The Evidence on 'Thinking Classrooms': How Vertical Whiteboards Are Rewiring Math Education

For decades, the architecture of the middle and high school mathematics classroom has remained stubbornly uniform. A teacher stands at the front of the room, modeling a procedural algorithm on a board, while students sit quietly at their desks, dutifully copying the steps into their notebooks.

But according to Peter Liljedahl, a professor of mathematics education at Simon Fraser University, this traditional setup inadvertently fosters a culture of "non-thinking." After conducting thousands of hours of classroom observations, Liljedahl concluded that in a typical seated math lesson, only about 20% of students are actively engaged in independent cognitive work.[1]

The remaining 80% of the room, his research found, falls into three distinct behavioral categories: slacking, stalling, or faking. Even the students who appear to be diligently taking notes are often just "mimicking"—following a rote algorithmic path laid out by the teacher without actually understanding the underlying mathematical concepts.[1]

To break this cycle of passive compliance, Liljedahl spent 15 years developing a framework known as "Building Thinking Classrooms" (BTC). Outlined in his 2020 book, the framework consists of 14 specific teaching practices designed to dismantle the institutional norms that inhibit student thinking.[1][3]

By 2026, the BTC framework has transitioned from a niche pedagogical theory into a dominant force in North American mathematics education. Its core practices are now ubiquitous at major educational conferences, and school districts across the U.S. and Canada are overhauling their math departments to align with its principles.[2][3]

The most visible and transformative element of the BTC framework is the use of Vertical Non-Permanent Surfaces (VNPS)—essentially, having students stand up and work together on large, wall-mounted whiteboards, chalkboards, or even windows.[1]

Liljedahl's research tested various workspaces, including horizontal whiteboards, vertical paper, and traditional notebooks. Vertical, erasable surfaces emerged as the undisputed winner for maximizing time on task, peer discussion, and mathematical persistence.

The psychology behind VNPS is surprisingly straightforward. When students sit at desks, their physical posture provides a sense of anonymity that makes it easy to disengage. Standing up removes that shield. Furthermore, the non-permanent nature of a whiteboard lowers the stakes for making mistakes; a student is much more willing to attempt a difficult problem if an error can be wiped away with a finger.[1]

This physical shift is paired with a practice called "Visibly Random Groups" (VRG). Instead of allowing students to choose their partners or grouping them by perceived ability, teachers use playing cards or digital randomizers to form groups of three at the start of every class.[1][3]

According to the framework, groups of three strike the optimal balance between knowledge redundancy and diversity of perspective. Because the grouping is visibly random, students cannot complain about unfairness, and the constant shuffling breaks down social cliques, forcing students to collaborate with every peer in the room over the course of a semester.[1][3]

Once at the boards, students are given "thinking tasks." Rather than starting with a lecture, the teacher presents a problem that students haven't yet been explicitly taught how to solve. The goal is to induce a state of "flow"—a delicate balance between boredom and frustration—by using a technique called "thin-slicing," which breaks complex concepts into a sequence of micro-challenges.[3]

Proponents of the model report dramatic transformations in classroom culture. Teachers note that the energy in the room shifts from passive silence to active, noisy collaboration. The vertical surfaces also allow educators to scan the room instantly, identifying which groups are stuck and which have discovered a novel solution path, enabling highly targeted interventions.[3]

However, as the BTC framework has scaled, it has ignited a fierce debate within the broader educational research community. Critics, particularly those grounded in cognitive science, argue that the model's reliance on unguided problem-solving conflicts with decades of research on how the human brain acquires new information.[2][4]

Researchers advocating for "explicit instruction" point to Cognitive Load Theory, which posits that novice learners possess limited working memory. They argue that asking students to discover mathematical procedures from scratch overloads their cognitive capacity, whereas direct, teacher-led modeling is a far more efficient way to build foundational skills.[4]

Furthermore, skeptics caution that much of the evidence supporting BTC relies on qualitative action research and proxies for learning, such as "time on task" or "enthusiasm," rather than rigorous, randomized controlled trials measuring long-term retention and standardized test scores.[2][4]

As one critic noted, praising the chaotic, non-linear appearance of student whiteboard work as a marker of deep thinking can sometimes mask a lack of mathematical precision and structure. The aesthetic of a busy, collaborative classroom does not automatically guarantee that individual students are committing core concepts to long-term memory.[4]

In response, defenders of the framework argue that academic research often lags behind classroom innovation. They point out that the qualitative data gathered from thousands of BTC classrooms is overwhelmingly positive, and that the framework does not entirely eliminate direct instruction, but rather shifts it to the end of the lesson.[2][3]

This end-of-lesson phase is a process Liljedahl calls "consolidation." During consolidation, the teacher brings the class back together to review the various strategies generated on the whiteboards, formalizing the math and connecting the students' intuitive discoveries to standard algorithms.[3]

Ultimately, the rapid rise of Building Thinking Classrooms highlights a fundamental tension in modern education: the desire to foster critical thinking and collaborative problem-solving versus the need for efficient, measurable knowledge transfer.[4][5]

As more empirical data emerges in 2026, many school districts are finding a middle ground. They are integrating vertical whiteboards and random grouping to inject energy and collaboration into their math blocks, while still reserving time for the structured, explicit instruction necessary to ensure that every student masters the fundamentals.[5]