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?