Early Algebraic Thinking in Action

A Teacher's Guide for Grades K–5

Blanton and Gardiner have successfully transformed algebra from a high-school gatekeeper into an elementary-grade gateway. This book is an essential roadmap for school leaders who are committed to equity, providing teachers with the practical “thinking practices” necessary to ensure every student develops the mathematical confidence and foundational logic required for long-term academic success.

The authors do a fantastic job of helping to make algebra relatable and attainable to everyone in this deep dive into early algebraic thinking. They take the fear of the variable and replace it with a hefty portion of reasoning and understanding. Any educator in elementary math would find this text a valuable resource in guiding them to understand the reasons why it is necessary to teach algebraic skills to even our youngest students.

This book will change the way elementary teachers approach algebra. It makes the content feel attainable and approachable, all in a clear, easy read.

Part of the reason educators have not made more progress in improving math teaching and learning is that we continue to operate from an incomplete understanding of what math is; a definition originating in our own limited math learning experiences as students. This book shows what real mathematical reasoning can look and sound like. It offers easy-to-implement learning experiences to engage students in algebraic thinking, allowing students to learn mathematics with understanding and recognize themselves as innately math capable.

This book provides a clear research-based approach to integrating algebraic thinking into the core math curriculum. From a district leadership perspective, I’ve seen this approach build coherence across classrooms while strengthening both teacher practice and student understanding. It is an invaluable resource for educators committed to building a comprehensive approach to early algebraic reasoning.

Early Algebraic Thinking in Action provides teachers with a roadmap for integrating algebra concepts with their mathematics instruction. The authors explain how integrating algebra and arithmetic deepens students’ understanding of arithmetic while also providing a foundation for formal algebra. Useful examples of how teachers can modify their curriculum to “raise the algebra temperature” of their lessons appear throughout the book. This resource is a valuable addition to any teacher’s collection.

Early Algebraic Thinking in Action: A Teacher’s Guide for Grades K–5 is a welcome addition to support teachers with fostering and deepening students’ algebraic thinking during the elementary years. I particularly appreciated that the authors provided learning goals to address the Algebraic Thinking Big Ideas by grade band. These learning goals are great entry points for teams of teachers to engage in cycles of inquiry together to intentionally and strategically design sequenced tasks and lessons for their students.

Blanton and Gardiner spark our curiosity about young children’s algebraic reasoning and give us tools to explore, appreciate, and support that reasoning. This book is full of interesting tasks, clever adjustments to existing tasks, suggestions for conversation starters, tips for appreciating algebraic ideas in children’s informal language, and so much more. The authors provide practical advice for both individual teachers and entire schools so that the power of early algebra can be realized.

This book focuses on the foundational aspects of learning algebra. It dispels the idea that algebra is about manipulating symbols but rather emphasizes the importance of algebraic THINKING which is critical in building fundamental processes that lead to stronger achievement. I highly recommend the use of this book building an effective mathematics program.

A valuable resource for anyone involved in teaching mathematics in the elementary school grades. Content is easy to access and the Take a Look questions provide multiple opportunities for readers to make connections between the book’s ideas and readers’ individual contexts.