George Polya and Mathematical Problem Solving

George Polya was a Hungarian mathematician who penned a book titled How to Get it.  In that book, we comes up with a four-step guide to mathematical problem solving

  1. Understand the problem.

  2. Make a plan.

  3. Carry out the plan.

  4. Look back on your work. 

I am going to try and adopt this to a grade 5/6 class, with level friendly language to help guide them through the process.  Here is what I have so far;

I hope start doing a weekly Problem Solving class, where we work through the steps and train ourselves to think like problem solvers.

I would love some feedback.  What do you think?  Is there anything wrong with what I have up there?  Anything I should add?  Anything that is unclear?  Put your thinking hats on and deconstruct it.


  1. I really like the math problem solving guide that you have outlined here. The steps are clear and useful for the students. The questions under each heading help the students get a better understanding of what each step means. I think the example questions/ statements are quite clear as well.

    Two things to consider:

    In step 2 you have listed a number of different ways they can make a plan. While your students may be different, our students here may read that as they are required to do ALL of the steps instead of choosing the one that they think is the most appropriate. Not sure how you would combat that problem other than placing bullet points on those items and say "pick the most appropriate strategy".

    In step 4 you give excellent questions for the students to think about and put the emphasis clearly on the idea of checking for "reasonable answers" which is extremely important. For our students, they would also need some structure on what to do if the answer does NOT make sense and they are stuck. Perhaps there needs to be something like "go back and look for areas where you may have missed information or your calculations do not make sense."

    Overall I think it is wonderful and will be passing it on to our fifth grade team for sure! :) Great work!

  2. Hi!

    I love this! I think it is a great idea to provide this kind of experience to your students. To be nitpicky, you might want to change 'strategy' in the first sentence of the third box to 'plan' to keep the language consistent. I'm guessing if their plan didn't work in figuring out the problem they would start again at 2? or would they start again at 1 and re-read the problem? might be something to include.

    I think the idea of a weekly problem solving class is an interesting one. Would you use a problem from the current unit of study or another one? I can see the merits to both... Thanks for the idea!

  3. [...] « George Polya and Mathematical Problem Solving Oct 11 2011 [...]

  4. [...] it.  I don’t usually help with problems like this, I try and get them to do themselves by reviewing their problem solving process, or starting at the beginning, or listing what you know and what you need to know.  This time, I [...]

  5. Thanks for sharing this guide for students to solve their mathematical concepts. Math is an integral part of every student’s education. Child’s math exams are very important. After getting help from this problem solving guide students can reduce their math exam stress. I hope students will love math if they follow these tricks. If students use math assessment books they can work on weak points to pass their exams. Assessment books teach basic math topics.


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