Every math teacher knows the "zombie" look: students sitting passively, pencils poised, waiting for the teacher to write a step on the board so they can copy it. This is mimicking, not thinking. Peter Liljedahl’s research on Building Thinking Classrooms (BTC) offers a radical shift to break this cycle, transforming students from passive receivers into active problem solvers.
Two of the most visible and effective pillars of this framework are Vertical Non-Permanent Surfaces (VNPS) and Visibly Random Grouping. Together, they fundamentally change the chemistry of the classroom.
A VNPS is any vertical space where students can write and easily erase—think whiteboards, windows, or even erasable "wipe-book" posters mounted on walls. Instead of students working in notebooks at their desks, they stand in small groups at a designated board space. The teacher provides a single marker to the group, forcing them to discuss the problem before anyone writes anything down.
Liljedahl’s research found that when students write on paper, they are hesitant to start because mistakes feel "permanent." On a whiteboard, the "cost" of a mistake is zero. A quick swipe of a finger erases an error, which encourages students to take risks, try different strategies, and start writing within seconds rather than minutes.
It sounds simple, but moving students from their chairs to their feet changes everything. When a student is sitting, they can "hide" behind a laptop or a notebook. When standing at a board, their work is visible to the teacher and their peers. This visibility creates a natural social pressure to stay on task. In addition, standing keeps the body alert. It’s much harder to "zone out" when you are upright and physically moving the marker or pointing at a colleague's work.
As a teacher, you can scan the room in three seconds and see exactly where every group is stuck. You can provide a "hint" to one group that then ripples through the room as other groups glance over.
In a traditional classroom, students often sit with friends or are grouped by perceived ability. Both methods stifle thinking. Visibly Random Groups (VRGs) involve using a deck of cards or a digital randomizer to form groups of three at the start of every lesson. It helps break social barriers once students realize that every peer is a potential collaborator. The "cliques" that usually dictate classroom dynamics melt away over time.
In "ability-based" groups, students often fall into roles: the "smart one" does the work, and the others watch. In random groups, those roles are constantly shuffled, forcing different students to step up and explain their reasoning.
The ultimate goal of VNPS and random groups is to stop students from mimicking the teacher. When a teacher stands at the front of the room at a single board, they are the "source of all knowledge." Students wait for the teacher to show the "correct" way.
By moving the work to the perimeter of the room on vertical surfaces, the teacher becomes a facilitator rather than a lecturer. Students stop looking at the teacher for the next step and start looking at their own boards—and the boards of the groups around them. They begin to synthesize their own solutions, leading to deep, conceptual understanding that survives long after the bell rings. Let me know what you think, I'd love to hear. Have a great day.
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