Fostering mathematical inquiry by encouraging students to evaluate the quality of their questions, not answers.

by Kathryn Gillespie

Grades 6-8, Grades 9-12


I have devised a strategy to help students look at and evaluate questions instead of answers. I call it “Fostering Mathematical Inquiry”–the search for knowledge using mathematical skills and resources.

This procedure seems like it’s going to consist of asking and answering questions but the goal is to look only at the questions (we actually don’t even grade the answers).

I start this procedure by holding up a prop, like a vase, in front of the class and explaining what mathematical inquiry is. Then I distribute colored cards to the students (I have four cards of every color.) This starts the process I call Q.U.E.R.Y.

–Q: Question. I Ask students to write down a question of mathematical inquiry on their cards. In calculus they usually start out with questions like “What is the volume of the vase?” or “What is the surface area of the vase?”

–U: Unite the questions. Then I group students together by their card color, four in each group. The students in each group have to combine their questions together to make four new unique questions. So we have questions about questions and then come up with a completely new set.

–E: Explore the solutions. Then that set of questions moves to a different group who try and answer those questions. If they can’t answer the questions they have to explain why. The whole point is to focus on the questions, not the answers.

–R: Rate the questions. After that, there is a third rotation where the students grade the questions, not the answers. We measure rigor by Webb’s Depth of Knowledge, and we want to see questions that involve comparison and analysis. The students grade according to guidelines such as, “Was the question clear?”, “Does it involve math that we have within our grasp?”, “Do we have the resources to answer the question?”

–Y: You’re on your own. After the students have written, unified and rated questions, I propel them to write their own new question.

It’s the questions that are going to drive the future, not the answers.


What I did well:

Modelling the entire process for teachers gave teachers a chance to experience this strategy from a student’s point of view.   Effective teachers strive for that perspective.   There are many ways to do that in a classroom:  read the story and answer the questions, work the math problem, research the topics, perform the experiments, etc. before assigning the task to students.

What would I change in sharing this practice again?

The original presentation was aimed at high school teaching.   I would like to explore applications in the lower grades and provide suitable prompts for students in the wider realm of STEM instead of Mathematics only.

In what ways do I want to grow in this practice?

I never embark on a new teaching strategy without learning a great deal more than my students do!!  As I face each new class of students I will need to adjust rigor and relevance to match their capacity for inquiry.

About Kathryn Gillespie

Find out more