The Ultimate Guide to Teaching with Mathematical Discourse | Part 3

Posted by Richard Kingham on October 12, 2021


Children are naturally curious, always asking questions about this or that. As teachers, it is our responsibility to foster their curiosity about math, answer questions, and ask our own questions. Indeed, employing the Socratic questioning method in the math classroom has gained traction over the years for its many advantages.

Mathematical questioning fosters mathematical thinking

One of the greatest advantages of mathematical questioning is that it offers a beneficial alternative to rote learning. Educators have argued in recent years that rote learning instills the mechanics of mathematics, but fails to teach students how to think mathematically. Consequently, students cannot transfer knowledge from one context to another. The mathematical problems they mastered in a worksheet look utterly foreign in their daily life. 

Mathematical questioning prompts mathematical reasoning. For example, verbalizing the mathematical processes students have memorized encourages discursive and reflective thinking. Now, this can be a slow and frustrating exercise for even the brightest student. It is much easier for motivated matriculants to memorize and recite formuli and procedures than to articulate their reasoning. At the outset of lessons organized around mathematical questioning, teachers should set the expectation that articulating mathematical reasoning is challenging. Remember, you are trying to teach them a way of thinking—a new perspective. And that takes time.

Wide open questions

One of the best guiding principles to mathematical questioning is asking open-ended questions, as opposed to close-ended questions. Here are examples of each.

Close-ended question: Where is the x-axis?

Open-ended question: What skills have we learned that you can use to solve this problem?

The first question has one answer and furthers the notion, common among students, that math is primarily about getting the right answer. We want to consign this myth to the Dark Ages. The second question, by contrast, invites students to reason, to survey their catalogue of mathematical tools and select the right one for the job. After receiving a sufficient answer to the second question, the teacher can keep pressing the matter: “Why did you choose this method?” Teacher and student are now engaging in mathematical dialogue, also known as intentional discourse. During intentional dialogue, students not only verbalize their mathematical reasoning, they practice solving problems collaboratively through conversation—a skill that will serve them well in the professional world. All this goodness flows from the font of open-ended questioning.

STEMscopes Math: Your built-in Socrates

STEMscopes Math serves as an excellent resource for mathematical questioning. My Math Thoughts, for example, provides an opportunity for students to write their responses to open-ended questions. It is always more difficult to produce a thoughtful answer on the spot when asked a question than to reflect on it in writing. In My Math Thoughts, students express and refine their ideas. This exercise also promotes structured mathematical conversations among peers. Students can share their journals with others and plumb the infinite depths of their thoughts together. My Math Thoughts also engages students affectively, encouraging them to reflect on how they feel, and thereby bolstering SEL and making math more personal. 


If you haven’t done so already, strongly consider adding mathematical questioning to your array of teaching tools. We should note that rote learning does have its place. The novice athlete needs to learn the rules of basketball before she can fully appreciate the game. The ballet dancer spends hours at the barre practicing repetitive motions until they are automatic and they are able to move on to more complex moves. Mathematical questioning and intentional discourse are no different. Students need to memorize and recall algorithms and formulas to engage in meaningful mathematical dialogue, but their education needs to be multidimensional. Saying a mathematical education is well rounded when it emphasizes memorization and recall but denies students the chance to apply and exercise knowledge is like calling a square a cube. 

Topics: intentional discourse, math