Building Thinking Classrooms: A Paradigm Shift in Mathematics

What is Building Thinking Classrooms?

Building Thinking Classrooms (BTC) is a pedagogical framework, developed by Dr. Peter Liljedahl, consisting of 14 specific teaching practices that have been scientifically proven to increase student thinking and engagement. It is based on the premise that traditional classroom structures and routines—like learners sitting at desks facing a teacher—actually discourage active thinking.

The approach is built on three foundational pillars:

  1. Vertical Non-Permanent Surfaces (VNPS): Learners stand to work on whiteboards or windows. This increases risk-taking, as mistakes are easily erased, and makes thinking visible to the teacher and peers.
  2. Visibly Random Groups (VRG): Groups are changed every single lesson using a transparently random method (like playing cards). This breaks down social barriers and eliminates the “status” often associated with fixed ability groups. It also removes ‘ceilings’ that are placed on some learners through fixed groupings.
  3. Thinking Tasks: Lessons begin with engaging, open-ended tasks that require collaboration and problem-solving, rather than a lecture from the teacher followed by repetitive exercises.

Why Are Teachers Making the Switch?

The BTC approach tackles learner disengagement head-on by breaking down the physical and social barriers to learning. Here is how it redefines the mathematical experience:

  • Instant Engagement with VNPS: By moving learners to Vertical Non-Permanent Surfaces (whiteboards or windows), you instantly increase persistence. Students are more willing to take risks when they know they can easily erase and correct.
  • Breaking Social Hierarchies: Using Visibly Random Grouping every single day ensures that every learner works with everyone else. This eliminates “cliques,” builds a collaborative culture, and forces mathematical ideas to be the centre of classroom discussion.
  • Deep Thinking over Rote Memorisation: Instead of focusing on process-driven methods to solve abstract calculations, BTC starts with Thinking Tasks. Learners grapple with meaningful problems first, building an understanding of what they “need to know”, for conceptual fluency to be achieved. 
  • Dynamic Mathematical Discussion: Because groups are standing and visible to one another, “knowledge mobility” happens naturally. Ideas spread across the room, sparking high-level discussion and peer-to-peer coaching that a seated classroom can never achieve.

Who benefits from the approach and why?

While BTC is a win for the entire learning community, specific groups see unique benefits:

  • Reluctant or Lower-Confidence Learners: Because the environment is “non-permanent,” these learners feel safer making mistakes. They are no longer isolated but are supported by the collective brainpower of a random group.
  • High-Achieving Learners: These learners are challenged to move beyond “answer-getting.” They benefit from having to explain their reasoning to peers, which solidifies their conceptual understanding and develops leadership skills.
  • Teachers: The role of the teacher shifts from “deliverer of information” to “facilitator of thinking.” Teachers find they have more time to circulate, observe learner-thinking in real-time, and provide targeted, responsive support, through “hints and extensions”, rather than repeating the same teaching points.
  • The Classroom Community: The daily randomisation of groups builds a culture of “knowledge mobility,” where learners share strategies and solutions, and learn to trust and work with every one of their classmates, regardless of social standing.

Common Issues Building Thinking Classrooms Helps Address

BTC was designed specifically to solve the flaws in the traditional classroom teaching model:

  • Learner Passivity (“Mimicry”): In many maths lessons, learners simply copy the steps the teacher does. BTC forces learners to grapple with the logic themselves, making them the primary drivers of the lesson.
  • The “I’m Not a Maths Person” Myth: By removing the stigma of being “wrong” (thanks to the whiteboards) and the pressure of working alone, BTC helps dismantle maths anxiety and builds a growth mindset.
  • Classroom Management and “Hiding”: It is easy for a learner to disengage at a desk in the back of the room. It is nearly impossible to “hide” when standing at a whiteboard with two or more peers. Engagement becomes the default state.
  • The Expert/Novice Divide: Traditional ability grouping often reinforces who is “smart” and who isn’t, and creates ‘ceilings’ on learning. BTC creates a fluid environment where different learners bring different strengths to the table every day.