Reasoning Together

Vivian Quan is a teacher in Los Angeles, California. She has experience teaching and learning from prekindergarten through third-grade students, as well as supporting early childhood and elementary teachers in mathematics education. She believes that both learning mathematics and teaching mathematics can be spaces of agency, creativity, and joy.

• 1. What Are Collaborative Problem-Solving Routines, and Why Use Them? 2. How to Set Up for Collaborative Problem-Solving Routines 3. Collaborative Problem-Solving Routines: Target Number Routines 4. Collaborative Problem-Solving Routines: Story Problems 5. Collaborative Problem-Solving Routines: Finish the Sentence 6. Collaborative Problem-Solving Routines: Solve Multiple Ways 7. Collaborative Problem-Solving Routines: Sorting and Counting 8. Planning for Collaborative Problem-Solving Routines in Your Day, Week, and Year 9. Where You’ll Take Collaborative Problem Solving Next

After just a few pages of Reasoning Together, I paused to find a pen and notepad because I already needed to jot down important ideas. By the end of this lively and approachable book, I had (1) internalized a vision for teaching both collaboration and mathematics through collaborative problem-solving routines and (2) made a list of productive questions, facilitation moves, and teaching tips to start trying right away. Wherever you are in your teaching journey, Vivian Quan’s delightful book will inspire you to teach with curiosity, purpose, effectiveness, and joy.—Tracy Johnston Zager, author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant ClassroomsWhether you are interested in building a thinking classroom, or you are looking to implement innovative number strategies, or you want to increase the effectiveness of collaboration, Reasoning Together is for you. Through a brilliant use of real student interactions, Vivan Quan has put together an amazing collection of actionable routines that every grades 1-3 teacher can benefit from. This is how we get our students to think, talk, collaborate, and learn.— Peter Liljedahl, author of Building Thinking ClassroomsThis book offers a clear blueprint for turning math time in grades 1 to 3 into a place where thinking, talking, and belonging actually matter, not just answers. By weaving practical routines with real classroom stories, it shows how collaboration, not compliance, is what helps young students make sense of mathematics. If you want children to learn math by reasoning with others instead of performing in isolation, this is a guide worth checking out.— Robert Kaplinsky, author of Open Middle Math: Problems That Unlock Student ThinkingAs educators, we rarely have the opportunity to slow down time and really think about our practice in relation to our students and their brilliant mathematical ideas. Through engaging classroom vignettes and specific connections to practice, Vivian invites us to reflect and to imagine, to plan with intention, and to position all students competently as we consider a range of ways to facilitate mathematically meaningful opportunities that are collaborative, productive, and joyful.— Janene Ward, Graduate Student ResearcherThis book captures the magic of Vivian’s classroom - something I’ve witnessed live - and gives you the tools to do it yourself. An inspiring, practical, and detailed approach to nurturing collaboration and problem-solving.— Berkeley Everett, K-5 Math CoachAnyone who has worked to support deep collaboration — not just surface “partner A, partner B” kinds of structures, but true engaging with each other's ideas in ways that require negotiation, perseverance, and strategic in-the-moment support — knows that it’s not easy and doesn’t happen overnight. Quan knows this from her expertise working with children and teachers and has woven together important ideas and examples that help us get started (wherever we are), learn alongside students, and continue to reflect, deepen, and grow our teaching practice of supporting rich math collaboration. — Angela Chan Turrou, PhD, Senior Researcher, Teacher Educator, and Author“For educators committed to positioning every student as a capable mathematical thinker, Reasoning Together offers both inspiration and practical guidance. Vivian Quan beautifully connects the insights of Cognitively Guided Instruction with the collaborative structures of Building Thinking Classrooms, showing how routines can open space for all students—including those who have historically been marginalized in mathematics—to contribute ideas, make sense of problems, and learn alongside one another. Through vivid classroom stories and actionable routines, this book helps teachers create math communities where reasoning, collaboration, and belonging grow together.”— Joanna Hayman, CGI Math Coach, UCLA Mathematics Project