships.

It is more than sure, that if students get involved in the process of problem-solving regularly, over time they can develop routines and consistency in their approach; moreover, it helps them internalize the problems solving process into their individual decision making too.

A point of attention here – some researchers have explicitly pointed out the limitations of a group solving the problems – the status of the group members can have a strong effect on how much does a student internalize the problem-solving routine. Collaborative learning has its best effect the student group has a strong sense of group identity, an otherwise group, interferes with the students’ ability to form and retain the problem-solving routines, and this also lowers the member students’ ability to retain the problem-solving routine in their individual decisions.


Tips and strategies to teach problem-solving

Consider the following tips as suggested by the Vanderbilt University.

  1. Have students share what is their status on problems, if they are already comfortable with a problem, there’s no meaning in wasting time on those.

  2. Teach students to identify their specific issues with a problem – the difficulties they are facing, the confusions they have.

  3. Encourage students to identify the exact concepts and principles that they are having trouble with.

  4. Make students articulate their problem-solving process.

  5. Avoid giving students the answers. Pay more attention on the process, while walking them through a problem – walk them through as if a novice was trying to solve the problem.

  6. When students are going through a problem on their own, ask them direct questions about the process, give helpful suggestions.

  7. Recognize when a student comes to you asking for help – he must have done his best. Positive reinforcement works really well, makes the students realize that although they are having trouble with the problem – they have already mastered concept can go a long way.

Solve problems

What’s most important when teaching problem solving is to communicate that the process of solving the problem is more important than the answer. Students learn at their own pace – a teacher needs to accept that. As we have written in earlier articles, in certain cases, growth can be more important than proficiency. Problem solving is one such instance.  To some students, the process of problem solving would come as second nature, while others would find every step mystifying. Never let a students’ anxiety pressure you into giving them the right answer.  The best approach is to help them identify their own errors and learn from them. Students must imbibe that in the real world, the process of problem solving is more important than the answer.

As George Polya wrote –

“The teacher should put himself in the student’s place, he should see the student’s case, he should try to understand what is going on in the student’s mind, and ask a question or indicate a step that could have occurred to the student himself.”

We encourage you to explore PracTutor for teaching problem solving in your classrooms.  PracTutor helps students practice at own pace by personalizing their learning path. It provides students with several accommodations which ensure that students can explore problem solving at their own.


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