The TRU project produced two new books in 2023. These two books support pre-service and in-service teachers, individually and collectively, in learning about TRU and deepening their understandings about what happens in powerful mathematics classrooms. Importantly, they provide a series of tools that teachers can use for enhancing tasks and activities in ways that result in richer and more powerful classroom conversations. For a ton of evidence that these ideas really work, see the “papers” tab of this website.

We’d love to spend time with readers in person, working through the ideas. But, that’s impossible. So we’ve done what we hope is the next best thing – we’ve written both books like we’re in dialogue with you. We introduce some situations (whether they be case studies of interesting classrooms or problems or activities that could be enriched) and ask what you think. Then we make some suggestions, as though we were in dialogue with you; we ask you to consider the ideas, and maybe try out versions of them. By working through these books, an individual teacher will have a richer sense of what really counts in their teaching and a way of reflecting on it. But more importantly, if a learning community works through the cases and examples in these books together, they will have developed the practices of looking at instruction closely, and will be ready to continue the work on their own. Ongoing discussions and reflections are the way to career-long growth!

Here’s the front cover of the first book, and a description of its contents:

Helping Students Become Powerful Mathematical Thinkers supports teacher educators, teachers, coaches, administrators, math-ed faculty, and researchers in understanding and using the Teaching for Robust Understanding (TRU) Framework to improve instruction. Detailed case studies take readers on deep dives into five essential dimensions of classroom practice: The Mathematics; Cognitive Demand; Equitable Access; Agency, Ownership, and Identity; and Formative Assessment.

Three case studies form the core of the book. Each case uses the TRU framework to pose conversational questions to the reader on different aspects of the lessons, focusing on the ways that students are led to engage with mathematics and how they make sense of it. These include “What’s important in this classroom episode?,” “What might students be experiencing?,” or “What might the impact of alternative teaching decisions have been in this situation?”. The book concludes with guides for planning, observation, and reflection that readers can use in their own work, continuing the journey toward the ambitious and equitable instruction that each case study describes.

This book will support all mathematics educators in developing deeper understandings of mathematics classrooms and in problematizing their own mathematics instruction. By exploring the challenges students face, the decisions teachers make, and the ways that students learn, readers will experience TRU as a powerful way of thinking about instruction – one that can shape lesson planning and reflection and make teaching more impactful and equitable.

For more information about Helping Students Become Powerful Mathematical Thinkers visit

Here’s the second book, and a description of its contents:

Mathematics Teaching On Target is a guidebook for improving mathematics teaching, based on the Teaching for Robust Understanding (TRU) Framework and its five dimensions – The Mathematics, Cognitive Demand, Equitable Access, Agency, Ownership, and Identity, and Formative Assessment. You’ll be guided to refine your classroom activities across the five TRU dimensions, and your students will become more knowledgeable and resourceful thinkers and problem solvers.

Each chapter in Mathematics Teaching On Target introduces a set of easy-to-use questions for the hands-on improvement of lesson activities, such as:

  • Think of an activity you use with your students. Is it as mathematically rich as it might be?
  • Does it stretch your students in the right ways, inviting “productive struggle”?
  • Can all students engage with it, in ways that allow them to grow as mathematical thinkers?
  • What evidence will student work provide, helping you revise the activity so that it works better both in the moment and next time?

You’ll find examples at the elementary, middle, and secondary levels for each dimension that show how addressing these questions can enhance mathematics instruction.

Ideal for your individual classroom, learning community, or district-level and wider professional development efforts, this book will enable you to help more students engage with mathematics in increasingly powerful ways. Beyond individual lessons, this book will also accelerate teacher development by helping you focus and reflect on what really counts in your instruction.

You can find more information about On Target at

Next page: Papers