Using Socratic questions for math teaching is a great way to help students develop critical thinking skills and math strategies. Questions encourage students to think through their answer and apply current knowledge to solve a new problem. It is also a form of narration for mathematical studies.

There are six types of Socratic questions. Let’s explore how these six types of Socratic questions can be applied to math.

## Six Types of Socratic Questions for Math

- Questions that clarify.
- Questions that challenge assumptions.
- Questions that examine evidence or reasons.
- Questions about viewpoints and perspectives.
- Questions that explore implications and consequences.
- Questions about the question.

## Examples of Socratic questions for math

**Questions that clarify.**

- What is another way you could solve that problem?
- How does the radius of a circle relate to the diameter of a circle?
- Could you give me an example of congruent shapes?
- Could you explain that further?
- How does this relate to what you learned about angles?

**Questions that challenge assumptions.**

- What assumptions are you making to solve the problem?
- Could you solve the problem with different assumptions?
- Does this formula always apply or are there circumstances that require a different approach or formula?
- Is a rectangle always a parallelogram? Is a parallelogram always a rectangle?
- Why is a larger base more stable than a narrow base?

**Questions that examine evidence or reasons.**

- What would be an example of that principle?
- What other information do you need to know to solve this problem?
- Does the formula you learned yesterday apply to this problem?
- What is another example of when you would apply this rule/formula?
- Why are you using this formula?

**Questions about viewpoints and perspectives.**

- What is another way to approach this problem?
- Could you solve this problem if you assumed x=8?
- Would you explain why you used this unit of measure?
- How are the formulas for the area of a triangle and the area of a rectangle similar? How are they different?
- Would the formula apply to an isosceles triangle and a right triangle?

**Questions that explore implications and consequences.**

- What is an alternative way to solve this problem?
- If these are right angles and the opposite sides are parallel, what is this shape?
- What effect would changing this angle have on the shape.
- If this length is doubled, would the shape be classified the same?
- What generalizations can you make about squares?

**Questions about the question.**

- How can you prove that answer?
- Can you break this problem down into simpler components?
- Do you have all of the facts you need to solve this problem?
- What is the main question for which you need to find the answer?
- Does this question provide additional information that changes your answer to the previous problem?

You can read more examples of the six types of Socratic questions here or here.

### Math Narration Ideas

Evaluate your student’s understanding of math concepts with these narration ideas.

Lorie says

Thank you! I am a special education teacher and I am going to start using this method to teach my 6th grade math class. My students have not experienced much success in math in their past and do not know how to find answers on their own, even from their own notes. I firmly believe if I ask the right questions they will learn they are capable of so much more than they ever believed.

Crystal Wagner says

I am so glad these questions will be helpful for you and your classroom. I would love to hear how it goes!

Jen Lum says

Thank you for this post. I will be using these to help my students. I’m trying to get them to help eachother without giving the answer only or telling them how to solve. These questions will work wonderfully in my small groups.

Crystal Wagner says

You are welcome! I’d love to hear how it works in your small groups if you would update us later.