Book Study: Teaching for Thinking

Fostering Mathematical Teaching Practices Through Reasoning Routines

Chapter 1: Teaching for Thinking

In the compelling opening chapter of Teaching for Thinking, Grace Kelemanik and Amy Lucenta challenge educators to rethink their approach to teaching mathematics. They spotlight the pitfalls of traditional, procedure-heavy methods that often stifle students' ability to reason and solve problems. Instead, the authors call for a transformative shift prioritizing critical thinking and deep understanding over note memorization. With an eye toward practical change, Kelemanik and Lucenta inspire teachers to embrace a mindset that values the journey of learning just as much as the outcome, setting the stage for the powerful reasoning routines detailed throughout the book.

For teachers, this chapter is a call to action to rethink their instructional strategies and align them with the goal of fostering deep, transferable mathematical understanding. It outlines the potential impact of reasoning-focused instruction on student outcomes, including increased engagement and critical thinking. Teachers gain insights into the “why” behind the shift, which is essential for motivating changes in practice.

Chapter 2: The Power of Reasoning Routines

Chapter 2 introduces reasoning routines as tools to create consistent opportunities for students to develop their mathematical thinking. Reasoning routines are designed to make classrooms more equitable by providing all students with access to challenging and meaningful mathematical discussions. The authors highlight the five essential strategies embedded in these routines: Annotation, Asking Yourself Questions, The Four Rs, Sentence Starters and Frames, and Turn and Talks.

This chapter benefits teachers by showing them how reasoning routines can transform their classrooms into spaces where every student feels confident contributing. The routines also help educators establish a predictable structure for lessons, reducing the cognitive load for both students and teachers. The content provides actionable ideas for fostering a collaborative and reasoning-centered classroom culture.

Chapter 3: Decide and Defend: A Reasoning Routine to Support Constructing Arguments and Critiquing Reasoning

The "Decide and Defend" routine focuses on helping students make decisions based on mathematical evidence and articulate their reasoning. Students are encouraged to analyze problems, construct arguments, and critique the reasoning of their peers in a structured way. This routine supports the development of essential mathematical practices, such as constructing viable arguments and fostering a deeper understanding of concepts.

For teachers, this chapter offers practical strategies to engage students in meaningful discussions and build their confidence in sharing ideas. It provides a framework for teaching critical thinking and communication skills, both of which are essential for success in mathematics and beyond. Teachers implementing this routine can expect greater student participation and improved reasoning skills.

Chapter 4: Contemplate Then Calculate: A Reasoning Routine to Support Structural Thinking

Chapter 4 introduces the "Contemplate Then Calculate" routine, which encourages students to pause and analyze the structure of mathematical problems before diving into calculations. By focusing on structural thinking, this routine helps students recognize patterns and connections, fostering a deeper understanding of mathematical concepts. The authors illustrate how this routine can shift the focus from procedural fluency to conceptual understanding.

Teachers gain a powerful tool for showing students how to approach problems intentionally and thoughtfully. This routine reduces reliance on guesswork and encourages a more analytical approach to problem-solving. It also supports students in developing habits of mind that are transferable to various mathematical contexts, making this content particularly valuable for educators seeking to build deeper, more reflective learners.

Chapter 5: Design Your Own Reasoning Routine

In this chapter, the authors guide teachers through the process of designing their own reasoning routines tailored to their specific classroom goals. Teachers can create routines that meet their students' unique needs by analyzing instructional objectives and aligning them with tasks that promote reasoning. The chapter provides step-by-step guidance for selecting tasks, planning discussions, and fostering a culture of reasoning.

Designing your own reasoning routine empowers teachers to take ownership of their instructional practices by equipping them with the tools to innovate and adapt. Teachers will appreciate the flexibility this approach offers, as it allows them to integrate reasoning routines into any curriculum. The guidance in this chapter helps educators feel confident in their ability to create impactful and engaging learning experiences.

Chapter 6: Making the Essential Strategies a Routine Part of Your Practice

The final chapter focuses on integrating the essential strategies presented in the book into daily teaching practice. The authors provide actionable advice for making reasoning routines a consistent part of instruction, ensuring they become habitual for teachers and students. They also address common challenges and offer solutions for maintaining these practices over time.

This chapter serves as a roadmap for sustaining meaningful change in teachers' classrooms. By embedding reasoning routines into everyday instruction, educators can create a lasting impact on students' mathematical development. The chapter reinforces the importance of persistence and reflection, encouraging teachers to continually refine their practices for the benefit of all learners.

Benefits for Teachers

This book is an invaluable resource for educators looking to transform their teaching practices and foster deep mathematical understanding. Teachers can create equitable learning environments by incorporating reasoning routines, enhance student engagement, and build critical thinking skills. The practical strategies and routines outlined in this book empower teachers to shift their focus from procedural teaching to fostering mathematical reasoning, leading to more confident, capable, and reflective learners.