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Mathematics Instruction

The tools, tasks, and discourse routines that shift mathematics classrooms from places of doing into places of genuine student thinking.

Dr. Peter Liljedahl Featured ExpertDr. Peter LiljedahlHelping educators transform classrooms from places of doing into places of thinking — through 15 years of research-backed practice. Read bio

Topic Overview

What it takes to build a classroom where every student actually thinks.

Most K-12 math classrooms are not places of thinking. They are places of doing — students following procedures, mimicking examples, and producing answers without understanding why they work. Peter Liljedahl's research found that in a typical classroom, only about 20% of students are genuinely engaged in mathematical thinking at any given time. The rest are slacking, stalling, or performing the appearance of effort without engaging cognitively at all.

Building Thinking Classrooms is a framework developed from 15 years of classroom research to answer one question: how do we get more students to think — and to think longer? The answer, it turns out, is not a single intervention but 14 specific, interrelated teaching practices that together restructure the environment, the tasks, the groupings, and the norms of a mathematics classroom in ways that make thinking not just possible but inevitable.

Why most math classrooms produce doing, not thinking

The problem is structural. Traditional math instruction is built around the demonstration-practice cycle: the teacher shows, students copy, students practice. This produces competent mimics — students who can reproduce procedures in familiar contexts but cannot transfer, adapt, or reason when conditions change. Peter's research identified this as the core failure mode of math education, not a failure of students or teachers but of the classroom design itself.

The core insight

If you want students to think, you have to build the conditions in which thinking is more likely than not thinking. That means changing the task, the workspace, the grouping, and the norms — not just the curriculum.

The role of thinking tasks

Not all tasks produce thinking. Most textbook tasks are exercises — they require students to apply a known procedure to a familiar problem type. Thinking tasks require students to grapple with something genuinely unfamiliar. Peter's research distinguishes between curricular and non-curricular thinking tasks, and shows that beginning a lesson with a non-curricular thinking task increases the quality of thinking students apply even to the subsequent curricular work.

Vertical non-permanent surfaces

Of all 14 BTC practices, Peter's research identified one as having the single most positive and profound effect: having students work in random groups at vertical whiteboards. When students stand at a vertical surface, the anonymity of sitting disappears. Mistakes are visible and erasable. Collaboration becomes natural. Stalling and faking are nearly eliminated. The workspace itself changes the behavior.

In the 15 years that I have been engaged in thinking classroom research, nothing we have tried has had such a positive and profound effect on student thinking as having them work in random groups at vertical whiteboards.

Peter Liljedahl

Visible random grouping

One of the earliest and most counterintuitive BTC practices is visible random grouping — assigning students to new, randomly-formed groups for every class, displayed visibly so students can see the process is genuinely random. Peter's research found this single change shifts student identity from fixed ("I'm a low math student") to contextual, reduces social stratification in the classroom, and dramatically increases cross-group help-seeking and mathematical conversation.

Assessment and homework in a thinking classroom

Traditional assessment and homework structures can undermine a thinking classroom if left unchanged. Peter's 14 practices include specific approaches to formative assessment, check-your-understanding questions, and homework that are aligned to the thinking classroom norms — shifting the purpose of assessment from judgment to growth and the purpose of homework from practice to consolidation.

Where to start

The BTC framework is designed to be implemented incrementally — you do not need to adopt all 14 practices at once. Peter recommends starting with three: thinking tasks, visible random grouping, and vertical non-permanent surfaces. These three create the conditions for the others to take root. RocketPD's resources and cohort provide a structured path from first steps to full implementation.

Why This Topic Matters

Why This Topic Matters

Build real mathematical thinking

Students who think in math class develop reasoning and transfer skills that survive beyond the test — not just procedure recall.

Break fixed math identity

Visible random grouping disrupts the social stratification that tells students they are "not a math person" before they've had a real chance.

Make collaboration structural

Vertical non-permanent surfaces and random grouping make peer collaboration a natural outcome of the environment, not a forced activity.

Design tasks that demand thinking

The right task is the gateway to everything else in BTC — without thinking tasks, no other practice reaches its full potential.

Align assessment to growth

BTC assessment practices shift the purpose from judgment to growth — giving students feedback that builds confidence alongside competence.

Implement without burning out

BTC is designed for incremental adoption — three practices first, then the rest — making it sustainable for real teachers in real schools.

Topic FAQ

Common Questions

Building Thinking Classrooms is a research-based framework developed by Dr. Peter Liljedahl over 15 years of classroom research. It consists of 14 specific teaching practices that together restructure the mathematics classroom to make student thinking the default — not the exception.

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Explore More Resources on Mathematics Instruction.

Browse guides, cohorts, podcast episodes, and practical frameworks built around Dr. Peter Liljedahl's Building Thinking Classrooms research — the most widely adopted mathematics PD framework in K-12 education.