What School Leaders Need to Know Before — and After — a Math Classroom Observation

Pamela Seda
Apr 21
5 min read

Updated: 6 days ago

Dr. Pamela Seda · Mathematics Education Consultant

When the Answers Are Right But the Learning Isn't

Every school leader I've ever worked with has stood in the back of a math classroom and felt some version of the same quiet discomfort: something about this lesson isn't quite right — but I can't put my finger on it.

The students are working. The teacher is teaching. The curriculum is district-approved. The answers on the board are correct. And yet, something feels off.

Most principals walk out of that classroom and say nothing — or offer vague comments. They assume that naming what's wrong requires a deep understanding of mathematics. You might think, “I don’t have a math background. Who am I to say the task isn't rigorous?”

Here's what I want you to know: you don't need to understand the math to assess whether the task is rigorous. You just have to know what to look for in students.

Rigor Isn't in the Content — It's in the Demand

When most people think about rigor in math class, they often equate it with difficulty — harder problems, more complex numbers, higher-level content. But difficulty and demand are not the same thing.

A task can appear challenging yet only require following a set of directions. Conversely, a task can involve straightforward mathematics while demanding that students think deeply, explain their reasoning, and make genuine decisions about how to approach the work.

Rigor is not about the appearance of the math. It is about what the task asks of the student's mind.

The Standards for Mathematical Practice describe what that demand looks like in action: students are making sense of problems, explaining and defending their reasoning, choosing tools and strategies, and attending carefully to precision. When these elements are present, students are engaging in the work of mathematics — not just completing it.

The Yes / No Rigor Test

This is the test: not what's written on the board, not how difficult the numbers look — but what students are actually doing.

If students are making sense of the problem, explaining their thinking, making decisions about how to approach the work, and engaging with one another's reasoning, the task is rigorous.

If they are not, it isn't.

You don't need to know whether the algorithm is correct or whether the standard is being addressed. You need to watch students and ask:

Are they thinking, or are they following directions?

What You're Looking For — In Plain Language

You are not listening for correct answers. You are watching for evidence of thinking.

When a task is rigorous, students exhibit behaviors you can see and hear. They pause before they start, making sense of what the problem is asking. They discuss their reasoning with each other — agreeing, disagreeing, asking why. They make choices — trying different strategies, selecting tools, and representing their thinking in multiple ways. They are careful — labeling their work, using mathematical language, and checking whether their answers are reasonable.

The Standards for Mathematical Practice describe exactly what that looks like. Four of those practices belong in every math classroom, every day, regardless of grade level or content:

| Practice | Description |

|----------|-------------|

| MP 1 | Make sense of problems and persevere in solving them — students are figuring something out, not just following steps. |

| MP 3 | Construct viable arguments and critique the reasoning of others — students can explain how they got their answer and engage with someone else’s thinking. |

| MP 5 | Use appropriate tools strategically — students are making decisions about how to approach the work. |

| MP 6 | Attend to precision — students are using accurate language, checking their work, and labeling their thinking carefully. |

When a task is not rigorous, the classroom environment looks different. It may still appear productive — students are busy, answers are being produced, and the teacher is circulating. However, students are executing, not thinking. They are following a sequence of steps designed by someone else rather than making decisions of their own. Remove the directions, and they stop.

This is what I call GPS instruction — the teacher provides turn-by-turn navigation so precise that students never have to build their own understanding of the route. When you follow GPS directions, you arrive at your destination. But try it again tomorrow without the app, and you’re stuck. You followed instructions, but you didn't learn the route.

A lot of math instruction works exactly the same way. Compliance and rigor are not the same thing. Correct answers are not evidence of learning.

Why This Matters for Leadership

When leaders lack a clear lens for rigor, they often default to what's visible and comfortable: engagement, pacing, coverage, and correct answers.

Without realizing it, they may reinforce the very instruction they're trying to improve.

They leave classrooms affirming lessons where students were compliant but not thinking. They offer feedback that focuses on what the teacher did rather than what students experienced. They miss the opportunity to shift instruction because they don't yet have a way to name what matters.

This is not a failure of leadership. It's a missing lens.

What many leaders don't realize is that teachers often experience something just as complex on the other side of that same observation. Because leaders rarely have access to how their practices are experienced by teachers, this gap remains invisible. It doesn't close on its own.

The Question That Changes the Post-Observation Conversation

Once you have this lens, the post-observation conversation transforms entirely.

You are no longer trying to evaluate the mathematics — which was never your job anyway. Instead, you share what you observed in students and ask one question:

"What did the task ask students to work through and make sense of?"

This question does not evaluate the teacher. It does not require you to have a math background. It shifts the conversation from what the teacher did to what the task made possible for students.

And it opens reflection instead of defense.

If the answer is not much, the next question isn't why didn't you teach better? It's:

What would the task need to look like to give students more opportunities to think and make sense together?

That is a conversation about growth.

It is also a conversation most math teachers have never had with a school leader — because most school leaders didn't know they were allowed to have it.

You are allowed.

And now you have the lens to lead it.

About the Author

Dr. Pamela Seda is a mathematics education consultant and co-author of Choosing to See: A Framework for Equity in the Math Classroom. Her ICUCARE® Framework supports school leaders and teachers in creating effective, high-quality mathematics learning environments for every student.