What is Mathematics?

May 2023

In Catalyzing Change in High School Mathematics: Initiating Critical Conversations, NCTM encouraged us to consider the purposes of school mathematics. NCTM argues that “each and every student should learn the Essential Concepts in order to expand professional opportunities, understand and critique the world, and experience the joy, wonder, and beauty of mathematics” (2018, p. 9). In Catalyzing Change in Early Childhood and Elementary Mathematics (NCTM, 2020a) as well as in Catalyzing Change in Middle School Mathematics (NCTM, 2020b), “expand professional opportunities” is replaced with “develop deep mathematical understanding.”

Although considering the purposes of school mathematics is vitally important, I believe another, broader question must be addressed. We must consider how we define mathematics. Our definition of mathematics definitely affects how it should be taught as well as how to assess learning. I encourage you to stop for a moment and think about how you would define mathematics.

Did you define mathematics as finding the answer to a problem? I know this is how I likely would have responded as an early-career teacher; or perhaps I might have said that mathematics is the study of patterns. And too often with this view of math as obtaining answers, success is equated with speed. The faster you are at finding the correct answer, the better or smarter you are at mathematics. We know this is not the case, however.

Mathematics is more than answer getting, and in fact, technology can now do much of the calculating that many of us did years ago. Instead, mathematics must be about reasoning, sense making, and problem solving. Students must be able to explain their thinking and justify reasoning rather than just perform a step-by-step procedure that they are often expected to memorize. We must remember that humans have developed and used mathematics—and are still developing and using mathematics—to solve issues and problems in society. Our students should not only recognize this but also use mathematics to address current issues. They deserve to see a purpose for what they are learning.

I encourage us all to continue to think about what mathematics is and to consider the ramifications of our own definition on how we teach and how we assess. And, more importantly, we must continually examine how our students see and define mathematics. We must move past strictly defining mathematics as finding a correct answer. Let’s instead teach every single one of our students how to make sense of the mathematics and so increase their opportunities for success.

Kevin Dykema
NCTM President
@kdykema