Imagine walking into a classroom buzzing with energy. Students are scattered around the room, actively engaged, debating, scribbling on whiteboards, and genuinely excited about math. There’s no “front” of the classroom, no rows of desks, no passive note-taking. Instead, there’s a dynamic space where thinking is visible, mistakes are celebrated, and every student is a confident mathematical thinker.
I’m here to share a transformative approach to teaching mathematics that has the power to reshape our classrooms and ignite a passion for learning in our students.
As a math teacher with over 10 years of experience, I’ve had my fair share of challenges. I’ve stood at the front of the classroom, pouring my heart into lessons, only to be met with blank stares or the dreaded question: “Can you just tell us the answer?” It’s a disheartening feeling, realizing that despite our best efforts, students often aren’t truly engaging with the material.
This frustration led me on a quest to find a better way—a way to encourage deep thinking, genuine understanding, and a love for mathematics. That’s when I discovered Peter Liljedahl’s book, “Building Thinking Classrooms in Mathematics.”
Liljedahl conducted extensive research, observing over 400 classrooms, and identified a pervasive issue: students weren’t actually thinking. They were either slacking, stalling, faking it, or simply mimicking procedures without comprehension. Our traditional teaching methods, with an emphasis on rote learning and procedural mimicry, were unintentionally fostering these non-thinking behaviors.
So, how do we break this cycle? How do we create classrooms where thinking is the central focus? Liljedahl proposes a contrarian approach—a complete paradigm shift that transforms our classrooms into thinking classrooms. He outlines 14 practical, actionable practices to achieve this transformation. Today, I’d like to share a few that have profoundly impacted my teaching and my students’ learning.
1. Visibly Random Groups
In most classrooms, we carefully curate student groups—pairing strong students with those who struggle, or mixing personalities to minimize disruptions. But Liljedahl suggests we ditch this careful planning and embrace visibly random groups. Using playing cards or a random name generator, students are grouped anew each day.
At first, this idea terrified me. Wouldn’t random groups create chaos? How could I ensure that students receive the support they need?
But here’s the magic: when students work with new peers regularly, they’re forced to communicate their ideas more clearly, justify their thinking, and consider different perspectives. It diminishes established hierarchies and cliques, fostering a more inclusive and collaborative environment. Students become more adaptable, and the collective mathematical thinking in the room deepens.
2. Vertical Non-Permanent Surfaces
Next, Liljedahl introduces the concept of vertical non-permanent surfaces. Think whiteboards, windows, or even large sheets of paper taped to the walls—anything students can write on that’s vertical and easily erasable.
Why vertical? When students stand and work on vertical surfaces, they’re more engaged and active. It makes their thinking visible—not just to the teacher, but to their peers. It encourages a culture where students can see and learn from each other’s thought processes in real-time.
The non-permanent aspect reduces the fear of making mistakes. Students are more willing to take risks, try new strategies, and correct their errors. The classroom becomes a space of exploration rather than perfection.
I recall a day when one of my students, who rarely participated, was enthusiastically explaining his group’s approach to a problem on the whiteboard. His peers were gathered around, asking questions, challenging assumptions, and together, they arrived at a solution none had considered individually. It was a powerful moment of collective learning.
3. Defronting the Room
Traditionally, classrooms have a clear front—the focal point where the teacher stands, and students face. Liljedahl suggests we defront the room. By eliminating the designated front, we shift the focus away from the teacher as the sole source of knowledge and create a more student-centered environment.
In my classroom, this meant rearranging desks and workspaces to facilitate collaboration and discussion. The physical space now reflects our learning philosophy—it’s flexible, dynamic, and centered around student engagement.
Defronting the room encourages students to take ownership of their learning. They become active participants rather than passive recipients. The teacher becomes a facilitator, guiding and supporting rather than directing every action.
4. Handling Questions: Smile and Walk Away
One of the most challenging shifts was changing how I responded to students’ questions. Traditionally, when a student asks for help, we jump in to provide answers or guidance. But in a thinking classroom, Liljedahl recommends that we smile and walk away.
At first, this felt counterintuitive—even neglectful. But the purpose isn’t to abandon students; it’s to encourage them to think independently and collaboratively. By not immediately providing answers, we prompt them to wrestle with the problem, discuss with their group, and develop problem-solving resilience.
I’ve witnessed students who initially depended heavily on my input begin to trust their abilities. They engage more deeply with the material, and their confidence grows. The “aha” moments become more frequent and more meaningful because they’ve earned them through their own efforts.
5. Consolidation from the Bottom
When wrapping up a lesson, we often highlight the best solutions or the most efficient methods. Liljedahl suggests we reverse this approach by consolidating from the bottom—starting with the less successful solutions.
By examining common errors or less effective strategies first, we validate all students’ efforts and create learning opportunities from mistakes. It opens discussions about why certain approaches didn’t work and how they can be improved.
This approach demystifies failure. It teaches students that mistakes are not only acceptable but valuable. They become more willing to take risks and less afraid of being wrong, which is essential for deep learning.
6. Meaningful Notes
Note-taking is another area ripe for transformation. Instead of having students passively copy down everything from the board, we encourage them to create meaningful notes—notes that are taken by students, for students.
This means students focus on what they need to remember, summarizing concepts in their own words, creating diagrams, or jotting down lingering questions. It’s about processing information actively and making it personally relevant.
I noticed that when students took ownership of their notes, they referred back to them more often. Their notes became valuable study tools rather than forgotten pages in a notebook.
7. Assessment Through Data Gathering
Finally, we need to address assessment. Traditional grading systems often reduce learning to points and percentages, which can be discouraging and limit students’ willingness to take risks.
Liljedahl proposes a data-gathering paradigm—seeing assessment as a way to gather evidence of student learning rather than assigning scores to every task. We focus on understanding each student’s progress, their thought processes, and their growth over time.
This might involve using rubrics that highlight different levels of understanding or creating portfolios of student work. The goal is to provide meaningful feedback that guides further learning, rather than just a grade that marks the end of it.
In my experience, this approach has led to more meaningful conversations with students about their learning. They become more reflective and motivated to improve, not just for a better grade, but for their own development.
Transforming our classrooms into thinking classrooms is not an overnight process. It’s a journey that requires us to challenge long-held beliefs and step out of our comfort zones. But the rewards are immense.
I’ve seen students who were disengaged and indifferent become curious, enthusiastic learners. The energy in the classroom shifts. It becomes a place of exploration, collaboration, and genuine mathematical thinking.
As educators, we have the privilege and responsibility to shape the learning experiences of our students. By embracing the practices of a thinking classroom, we empower them to become confident, capable thinkers—not just in mathematics, but in all areas of life.
I encourage you to explore Peter Liljedahl’s “Building Thinking Classrooms in Mathematics.” It’s a resource filled with practical strategies and profound insights that can revolutionize your teaching and your students’ learning.
Let’s commit to creating classrooms where thinking thrives, where mistakes are stepping stones, and where every student realizes their potential as a powerful mathematical thinker.