“Why Mathematical Proficiency Begins with Language”

I struggled with math for most of my life. Through childhood, high school, and even into adulthood, until I had to teach it. Suddenly, I realized I didn’t truly understand math; I only knew how to follow steps, memorize rules, and get answers. I thought math was just about numbers and symbols (5, x, =). I had no idea that being proficient in math had anything to do with language.

Language is something we often take for granted. We assume most children come to school with basic language skills and that those skills automatically transfer to every subject. And we tend to think math is the one subject where language doesn’t matter—after all, it’s just numbers, right? But when we look closely at how we use math in our daily lives, in our standards, and in our assessments, it becomes clear: math is deeply connected to language.

That connection starts earlier than most people realize. Babies as young as 4 to 6 months are already following sounds, noticing rhythm, and babbling in speech-like ways. Counting, too, has rhythm (both forward and backward)! When parents count out loud (“one, two, three!”) while playing or reading, children begin to internalize that musical sequence. Later, they connect those words to actual quantities, building the foundation for one-to-one correspondence.

As children grow, the math words they hear shape their understanding. When adults naturally use words like “put together,” “take away,” “whole,” or “part,” children start to connect language to mathematical ideas. By the time they enter school, math language becomes even more important. Kindergarteners are expected to understand and use terms like “add,” “subtract,” “longer,” and “fewer.” But students can’t use these words correctly unless they’ve heard and spoken them often.

Imagine all of the mathematical conversations you can have with your young children through play!

That’s why a rich math classroom should be anything but quiet. Students need time to talk, reason, and explain. True mathematical understanding isn’t just about getting the right answer, it’s being able to explain how you got there and why it makes sense.

Our math standards make this clear. For example, one standard asks third graders to “explain arithmetic patterns using properties of operations.” Another asks eighth graders to “describe the relationship between two quantities by analyzing a graph.” Notice the verbs—describe, explain, identify. Each one demands language. Students can’t meet these expectations without having opportunities to speak and write mathematically. And before they can write, they must be able to talk about their thoughts.

These kindergarten students are comparing numbers. The teacher is giving them the oral sentence frames “_ is greater than _ ” and “ _ is fewer than _” to help them have mathematical discussions.

So how do we support that?
Teachers can intentionally create spaces where students talk about math every day. That might mean using partner discussions, number talks, or structured routines that encourage everyone to share ideas aloud. High-quality instructional materials often embed these kinds of opportunities, but even when they don’t, teachers can add them in. The key is to make math discourse a normal, expected part of learning.

Stanford University’s Principles for the Design of Mathematics Curricula outlines ways to promote both language and content development. The resource includes powerful routines that can be adapted for any grade level. When students regularly participate in these discussions, they start to own the language of math—using words like “decompose,” “justify,” and “pattern” with confidence and understanding.

Because math is a language in itself, the words we use as educators and parents matter deeply. When we talk about math intentionally (naming, describing, and reasoning out loud) we help children make sense of the ideas behind the symbols.

If we want students to think mathematically, we have to let them talk mathematically.