For a long time, I thought I knew what rigorous math instruction looked like.

Harder problems. More steps. More complicated numbers. More practice.

If students were struggling, I assumed the work must be rigorous. If they finished quickly, I’d give them more. If they mastered a skill, I’d make the next set of problems harder.

I wasn’t trying to overwhelm students. I genuinely thought I was helping them grow.

But eventually, I started noticing something.

Some of my most capable students were checking out.

Not because they couldn’t do the mathematics. They were checking out because they were doing the same kind of thinking over and over again.

Problem number three required the same reasoning as problem number twenty-seven. The numbers were different. The thinking wasn’t.

That’s when I started asking myself a question that has completely changed how I plan instruction:

Am I increasing the workload, or am I increasing the thinking?

Those are not the same thing.

Rigor and Difficulty Aren’t Synonyms

We use the word “rigor” a lot in education.

We talk about rigorous math lessons, rigorous standards, rigorous assignments, and rigorous expectations. But somewhere along the way, I think we’ve started confusing rigor with difficulty.

A lesson can be difficult without requiring much meaningful thought.

Students can spend an hour completing twenty-five problems and barely have to make a decision, explain their reasoning, compare strategies, or figure out why something works.

And the opposite can also be true.

Students can spend significant time wrestling with one carefully designed task and experience an incredible amount of mathematical rigor.

The difference isn’t the number of questions.

It’s the quality of the thinking.

One of the things I appreciate about Illustrative Mathematics is that it pushed me to rethink what cognitive demand can actually look like in a math classroom.

There are lessons where students may only solve a handful of problems. If you looked strictly at the quantity, you might wonder whether students are getting “enough” practice.

But then you watch what they’re actually doing.

They’re comparing strategies. Defending their reasoning. Looking for patterns. Making conjectures. Explaining why something works. Critiquing someone else’s thinking.

One rich problem can create more opportunities for mathematical thinking than twenty repetitive problems ever could.

That doesn’t mean practice isn’t important. It absolutely is.

It means practice and rigor aren’t synonyms.

The Question That Changed My Planning

One of the biggest shifts in my teaching has been changing the question I ask when I’m planning a lesson.

I used to ask:

“How can I make this harder?”

Now I ask:

“How can I make students think more?”

Those questions lead to very different instructional decisions.

Making something harder often means adding more numbers, more steps, more problems, more complexity, or more homework.

Making students think more might mean slowing down and asking why. It might mean comparing methods, looking for patterns, justifying reasoning, predicting before calculating, finding mistakes, or explaining connections.

The goal isn’t simply to give students something difficult to complete.

It’s to give them something worth thinking about.

And honestly, that’s where I think students begin experiencing mathematics instead of simply completing it.

Where Does the Rigor Actually Live?

Let me give you an example from my classroom.

If you walked into my classroom during a Math Wars routine, you might think you were watching a fairly traditional practice session. Students are solving problems. We’re working through examples together. There are correct answers. There’s repetition.

On the surface, it looks like practice.

But the rigor isn’t necessarily in the worksheet.

It’s in the conversations.

We’ll work through a problem together, and then I’ll ask a student to explain why their strategy works. Maybe another student solved it differently, so now we’re comparing approaches.

Sometimes I’ll ask:

“Do you agree with that answer? Why?”

Not because I’m trying to catch someone making a mistake. I want students listening mathematically. I want them evaluating reasoning instead of waiting for me to tell them who’s right.

Other times, I’ll put up a common mistake and ask students to convince us why it doesn’t work.

Those moments create some of the richest mathematical conversations we have.

The worksheet didn’t become rigorous because I added harder numbers.

It became more rigorous because students had to think about mathematics instead of simply doing mathematics.

That’s a really important distinction.

Sometimes We Need to Stop Rescuing Students

Another shift I’ve made over the years is resisting the urge to answer students’ questions too quickly.

This is still something I have to be intentional about.

When a student is stuck, every teacher wants to help. Sometimes helping means explaining. But sometimes helping means asking a better question and giving the student enough space to work through the discomfort.

I’ve learned that if I immediately rescue students every time they get uncomfortable, I may also be rescuing them from the opportunity to think.

That doesn’t mean leaving students frustrated or refusing to support them.

It means giving them enough support to keep moving without taking the thinking away.

Sometimes I’ll ask:

“What do you already know?”

Or:

“Can you represent it another way?”

Or simply:

“Talk me through what you’re thinking.”

Those questions don’t make the mathematics harder.

They make the thinking deeper.

Students Don’t Need Less Thinking. They Need Better Support.

This has been especially important for me when working with students who have struggled with mathematics.

It’s tempting to lower the cognitive demand because we want students to experience success. I’ve absolutely been guilty of that.

But I’ve learned something from teaching intervention classes:

Students don’t need less thinking. They need better support while they’re thinking.

That’s a huge difference.

I can scaffold a task. I can chunk a problem. I can provide sentence stems, visual models, partner discussions, and immediate feedback.

None of those things automatically reduce rigor.

They can actually make rigorous thinking more accessible.

That’s what I want to be more intentional about.

Not lowering expectations.

Building better pathways toward them.

Rigor Doesn’t Have to Happen Every Minute

There’s another piece of this conversation that I think gets overlooked.

I don’t believe rigor means every minute of a math lesson needs to involve deep cognitive demand.

Students need fluency.

There are skills where repetition matters. Accuracy matters. Efficiency matters. Automaticity matters.

But there are also moments when I want students to wrestle with ideas.

So now, when I’m planning a lesson, I ask myself two questions:

Where do students need fluency?

And:

Where do I want students to think?

Those moments don’t have to look the same.

If every minute requires deep cognitive demand, students can become exhausted. If every minute is procedural practice, students can become disengaged.

Great lesson design requires knowing when students need to practice a skill and when they need to wrestle with an idea.

That’s the balance I’m always chasing.

What Does Rigorous Math Instruction Actually Look Like?

I don’t think there’s one answer.

It might be

• a rich task where students have to make decisions.
• a mathematical discussion where students compare two strategies.
• asking students to analyze an incorrect solution and explain where the reasoning went wrong.
• a carefully chosen question that forces students to explain why instead of simply giving an answer.
• a fairly ordinary practice routine that becomes much more rigorous because of the conversations surrounding it.

The common thread is student thinking.

That’s the part I want to pay more attention to.

Not how many problems are on the page, how long the assignment is, or how complicated the numbers look.

What are students actually being asked to do with their minds?

Before You Make Your Next Lesson Harder…

The next time you’re planning a lesson and think, “This needs to be more rigorous,” pause before adding five more problems.

Instead, ask yourself:

Where do I want my students to think more deeply?

Maybe you need to add a question.

Maybe students need to compare strategies.

Maybe you need to create space for discussion.

Maybe they need to defend their reasoning.

Maybe the lesson doesn’t need more work at all.

It needs a better opportunity for thinking.

Because rigor isn’t measured by how much students do.

It’s measured by the quality of the thinking we ask them to do.

And that’s something we can design intentionally.

Want Help Deciding What Your Lesson Needs?

Not every lesson should become a project.

Not every lesson should be direct instruction.

And not every lesson needs to be completely redesigned.

Sometimes the best choice is focused practice with opportunities for deeper mathematical thinking. Other times, a project or richer learning experience might make more sense.

That’s why I created the Project or Practice Guide.

It walks you through the questions I use when deciding how to design an instructional experience, with student thinking and learning goals at the center.

Download the free Project or Practice Guide

One Question to Take Into Your Next Lesson

Before you teach tomorrow, ask yourself:

Where will my students simply practice, and where will they truly think?

Because the goal isn’t to make math harder.

The goal is to make mathematical thinking richer.

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