When Our Words Expire

Why instructional coherence begins with the language we choose.

Every August, teachers welcome a new group of students into their classrooms.

We look at the standards, examine the curriculum, and begin planning from the assumption that students are arriving with the understanding developed during the previous year. We expect them to recognize familiar ideas, build on established concepts, and use mathematical language that allows us to move learning forward.

Too often, that's not the reality.

Instead, we discover that students know a procedure but can't explain why it works. They recognize a classroom phrase but not the mathematical concept behind it. Sometimes they confidently use vocabulary that, while familiar, is no longer mathematically accurate. Other times, the language they've learned has simply... expired.

That's one of the hidden costs of instructional inconsistency.

Students don't just carry knowledge from one grade level to the next.

They carry language.

And language shapes understanding.

One of the books that has challenged my thinking recently is The Math Pact: Achieving Instructional Coherence Within and Across Grades. The authors identify dozens of words and phrases that are commonly used in elementary classrooms but quietly become obstacles as students progress through mathematics.

That idea stopped me in my tracks.

Not because teachers are intentionally teaching students incorrectly.

But because we're often teaching language that serves today's lesson without considering tomorrow's learning.

Take a phrase like "show your steps."

Most of us have said it. I've certainly said it.

The problem isn't the intention. The problem is the message students receive.

"Show your steps" suggests there is one correct procedure to follow. "Explain your thinking" invites students to justify their reasoning, compare strategies, and communicate mathematically. One phrase values compliance. The other values understanding.

The same thing happens when we tell students to "borrow," "carry," "plug in," or "cancel out."

Those words may help students complete today's assignment.

But what happens when they enter the next classroom?

Receiving teachers aren't building on those phrases. They're talking about regrouping, substitution, properties of equality, composing and decomposing numbers, and equivalent representations. Suddenly, students feel like they're learning an entirely new language when, in reality, they're learning mathematics through more precise language.

The disconnect isn't always conceptual.

Sometimes it's linguistic.

That doesn't mean every classroom must sound identical. It does mean we should think carefully before replacing academic language with catchy acronyms, clever sayings, or memorable shortcuts. There's nothing inherently wrong with making mathematics engaging. There's nothing wrong with creating memorable experiences.

But memorable should never replace meaningful.

If you choose to use an acronym, teach the mathematics first.

If you create a catchy phrase, anchor it in accurate mathematical language.

If you simplify vocabulary for accessibility, make sure students eventually hear, use, and understand the language they'll encounter in future grades.

Lead with the mathematics.

Support it with the memory aid.

Not the other way around.

John Hattie reminds us that students develop deeper understanding when mathematical language is introduced intentionally and revisited over time rather than replaced with memory tricks. Precision isn't about sounding more academic. It's about helping students build concepts that endure long after they've forgotten a particular lesson.

I've become increasingly aware of this in my own practice.

There are phrases I used early in my career that I no longer use today. Not because I was careless, but because I know more now than I did then. Like every educator, I've had to unlearn habits before I could help students build stronger ones.

When we know better, we do better.

Instructional coherence isn't built only through aligned standards or carefully sequenced curriculum.

It's also built one conversation at a time.

One explanation.

One definition.

One carefully chosen word.

Because students don't need language that expires.

They need language that grows with them.

Reflection

As you prepare for your next lesson, ask yourself one question:

Will the language I'm using today still serve my students next year?

If the answer is yes, you're doing more than teaching today's lesson.

You're helping write the next chapter of their mathematical story.

Listen to Words Matter: How Consistency in Language Builds Math Understanding