building thinking classrooms pdf
Building Thinking Classrooms represents a transformative approach to mathematics education, shifting focus from rote memorization to fostering deep conceptual understanding.
Peter Liljedahl’s research, spanning fifteen years, culminated in a practical guide detailing fourteen optimal teaching practices designed to cultivate a truly thinking classroom.
This methodology aims to engage students in rich mathematical tasks, promoting active participation and enhancing learning across all grade levels, K-12.
What are Building Thinking Classrooms?
Building Thinking Classrooms (BTC) isn’t a curriculum or a set of lesson plans; rather, it’s a pedagogical shift. It’s a deliberate move away from traditional, teacher-centered instruction towards an environment where students are actively engaged in the process of thinking and problem-solving.
Inspired by observing teachers struggling to implement rich mathematical tasks effectively, Peter Liljedahl developed BTC as a framework to unlock student potential. The core idea revolves around creating a classroom culture that prioritizes thinking over performing;
This means structuring lessons and the learning space to encourage students to wrestle with complex ideas, collaborate with peers, and develop a deeper, more conceptual understanding of mathematical principles. It’s about fostering independence and metacognition, empowering students to become self-directed learners. The approach is detailed in his book, and supported by companion website resources.
The Core Philosophy of Peter Liljedahl’s Approach
Peter Liljedahl’s core philosophy centers on the belief that students learn best when they are actively thinking, not simply following procedures or memorizing facts. He observed that many traditional math classrooms inadvertently stifle thinking by prioritizing correct answers over the process of reasoning.
His approach challenges this by intentionally designing learning experiences that demand cognitive effort. This involves creating tasks that are accessible yet challenging, and implementing teaching practices that encourage students to grapple with ideas, make mistakes, and learn from them.
Liljedahl emphasizes the importance of creating a non-threatening environment where students feel safe to take risks and share their thinking. The goal isn’t just to get the right answer, but to develop a robust understanding of mathematical concepts and the ability to apply them in novel situations, as detailed in his book and companion resources.

The 14 Teaching Practices

Building Thinking Classrooms introduces fourteen optimal practices, meticulously researched and refined, to transform mathematics instruction and foster deeper student engagement and learning.
Practice 1: Vertical Non-Permanent Surfaces (VNPS)
Vertical Non-Permanent Surfaces (VNPS) represent a cornerstone of the Building Thinking Classrooms approach, fundamentally altering how students interact with mathematical problems.
Traditionally, students solve problems horizontally on desks, limiting visibility and collaboration. VNPS – utilizing walls, windows, or large paper – encourages all students to simultaneously work and see each other’s thinking.
This practice isn’t merely about changing the surface; it’s about making thinking visible. Students can easily observe diverse solution pathways, critique reasoning, and build upon each other’s ideas.
The “non-permanent” aspect is crucial, allowing for quick iteration, error correction, and a low-stakes environment for experimentation. It fosters a culture where mistakes are seen as learning opportunities, not failures. VNPS promotes active participation and a collective sense of ownership over the mathematical process.
Practice 2: Random Selection of Students
Random Selection of Students is a deceptively powerful practice within Building Thinking Classrooms, designed to ensure equitable participation and combat the tendency for the same students to dominate discussions.
Rather than relying on volunteers – who are often the most confident or outspoken – random selection techniques (like popsicle sticks, cards, or digital tools) give every student an equal opportunity to share their thinking.
This practice isn’t about “calling on” students to provide the right answer; it’s about creating a safe space for all voices to be heard and valued. It encourages students to consistently engage with the material, knowing they might be asked to articulate their reasoning at any moment.
Random selection fosters a more inclusive classroom environment and promotes deeper learning by exposing students to a wider range of perspectives.
Practice 3: Wait Time
Wait Time, a cornerstone of Building Thinking Classrooms, directly addresses the common impulse to immediately fill silence after posing a question. Liljedahl advocates for intentionally pausing – providing students ample time to formulate thoughtful responses.
This isn’t merely about giving students a chance to recall facts; it’s about allowing them to engage in deeper cognitive processing, connect concepts, and articulate their reasoning.
Effective wait time isn’t a fixed duration, but rather a deliberate practice of resisting the urge to jump in with answers or rephrase the question prematurely.
Increased wait time demonstrably leads to more complex and nuanced student responses, fostering a classroom culture where thinking is valued over speed.
Practice 4: Think-Pair-Share Variations
Think-Pair-Share, a familiar collaborative learning strategy, is significantly enhanced within the framework of Building Thinking Classrooms. Liljedahl emphasizes moving beyond the standard implementation to unlock its full potential for deep thinking.
Variations include “Think-Pair-Square,” where pairs join with another pair to discuss and refine their ideas, and “Think-Pair-Write,” adding a written component to solidify understanding.
The key is to ensure the “Think” phase is substantial, providing genuine individual processing time before collaboration.
These variations promote active participation, peer learning, and the articulation of mathematical reasoning, creating a more inclusive and intellectually stimulating environment for all students.
Practice 5: Collaborative Work Structures
Building Thinking Classrooms champions diverse collaborative work structures beyond traditional grouping. Peter Liljedahl advocates for intentionally designed arrangements that maximize student engagement and thinking.
These structures include “expert groups” where students specialize in a portion of a task, then share their expertise, and “jigsaw” activities promoting interdependence.
Randomly assigned groups, facilitated by Practice 2, prevent predictable dynamics and encourage broader participation.
The goal isn’t simply collaboration, but productive collaboration – where students actively build upon each other’s ideas, challenge assumptions, and collectively construct deeper understanding of mathematical concepts.

Implementing the Practices
Building Thinking Classrooms’ success hinges on deliberate implementation of the 14 practices, requiring adjustments to physical space and pedagogical approaches for optimal student learning.
Setting Up the Physical Space for VNPS
Vertical Non-Permanent Surfaces (VNPS) are central to the Building Thinking Classrooms approach, fundamentally altering the learning environment. Traditional horizontal desks often encourage passive learning and limit visibility of student work.
Transforming classrooms involves utilizing walls, windows, and even furniture as writable surfaces – think chart paper, whiteboard paint, or large sticky notes. This allows all students’ thinking to be visible to themselves and their peers, fostering a collaborative atmosphere.
The key is to ensure ample surface area for every student to independently engage with the task. This isn’t about neatness; it’s about capturing the process of thinking, the false starts, and the evolving ideas. VNPS encourages students to externalize their thoughts, making them more concrete and accessible for discussion and refinement.
Consider the flow of movement and accessibility when arranging these surfaces, ensuring all students can easily reach and contribute to the collective thinking space.

Strategies for Effective Wait Time
Implementing effective wait time is crucial within Building Thinking Classrooms, moving beyond simply pausing after posing a question. It’s about deliberately creating space for students to grapple with complex ideas and formulate thoughtful responses.
Liljedahl advocates for a minimum of five seconds, often extending to ten or more, resisting the urge to fill the silence. This allows more students to access prior knowledge, consider multiple approaches, and develop more sophisticated thinking.

To manage the discomfort of silence, teachers can use non-verbal cues like maintaining eye contact or nodding to signal encouragement. Avoid rephrasing the question prematurely, as this can inadvertently signal the ‘correct’ answer.
Furthermore, wait time isn’t just after initial questioning; it’s also vital after a student response, allowing peers time to process and build upon the idea.
Maximizing Think-Pair-Share for Deep Thinking
Within Building Thinking Classrooms, Think-Pair-Share isn’t merely a collaborative activity; it’s a powerful tool for fostering deeper conceptual understanding when implemented strategically. The “Think” phase is paramount – students require dedicated, silent time to wrestle with the task individually before discussion.
Avoid rushing to the “Pair” stage. Encourage students to articulate their reasoning, not just their answers, during paired discussions. Teachers should circulate, listening for varied approaches and prompting further explanation.
The “Share” component should extend beyond simply reporting answers. Select students to share how they arrived at their conclusions, highlighting different strategies and challenging assumptions.
Variations, like Think-Pair-Square, can expand the collaborative network, enriching the exchange of ideas and promoting metacognitive reflection.

Tasks and Activities
Building Thinking Classrooms thrives on rich mathematical tasks, designed to provoke thought and discussion, moving beyond procedural exercises to cultivate genuine understanding.
Designing Rich Mathematical Tasks
Creating tasks that foster deep thinking is central to the Building Thinking Classrooms approach. These aren’t simply problems with a single correct answer; they are intentionally designed to be ambiguous, multi-faceted, and accessible to all learners, regardless of their current skill level.
A rich task encourages multiple entry points, allowing students to engage with the material in ways that align with their individual understanding. It should provoke curiosity, stimulate discussion, and require students to justify their reasoning; The goal isn’t necessarily to find the answer, but to explore different solution pathways and learn from each other’s approaches.
Effective tasks often involve real-world contexts or open-ended questions, prompting students to apply mathematical concepts in meaningful ways. The companion website provides numerous examples of such numeracy and thinking tasks, serving as a valuable resource for educators seeking inspiration and practical ideas.
Numeracy and Thinking Tasks Examples
The Building Thinking Classrooms companion website offers a wealth of numeracy and thinking tasks designed to ignite student curiosity and promote deeper mathematical understanding. These examples demonstrate how to move beyond traditional procedural exercises towards problems that demand reasoning, justification, and collaboration.
Tasks range in complexity and cater to diverse grade levels, often presented as visual puzzles, pattern recognition challenges, or open-ended investigations. Many tasks intentionally lack explicit instructions, forcing students to clarify the problem, devise strategies, and communicate their thinking effectively.
Examples include tasks involving geometric arrangements, number sequences, and spatial reasoning, all crafted to encourage multiple solution paths and robust mathematical discourse. Utilizing these resources allows educators to seamlessly integrate thinking-focused activities into their existing curriculum.
Utilizing the Companion Website Resources
The companion website for Building Thinking Classrooms in Mathematics serves as an invaluable extension of the audiobook and core text, providing educators with readily accessible support for implementation. It’s a dynamic hub filled with practical tools designed to facilitate the transition to a thinking classroom environment.
Resources include downloadable numeracy and thinking tasks, categorized by skill and complexity, alongside a comprehensive book study guide perfect for professional learning communities (PLCs). Each chapter benefits from an executive summary, distilling key concepts and actionable strategies.
Furthermore, the website offers direct links to Peter Liljedahl’s personal website (www.peterliljedahl.com) for continued learning and exploration. These resources collectively empower teachers to confidently embrace and sustain the principles of Building Thinking Classrooms.

Benefits of a Thinking Classroom
A thinking classroom fosters enhanced student engagement, deeper conceptual understanding of mathematics, and actively promotes metacognition—thinking about one’s own thinking processes.
Enhanced Student Engagement
Building Thinking Classrooms dramatically boosts student engagement by shifting the focus from teacher-led instruction to student-centered exploration. The 14 teaching practices, rooted in Peter Liljedahl’s research, create an environment where students are actively involved in the learning process, rather than passively receiving information.
Vertical Non-Permanent Surfaces (VNPS) encourage all students to participate simultaneously, eliminating the anxiety of public display and fostering a collaborative atmosphere. Random selection ensures equitable participation, preventing the same students from dominating discussions.
These practices, combined with carefully designed rich mathematical tasks, spark curiosity and motivate students to grapple with challenging problems, leading to a more profound and sustained level of engagement. Students become invested in their learning, driving deeper understanding and retention.
Deeper Conceptual Understanding
Building Thinking Classrooms moves beyond procedural fluency, fostering a significantly deeper conceptual understanding of mathematical principles. By implementing the 14 teaching practices, educators create a learning environment where students aren’t simply memorizing steps, but actively constructing their own mathematical knowledge.
Rich mathematical tasks, central to Liljedahl’s approach, demand more than rote application; they require students to reason, problem-solve, and make connections between different concepts. Practices like Wait Time and Think-Pair-Share encourage thoughtful reflection and collaborative sense-making.
This approach cultivates a robust understanding that transcends superficial knowledge, enabling students to apply their learning to novel situations and demonstrate genuine mathematical proficiency. The focus shifts from doing math to understanding math.
Promoting Metacognition
A key benefit of Building Thinking Classrooms is the deliberate promotion of metacognition – students’ ability to “think about their thinking.” The 14 teaching practices aren’t just about what students learn, but how they learn, encouraging self-awareness and reflective practice.
Vertical Non-Permanent Surfaces (VNPS) and collaborative work structures provide opportunities for students to externalize their thought processes, making them visible to themselves and peers. Random selection ensures equitable participation, pushing all students to articulate their reasoning.
This fosters a classroom culture where students monitor their own understanding, identify gaps in their knowledge, and adjust their strategies accordingly. Ultimately, this empowers them to become independent, self-regulated learners capable of tackling complex mathematical challenges.

Resources and Further Learning
Peter Liljedahl’s website (peterliljedahl.com) and the audiobook’s companion website offer valuable resources, including tasks, guides, and executive summaries for implementation.
Peter Liljedahl’s Website

Peter Liljedahl’s personal website, www.peterliljedahl.com, serves as a central hub for educators seeking to deepen their understanding and implementation of Building Thinking Classrooms. Beyond being a biographical source, the site provides a wealth of supplementary materials not fully contained within the book itself.
Visitors can expect to find additional insights into the core philosophy underpinning the 14 teaching practices, alongside expanded explanations of each practice’s nuances. The website frequently features blog posts detailing real-world classroom applications, addressing common challenges, and offering practical solutions.
Furthermore, Liljedahl often shares updates on his ongoing research, ensuring educators remain abreast of the latest developments in the field. It’s a dynamic resource, constantly evolving to support teachers in their journey toward creating truly thinking-centered learning environments, and a key companion to the book.
Companion Website for the Audiobook
The official companion website for the audiobook, Building Thinking Classrooms in Mathematics, Grades K-12, offers a robust collection of resources designed to enhance the learning experience. Accessible through links provided with the audiobook purchase and on Peter Liljedahl’s website, it extends the book’s content in valuable ways.
Key features include a curated selection of numeracy and thinking tasks, ready for immediate classroom use, categorized by skill and complexity. A comprehensive book study guide facilitates collaborative professional development, prompting insightful discussions among educators.
Additionally, each chapter benefits from an executive summary, providing a concise overview of key takeaways. This website is an invaluable tool for teachers seeking to fully integrate the 14 teaching practices into their mathematics instruction.
Frequently Asked Questions (FAQs) from the Book
Building Thinking Classrooms in Mathematics proactively addresses common challenges and uncertainties educators face when implementing these new pedagogical approaches. Each chapter concludes with a dedicated Frequently Asked Questions (FAQs) section, offering practical guidance and clarifying potential roadblocks.
These FAQs cover a wide range of topics, from logistical considerations like classroom setup for Vertical Non-Permanent Surfaces (VNPS) to deeper philosophical questions about student thinking and the role of the teacher.
The book also provides a summary of micro and macro moves teachers can make to effectively enact each strategy, alongside thought-provoking questions for Professional Learning Communities (PLCs) and “Try This” tips for immediate implementation. This ensures a smooth transition towards a truly thinking classroom.




















































































