The Ultimate Guide to Teaching with Mathematical Discourse | Part 1

Posted by Lindsey Sönmez on January 07, 2020

Math education means flipping flashcards, regurgitating formulas, powering through endless worksheets, and a whole lot of memorization, right? Think again.

Rote memorization has long been the norm when it comes to teaching math. But an increasing number of credible studies have revealed that intentional discourse is the key to instilling the concepts, skills, and thought processes that are necessary for students’ long-term mathematical success. 

One school even found that mathematical discussion caused a jump of more than seven percent in K-through-8th-grade students’ test scores over the course of one year. And since higher test scores and better understanding are goals we can all get behind, let’s dive in.

What is Mathematical Discourse?

You’ve likely heard of the phrase, but what exactly is intentional discourse? And how is it used within the scope of teaching math?

The National Council of Teachers of Mathematics (NCTM) defines intentional discourse as “students comparing and contrasting ideas and methods, constructing viable arguments, critiquing each other’s reasoning, and helping each other make sense of mathematics.” 

So rather than purely memorizing various equations and formulas, this research-backed technique encourages your students to share their mathematical reasoning (questioning, conjecturing, defining, and explaining) through verbal communication with classmates or a written explanation. And through that sharing, students are able to clarify concepts, draw out different perspectives, identify any misconceptions, create new connections and solidify once-vague connections. So in the end, the nature of this whole transfer of ideas makes new concepts more memorable.


intentional discourse learn more

As you might guess, intentional discourse will look different depending on the grade level you’re working with. Early learners, for instance, might conduct a “turn and talk”, while high school students identify flawed logic in a complicated equation through a written response. Specific strategies vary, but no matter the age of your students, discourse is beneficial to their mathematical growth.

Why Discourse is Important in Math

Valuable skills. Intentional discourse allows your students to bounce ideas off of each other, construct persuasive arguments, and question the how and the why behind the methods they’ve used to solve a problem. So while developing a deeper understanding of the concepts at hand, they’re also learning valuable skills in verbal communication and mathematical reasoning.

And while this may seem like a simple concept to implement in your classroom, it actually takes a lot of time and practice, consistently encouraging your kids to think metacognitively about their mathematical choices. But we’re sure you’ll find that the end result is well worth the effort. A mantra to keep in mind: consistent intentional discourse leads to intentional thinkers.

Mathematical reasoning. When an answer is not obvious, students naturally resort to questions and discourse to reach a resolution. These tasks strengthen your students’ neural networks, forming a deeper and more memorable conceptual understanding. Your students are more likely to remember the problem-solving strategies that they used—and more importantly, the reasoning behind those strategies—through their productive struggle

With every new problem they encounter, students build upon their reasoning skills while asking those important questions: “Which strategies are most efficient where, and why? What if one doesn't yield a reasonable answer? What comes next?” And it’s these questions that really get the wheels turning, further instilling the process of mathematical reasoning. 

Various approaches. Despite popular belief (and what most of us learned growing up), math is not a one-way street to the correct answer. Through discourse, you’ll find that students can  approach multiple avenues and pathways, all to arrive at the same solution. When we teach the traditional route, oftentimes kids just see numbers and dive right into problem-solving before considering the best approach. In short, reasoning matters.

Now that you’re familiar with the concept and importance of intentional discourse, you’re ready to put it into practice. 

Stay tuned for our next post, where we’ll share how you can start implementing these strategies into your math instruction, plus what to expect when you do.

Topics: intentional discourse, mathematical reasoning, productive struggle, math