Student-centered mathematical thinking

What Is a Building Thinking Classroom?

A teacher-focused guide to Peter Liljedahl’s Building Thinking Classrooms framework, including core practices, lesson flow, implementation steps, and common mistakes.

Published and reviewed by STEMEngine AI · Updated August 2, 2026

Definition

Building Thinking Classrooms (BTC) is a research-informed framework developed by mathematics education researcher Peter Liljedahl. Its 14 practices are designed to replace passive classroom routines with conditions that sustain student thinking. Widely recognized practices include thinking tasks, visibly random groups, vertical non-permanent surfaces, purposeful teacher questioning, responsive hints and extensions, consolidation from student work, and student-created notes.

Best used for

Increasing student participation, discussion, and mathematical risk-taking
Moving from teacher demonstration toward student sense-making
Supporting mixed-readiness groups with responsive hints and extensions
Making student thinking visible for formative assessment

Core ideas

Thinking is the central classroom activity

Tasks, grouping, workspace, and teacher moves are selected for their effect on student thinking—not because they are routines to check off.

Visibly random groups change participation

Students see that groups are formed randomly and change frequently. This reduces fixed social roles and communicates that everyone is expected to contribute.

Vertical non-permanent surfaces support risk-taking

Standing groups work on erasable vertical surfaces. Work becomes visible, easy to revise, and available for the teacher to monitor across the room.

Teacher responses should keep students thinking

Instead of immediately resolving uncertainty, teachers answer with prompts, hints, and extensions that return intellectual responsibility to students.

Consolidation is built from student work

The teacher sequences selected strategies from accessible to sophisticated, helping students connect their work to the intended mathematical ideas.

How to implement it

1
Begin with one practice cluster
Start with a worthwhile thinking task, visibly random groups, and vertical non-permanent surfaces. Establish routines before adding more practices.
2
Launch quickly
Give the minimum information needed to begin. Avoid demonstrating the central strategy students are meant to develop.
3
Monitor for thinking and flow
Notice where groups are stuck, ready for a hint, or ready for an extension. Avoid moving every group through an identical script.
4
Select work for consolidation
Choose student approaches that reveal the lesson’s progression, including a useful partial strategy or misconception when appropriate.
5
Create meaningful notes and checks for understanding
Students record what their future selves need, then complete a short assessment that reveals current understanding rather than merely task completion.

Classroom example

Example: linear relationships

Goal: students move from a growing visual pattern to a general linear rule.

1.Build or draw figures 1–3 of a growing tile pattern.
2.Predict the number of tiles in figure 4 and justify.
3.Find figure 10 without drawing every figure.
4.Compare two group strategies and identify what remains constant.
5.Write a rule for figure n and connect each term to the visual pattern.

Consolidation

Sequence a recursive count, a table-based strategy, and an explicit rule; connect the constant rate and initial value to visible parts of the pattern.

Common mistakes

Treating BTC as “students at whiteboards”

The surfaces matter because they change risk-taking and visibility, but they do not replace task quality, teacher moves, consolidation, or assessment.

Giving procedural tasks that require little thought

Collaboration cannot make an imitation exercise into a thinking task. Use tasks with decisions, patterns, constraints, or multiple viable approaches.

Helping too quickly

Immediate correction can end productive struggle. Ask what students know, what they have tried, or what they notice before supplying information.

Consolidating from the teacher’s preferred solution only

Use student work to build the conceptual story from the bottom up rather than replacing it with a polished lecture.

Frequently asked questions

Who developed Building Thinking Classrooms?

Building Thinking Classrooms was developed by Dr. Peter Liljedahl, a professor of mathematics education at Simon Fraser University, through extensive classroom research.

What are vertical non-permanent surfaces?

They are erasable vertical workspaces—often whiteboards, windows, or similar surfaces—where small groups stand and make their thinking visible and revisable.

Does BTC eliminate direct instruction?

No. It changes when and how explicit instruction occurs. Teachers still clarify, formalize, connect, and model, especially during consolidation, but avoid doing the key thinking before students have engaged with the task.

Can BTC practices be implemented gradually?

Yes. Teachers commonly begin with the first practice cluster—thinking tasks, visibly random groups, and vertical non-permanent surfaces—then add questioning, hints and extensions, consolidation, notes, and assessment practices.

Sources and further reading

STEMEngine AI is an independent educational tool and is not affiliated with or endorsed by the referenced authors or organizations.

Build a Building Thinking Classrooms lesson

Turn a topic and standard into a scaffolded lesson progression with teacher notes, differentiation, and print-ready materials.

Create a lesson