Math Education · Curriculum · Instructional Design

Math Class Has Run the Same Script for a Century. Here's the Rewrite.

The four steps a district used to move math class from copying patterns to asking questions.

Christy Vehe · Valley View School District

7 min read

K–12 · Math Education · Instructional Design

Step 1Say out loud what kind of learner you are building

Step 2Swap in routines that cannot be shortcut to one answer

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Step 3Ask students to describe what doing math looks and sounds like

Step 4Run the activity, then let students debrief what they saw

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ResultStudents who question and wonder, not students who recall

Key takeaways The "watch me, then copy me" trap Build the room before the lesson Four steps A room where being wrong is part of the plan FAQs

Key takeaways

Valley View's math department built student curiosity by setting classroom norms first, then adding notice and wonder and think-pair-share.

Christy Vehe's four steps start with a math department naming the kind of learner it wants, and cost a district nothing beyond one meeting.

Ninth graders who learned standard deviation through productive struggle showed stronger conceptual understanding than peers given direct instruction.

01

The "watch me, then copy me" trap

A student whose only skill is copying a pattern has nothing left the second the pattern changes.

Plenty of people once beat "Through the Fire and Flames" on Guitar Hero's expert level, then picked up an actual guitar and produced a sound like a cat falling down a staircase. Every note hit. Zero songs learned.

That gap shows up in math class daily. Students run a memorized process perfectly on problems one through four, then freeze the second the numbers get rearranged.

Christy Vehe has spent 21 years at Valley View School District working on that gap. As Director of Math and Science, Secondary, now finishing year 24 in education, she is going after the oldest habit in the subject.

"I am working to disrupt the traditional thinking that math is a memorized subject matter. It's a place and a space where kids need to question, they need to wonder, they need to invoke their curiosity."

— Christy Vehe, Director of Math and Science, Secondary, Valley View School District

The "watch me, then copy me" trap

Christy knows the format she is up against because it is the format that produced her. "Watch me show you how to do a lot of math," she says, describing every degree she earned.

The script has barely changed in a century. Teacher works three problems on the board. Students copy the pattern onto problem four. Worksheet for homework. Bell.

It survives because it moves fast and because it fits inside a 47-minute period when there are still 12 standards left to cover in April. Every math teacher has run it.

The cost lands later, on the problems that look unfamiliar. Nationally, 27% of eighth graders scored proficient or advanced on the 2024 NAEP math assessment, and the small gains that did happen came from the highest performers while the lowest performers lost more ground. A student whose only skill is copying a pattern has nothing left the second the pattern changes.

Then there is what the format does to the room. When a correct answer is the only acceptable thing to say out loud, saying anything at all becomes a risk, and a room full of teenagers will do that math instantly.

02

Build the room before you build the lesson

Curiosity has to live in the culture of a room before it shows up in a lesson plan.

Christy's first move had nothing to do with resources.

"If we have this vision that we're going to create learners who are curious and have questions, then we have to build that community and the classroom environment to have that openness."

— Christy Vehe

Curiosity has to live in the culture of a room before it shows up in a lesson plan.

The four steps below only work once students believe they can think out loud and be wrong on purpose. Skip that part and think-pair-share becomes 90 seconds of teenagers awkwardly staring at each other (and nobody likes that sort of cringe).

03

How to rebuild math class in four steps

It costs nothing and takes one department meeting.

Step 01

Say out loud what kind of learner you are building.

Before her department touched a lesson plan, Christy's team named the goal in plain language: students who question and wonder, instead of students who recall.

That sentence became the filter for everything that followed, including which resources to buy and which professional learning to run. It costs nothing and takes one department meeting. It also gives teachers something to point at when a new product shows up looking modern and delivering the same worksheet.

Step 02

Swap in routines that cannot be shortcut to one answer.

Christy wanted a curriculum that "allows students to not always mess into one right answer."

"Consider using instructional routines like notice and wonder, or the idea around 'think-pair-share,' where I get to think of an idea, share with you an idea, and then we see where that goes as a group," she says.

Both routines put a pause between the problem and the answer, which is the exact space memorizing skips. Notice and wonder throws an image or a problem in front of students and asks what they see before anybody is allowed to solve it. Think-pair-share gives every kid a private draft of an idea before it goes public, which lowers the cost of being wrong from humiliating to mildly interesting.

Step 03

Ask students to describe what doing math looks and sounds like.

A routine only works when students know what they are supposed to be doing inside it. Christy's teachers build the new norms with the kids, in the kids' own words.

"Thinking about how do I build community? What does it look like to do math? What does it sound like? What should you see?" Christy adds, citing some examples teachers could ask themselves.

Students write that description themselves, then they enforce it on each other, which saves a teacher running five sections a day a considerable amount of energy.

Step 04

Run the activity, then let students debrief what they saw.

Christy's teachers announce nothing about culture. They run a lesson and ask students what they noticed about it.

"We really go through activities with kids in the classroom and then have them tell us their experience," she says. "What did they see in the activity? Oh, they saw other people talking, and they saw people walking around the classroom."

Then students make the comparison on their own: "'Wait, I sat in a math classroom and I saw somebody show me how to do three examples and then I was expected to do that,'" Christy recalls a student saying.

Kids name the shift in their own language, which holds up better than a teacher explaining it to them.

04

A room where being wrong is part of the lesson plan

The first thing that changes is what students are willing to attempt.

The first thing that changes is what students are willing to attempt. They start working on problems they do not already know how to solve.

"They can have productive conversations, some productive struggle, an ability to be thinkers and not necessarily just memorizers."

— Christy Vehe

The second change shows up in who owns the rules. Students can describe what a functioning math class looks like, which gives teachers a way to read the room separately from checking content mastery. When things drift, the kids usually notice before the adults do.

Rigor is the objection that comes up at every department meeting where this gets raised. Christy is firm that student thinking still ties back to "the mathematical language" and "the big concepts and ideas." The destination stays exactly where it was.

The research points the same direction. In one Carneige Learning study, ninth graders who worked their way into standard deviation through productive struggle reported spending much more mental effort than classmates who received direct instruction, and their post-test results showed stronger conceptual understanding and better transfer. The struggle cost them more. It bought them more.

All of it starts with a department deciding what a math classroom should sound like, then asking the kids to help build it.

Want the version with the classroom stories attached? Christy tells them on our podcast, along with what she would do differently.

05

FAQs

Common questions about productive struggle and math classroom design

What is productive struggle in math class?

Productive struggle is the mental effort students spend working on a math problem before anyone shows them a method. Christy Vehe uses routines like notice and wonder so students describe what they see before solving. Research links that effort to stronger conceptual understanding.

How do teachers build curiosity in a math classroom?

Teachers build curiosity by setting classroom culture before changing lessons. Christy Vehe's department first named the kind of learner it wanted, then asked students to describe what doing math should look and sound like. Students who write those norms tend to enforce them.

Does teaching math through student questioning lower rigor?

Student questioning does not lower rigor as long as student thinking ties back to mathematical language and the big concepts. Christy Vehe keeps the same standards and the same assessments. The classroom routines change while the expectations stay put.

What is the notice and wonder routine?

Notice and wonder is a classroom routine where students look at an image or a problem and say what they see before solving anything. The pause blocks the memorized shortcut. Christy Vehe pairs it with think-pair-share so every student drafts an idea privately first.