Building Thinking Classrooms (BTC)

Building Thinking Classrooms (BTC), developed by Peter Liljedahl, is an approach to mathematics instruction focused on increasing student thinking, participation, problem-solving, and engagement.

Rather than positioning students as passive recipients of procedures, BTC emphasizes classrooms where students actively explore ideas, collaborate, reason through problems, and build understanding together.

Many BTC practices align naturally with inclusive and neurodiversity-affirming mathematics classrooms because they shift the focus away from speed, answer-getting, and silent individual work toward visible thinking and meaningful engagement.

At the same time, thoughtful implementation matters. Any classroom structure can either expand or limit access depending on how it is used.

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Traditional mathematics classrooms often center:

• note-taking,

• teacher explanation,

• procedural repetition,

• and individual completion of similar problems.

In these environments, students may become focused on:

• memorizing procedures,

• avoiding mistakes,

• or trying to determine the “correct” method as quickly as possible.

BTC shifts the focus toward:

• problem-solving,

• reasoning,

• collaboration,

• exploration,

• and visible mathematical thinking.

The goal is not simply getting answers, but engaging students in the process of thinking mathematically.

A central idea in BTC is the use of thinking tasks: problems that encourage students to reason, explore patterns, make connections, and develop strategies rather than immediately applying a memorized procedure.

Thinking tasks:

• often have multiple entry points,

• encourage discussion,

• allow different approaches,

• and create opportunities for productive struggle.

These types of tasks can help students see mathematics as something they actively engage with rather than something they passively receive.

For many neurodivergent students, flexible tasks may also reduce the pressure of finding one “correct” pathway immediately.

One well-known BTC practice involves students working collaboratively at vertical non-permanent surfaces such as whiteboards.

These environments can support:

• visible thinking,

• discussion,

• revision,

• experimentation,

• and shared problem-solving.

Mistakes become easier to revise because work is temporary and public thinking becomes normalized.

Collaboration can also help students externalize thinking that might otherwise remain internal.

However, collaborative environments are not automatically accessible for every student. Some students may experience barriers related to:

• communication,

• sensory overload,

• processing time,

• anxiety,

• or unclear participation expectations.

Supportive implementation matters.

Students benefit when teachers:

• clearly define collaboration expectations,

• provide processing time,

• allow multiple forms of participation,

• and recognize that engagement may look different across students.

BTC often emphasizes visibly random groupings to reduce status hierarchies and encourage broader participation.

When implemented thoughtfully, this can help:

• reduce fixed perceptions of ability,

• create more equitable participation opportunities,

• and encourage students to see mathematics as collaborative rather than competitive.

At the same time, participation should not be defined narrowly.

Some students may:

• process internally before speaking,

• need additional time to organize thoughts,

• communicate differently,

• or participate more comfortably through writing, diagrams, or smaller discussions.

Creating inclusive thinking classrooms means valuing multiple forms of participation rather than assuming all students engage in the same ways.

BTC emphasizes productive struggle: students grappling with meaningful mathematical ideas rather than immediately receiving procedures.

However, it is important to distinguish between:

• productive mathematical struggle

and

• unnecessary barriers.

Students should struggle with mathematical reasoning, not with:

• unclear instructions,

• inaccessible formatting,

• hidden expectations,

• excessive cognitive overload,

• or avoidable confusion.

Inclusive implementation means carefully considering whether barriers are supporting thinking or interfering with access.

Many BTC practices can support neurodivergent learners because they:

• emphasize reasoning over speed,

• value student thinking,

• encourage multiple approaches,

• normalize revision,

• and create opportunities for collaborative sense-making.

However, neurodiversity-affirming implementation also requires flexibility and reflection.

For example:

• some students may need additional processing time before group discussion,

• some may benefit from written directions alongside verbal instructions,

• some may require clearer structure during collaborative tasks,

• and some may need sensory or environmental supports to fully engage.

The goal is not to abandon BTC practices, but to thoughtfully adapt classroom structures so more students can meaningfully participate.

One of the most powerful aspects of BTC is its emphasis on student thinking rather than student performance.

Students are encouraged to:

• explore,

• revise,

• make mistakes,

• ask questions,

• and build understanding collaboratively.

This shift can be especially meaningful for students who have previously experienced mathematics as:

• timed,

• rigid,

• procedural,

• or centered around getting answers quickly.

When classrooms visibly value thinking, more students may begin to see themselves as capable mathematical thinkers.

Students are more likely to engage deeply with mathematics when classrooms communicate that their thinking matters, even before their answers are complete.