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?

Newsletter:

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**.

- Creating a WiiMote interactive white board at my school for under $50.
- 20 reasons not to use a one to one laptop program in your school (and some solutions)
- What is Edcamp?
- For whom are Interactive White boards Interactive?
- Mathematics education blogs
- Forget the future: Here's the textbook I want now
- Eight Videos to Help Teachers Get Started Using Twitter
- Why educators should blog: A helpful flowchart
- There are no aha moments
- Paper use in schools
- 15 things kids can do instead of homework
- Online Geogebra training
- The difference between instrumental and relational understanding
- What is The Effect of Technology Training for Teachers on Student Achievement?
- Why teach math?
- Using Google forms for a "Choose your own adventure" style story
- Ways to use technology in math class
- A Fundamental Flaw in Math Education
- We are homeschooling our son
- A Restitution Guide to Classroom Management
- 25 Myths About Homework
- The Death of the Amateur Mathematician
- Migrating away from Google Reader
- Free tools for math education
- The Role of Immediacy of Feedback in Student Learning

**Subscribe** to my blog

Theme by Danetsoft and Danang Probo Sayekti inspired by Maksimer

## Comments

## I might use this for my

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!

## Polya and others and more questions

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'.

## Questions to ask while problem solving

David:

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

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.

## Computer Science and Education

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

## I don't know if there is a

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

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

Thanks..

## Add new comment