Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

Introduction

"Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning" by Peter Liljedahl is an essential guide for math educators seeking to revolutionize the way their students learn, think, and engage with mathematics. Drawing on years of research and practical experience, this book provides a roadmap for creating a collaborative and stimulating classroom environment where students actively participate in problem-solving and develop as independent thinkers. By shifting the focus from answer-getting to learning through engagement, the book equips teachers with innovative strategies to foster deep understanding of mathematical concepts.

The education landscape, especially in mathematics, often prioritizes procedural knowledge — tasks and problems are presented merely as puzzles to be solved for correct answers. However, this book challenges that traditional setup by introducing actionable teaching practices that encourage students to think critically, reason logically, and work collaboratively. Whether you are an experienced mathematics educator or new to teaching, this book will serve as a practical, research-based guide to transforming your classroom into a space of inquiry, innovation, and meaningful learning.

Detailed Summary of the Book

The book delves into the core elements of what defines a "thinking classroom" — an environment where students are fully engaged in the learning process by actively working through rich mathematical problems and collaborating with peers. It introduces 14 research-backed teaching practices that promote a shift from teacher-centered instruction to student-centered learning. These practices cover every aspect of classroom culture, from how students work in groups to how tasks are presented and how feedback is given.

Each chapter focuses on a specific practice, such as selecting random groups to break away from pre-assigned hierarchies, using vertical non-permanent surfaces (e.g., whiteboards) to encourage visible thinking, and crafting problems that inspire deep thinking rather than rote recall. What makes this book particularly powerful is its balance between rigorous research and practical implementation. The strategies presented have been tried and tested in classrooms around the world, and real-life examples illustrate their effectiveness.

The book also emphasizes the importance of building a culture of trust and curiosity in the classroom. Small but deliberate changes in how students are grouped, how teachers respond to questions, and how hints are given can significantly impact student engagement and learning outcomes. Ultimately, the book advocates for shifting students' mindsets—from passive learners to active thinkers—and equipping them with the tools to solve complex problems well beyond the classroom.

Key Takeaways

• Foster a culture of active problem-solving and engagement through group collaboration.
• Encourage student thinking by using open-ended questions and tasks designed to provoke inquiry.
• Use vertical surfaces (such as whiteboards) to make thinking visible and improve collaboration.
• Randomly assign groups to break down social barriers and ensure equity.
• Focus on formative assessment strategies that promote growth, instead of summative results.
• Create an environment where mistakes are seen as learning opportunities, not failures.

Famous Quotes from the Book

Here are a few impactful quotes from "Building Thinking Classrooms in Mathematics" that capture its essence:

• “Thinking is the vehicle of learning. Without thinking, students are simply regurgitating information.”
• “To rethink how we teach, we must rethink what we value in the classroom.”
• “Engagement happens when students have a reason to think and a task worthy of their effort.”
• “Mistakes are evidence of learning. They help us move forward.”

Why This Book Matters

Mathematics education is at a crossroads. The traditional model of instruction, focused on procedural learning and answer-getting, is quickly becoming outdated in a world that demands creative and critical problem-solvers. "Building Thinking Classrooms in Mathematics" is not just a book for math educators — it is a call to action to rethink classroom practices to better align with the way students naturally learn and thrive.

The book matters because it provides concrete, research-supported methods for fostering a generation of students who are not afraid to think. It shifts the focus from memorizing algorithms and solving worksheets to engaging with meaningful problems and working collaboratively. By prioritizing student thinking, the strategies outlined in this book help teachers nurture skills such as resilience, curiosity, and a willingness to tackle challenging problems — abilities that are invaluable in life beyond the classroom.

For educators who have long wished to break convention and breathe fresh air into their teaching practice, "Building Thinking Classrooms in Mathematics" offers both inspiration and practical guidance. Its relevance spans all grade levels and educational contexts, making it a must-read for those who are passionate about creating transformative learning experiences.