## 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.

Questions to ask during problem solving

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

Is there another way to solve it?

• 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)?

• 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)?

Can you reflect on your problem solving process?

• How could you change this problem?
• Can you think of related problems?
• How could you generalize this problem?

• 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’.

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

• Kayla Szymanski wrote: