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Questions to ask while problem solving

I'm working on a set of possible questions one can ask their students (and teach their students to ask themselves) while they are problem solving in math. Note that these questions are related to the work of George Pólya from his book How to Solve It.

What would you add?


Questions to ask during problem solving

What are your assumptions?

  • What happens if you change those assumptions?
  • What assumptions have other people made?

Is there another way to solve it?

  • Within your current assumptions?
  • With different assumptions?

How is this problem related to other problems you have done?

  • Can you solve a related problem?
  • Can you simplify the problem, and then solve it?
  • Can you find connections between this problem and other problems?

Can you explain the solution to someone else?

  • Can they explain your solution to you?
  • Can they explain your solution to someone else?
  • Can you explain your solution without words?
  • Can you explain your solution using only words (no symbols or drawings)?

What tools could you use to help you solve this problem?

  • Are there any technological tools that might make the problem easier to visualize or manipulate?
  • Are there any mathematical techniques that might be connected to this problem?

How can you justify your solution?

  • How can you prove your answer is unique (if it is unique)?
  • If your answer is not unique, how many different answers are there?
  • How do you know your answer is reasonable?

Can you reflect on your problem solving process?

  • How could you change this problem?
  • Can you think of related problems?
  • What is interesting about this problem?
  • How could you generalize this problem?



About David

David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.


I might use this for my beginning of year problem solving challenge (this year it will incorporate building a gumdrop structure)! Cool way to think about it abstractly!

I grew up with the books of Polya and also W.W.Sawyer, both geniuses in the 'What is going on? Have I seen anything like this before? Are there other ways of looking at it?' business. Polya asks other questions, often really useful ones such as 'Is there a simpler problem buried in here, which I might have more success with?' and 'Are there any special cases?'. Questions I like to ask are "If you had the solution, what would it look like?' and 'So you have a solution, how can you convince me,or anybody else, that it is right?'. Also, 'Can you visualise the situation, draw a picture or two or a diagram?', and 'Is there any structure in the situation that I have overlooked?'. Advice I have often given is 'Give it a break, think of something else, let the brain get on with the job, it doesn't need your attention constantly'.

There are two other books by Polya:
Induction and Analogy in Mathematics, and
Patterns of Plausible Reasoning

Well worth a read if you havent already done so

Hi, my name is Kayla Szymanski and I am currently enrolled in the EDM310 course. I have been assigned your blog for this week, and by this being done I have read your current post. I think that it is a very good idea to give your students questions they can ask themselves while problem solving. As a former math student myself, sometimes just seeing a math problem will freak you out enough to where you don't even want to begin. I think by giving your students these quick questions it will ease this sensation that I repeatedly felt while taking math courses. Also just a tip I think maybe you could condense these rules into about 10 quick easy steps. This would be a great class motto or easy memorizing learning tool for each of your students. They could use it as a way to self check themselves while solving problems too. I had a teacher that once gave us a saying, and each word meant; subtract, multiply, etc.,and it worked. You will be surprised what works and sticks in your students heads.

My name is asad.Sir please answer me of this question.

When student solve mathematics problem then some question would create in mind like "Yes i understood" or "i have not understood" or "I have not learned that" or " i have no idea to solve problem" or "what does means of one third" so please any can know that what is name of this cognitive/meta cognitive activity. Thanks

David Wees's picture

I don't know if there is a more specific name to it or not. I would call it "questioning oneself" and classify it broadly as a meta-cognitive strategy.

Thanks Sir. You said  "questioning onself" so can we say it "Self questioning " ?



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