If you have recently attended a math conference, you have likely heard discussion concerning “questioning” and its importance in the classroom. Though this is something teachers have been doing for centuries, the types of questions teachers ask may be changing. Questions such as, “What is the square root of 9?” are becoming more thought-provoking: “How can we use the area of a square and unit tiles to help us determine the square root of 9?” Students still determine the square root of 9, but they employ much more thinking and develop a visual model in the process.

Then there is the follow-up question: “How did you determine your answer?” This can be quite challenging for students to puzzle out because it requires them to explain their thinking, which means they must think about their own thought processes, or engage in metacognition. This skill, as it develops in mathematics students, can lead to deeper understanding of mathematical principles. Once students begin to make connections between previously learned concepts and current topics, they can extend the connections across the curriculum to other subjects.

This trend in teaching may seem fairly new, especially in the mathematics classroom, however, its roots are found in the Socratic method. Yes, it works for math too! Teachers employ this method in their math classes by asking probing questions to foster critical thinking and encourage dialogue.

In her article, “Thinking to Learn the Socratic Way,” Dr. Sandra Love lists numerous question prompts to engage students and encourage deeper and more critical thinking. I am particularly drawn to the Compare and Contrast prompts for a mathematical discussion:

  • How are _______ and _______ alike/different?
  • How does _______ remind you of _______?
  • What is _______ similar to?

These are fantastic question starters for teachers to use to help students learn how to make connections between mathematics concepts.

Here are some examples of how these questions might be used in both elementary and secondary math classes:


There are infinite possibilities for you to implement these strategies using thoughtful questions in your mathematics class, no matter what grade level you teach. Your students will be challenged to think more critically about math concepts and so will you!

I would love to hear how you use these and other strategies in your math class! Leave a comment or tweet to @mentoringminds and let’s get some dialogue going! Happy thinking!


About Mathematical Matters

This article is part of the Mathematical Matters series, which examines all things math for elementary and middle school teachers, from the nitty gritty to the philosophical. Look back in the archives for classroom tips, activities, and strategies for making math fun and impactful for your students . . . because math matters!