Top Tips for Building Thinking Classrooms in Mathematics

Hey, math teachers, does this scenario sound familiar?

You’ve done it. You’ve planned the perfect math lesson! It’s chock full of relevant content that connects with students’ interests and differentiates to meet all learner needs. You’ve painstakingly grouped students for ideal mixed abilities. 

This lesson is going to be great! It's time to get your math on.

But you get to the end of your perfect lesson, and... Crickets. Yawns. Kids are trying to pack up early to beat the bell. 

You realize only a handful of students gained any real understanding of the content. The rest passively drifted through the work.

Even with over three decades of combined teaching experience, this happened to us all too often. The grind of intensive planning and running ragged during class with little payoff is exhausting. Something has to change, but what?

In a quest to avoid these defeating lessons, we came across Peter Liljedahl’s Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning. Instead of classrooms where teachers do all the thinking, Liljedahl promises something different: math lessons rife with student engagement. Kids are actively moving, talking, collaborating, and developing their own ideas. Student work shows conceptual mastery. They’re doing the thinking—not the teacher!

Liljedahl calls these “thinking classrooms,” and they’re where the math magic happens.

Peter Liljedahl's philosophy on “building thinking classrooms”

Dr. Peter Liljedahl, a Math Education Professor at Simon Fraser University in Canada, wrote his book about what works best in engaging math classrooms.

During his research, he examined the efficacy of a slew of classroom practices. Liljedahl considered everything from traditional paper/pencil tasks to using whiteboards or projectors to various seating and standing arrangements. He looked at classrooms where students were passive participants and those where they actively collaborated.

This research laid the foundation for the pedagogical insights in Building Thinking Classrooms. The book presents a fresh perspective on classroom dynamics, task allocation, and collaborative learning methodologies. Just what tired teachers need to switch things up a bit! 

Liljedahl offers 14 practices for math classrooms, complete with micro and macro moves appended to each chapter. These strategies encourage students to take charge of their learning through inquiry-based methods. And spoiler alert: we'll be showing off these moves at The National Institute this summer!

Sneak peek on how to build a thinking classroom

Interested in seeing your math students actively collaborate, problem-solve, and own their learning? Here’s a summary of some of Liljedahl’s top tips.

1. START WITH “THINKING TASKS” AND A CULTURE OF VULNERABILITY

To build a thinking classroom, you must first foster a culture of vulnerability. Students need to feel safe taking risks and understand failure is normal—especially in math! It's important for kids to feel comfortable in math class. This helps them move from simply sitting to actively participating in math.

Once your students understand it’s okay to take risks, you're ready for the next step. It's time to prioritize group engagement with problem-solving exercises and mental puzzles. 

These tasks, mathematical but initially non-curricular, spark student motivation and instill a mindset of self-challenge. As students become comfortable with interactive group math, you’ll gradually transition them to curriculum-aligned activities and progressively increase in complexity.

2. RANDOMIZE STUDENT GROUPS

At the core of Liljedahl's methodology lies randomized group work, which breaks down social barriers and enhances student participation. Randomized groupings are especially effective when you build them on a previously established foundation of trust and vulnerability.

To keep your students on track, assign specific roles. Doing so ensures inclusivity and effective task management. 

Finally, get your students standing while they’re in their groups. Getting out of the desk-and-chair rut is a research-based method to promote active engagement. No more sitting and spacing out or watching the clock for your students!

3. VERTICAL, NON-PERMANENT SURFACES

Another tactic Liljedahl emphasizes is the use of vertical, non-permanent work surfaces. These surfaces can include whiteboards, poster-sized sticky notes, or anything that gets your students up and moving. Non-traditional work areas are fun and allow your students to think clearly. They also create an organic flow of knowledge by observing others’ work. 

Additionally, research shows students are less distracted by electronic devices when standing up. And what teacher doesn’t want fewer power struggles over technology in the classroom?

4. QUESTIONING STRATEGIES

How many times has a student asked you, “Is this right?” Probably more than you can count if your experience is anything like ours! Liljedahl has a suggestion for that.

According to Liljedahl, teachers play a pivotal role in facilitating learning by prioritizing questions that encourage independent thinking. Answering “Is this right?” should be avoided at all costs.

Instead, foster essential metacognitive skills and resilience by engaging in questioning strategies that extend thinking and encourage students to persevere. By simply never answering the “Am I right?” question, you inspire students to master their learning and emphasize the value of perseverance and collaboration.

5. EVALUATING STUDENTS’ UNDERSTANDING

In terms of assessment, Liljedahl advocates for evaluating student processes rather than solely focusing on end products. 

After all, math is a subject that builds and is full of complex moves to get to an end solution. Don’t discount all of the work your students do to get there. It’s often the most fascinating way to peek into their brains and understand them as learners.

Use formative assessments to guide learning progress. Summative assessments should encompass individual and group contributions, reflecting the collaborative nature of the learning environment.

Want to learn more about math thinking classrooms?

Have we piqued your interest in thinking classrooms? We suggest grabbing a copy of Liljedhal's book for the best information, but applying it in real life is a whole new challenge.

Let us help! The best way to turn an idea into action is to try it yourself. We’ll be doing just that at this summer’s LONG + LIVE + MATH: The National Institute (TNI). We’ll be moving and grooving and having fun in our sessions about Building Thinking Classrooms at each of the three math institutes.

Learn how to make your classrooms more engaging. Share your ideas with others. Connect with math teachers from all over the country. Leave the event feeling energized and ready for the new school year.

We can’t wait to see you there!