The routines in this book will help students:
  • Frequently revisit essential mathematical concepts
  • Foster and shore up conceptual understanding
  • Engage in mental mathematics, leading to efficiency and fluency
  • Engage in mathematical discourse by constructing viable arguments and critiquing the reasoning of others
  • Reason mathematically, and prepare for high stakes assessments
  • Move learning beyond "correctness" by valuing mistakes and discourse and encouraging a growth mindset

Misconceptions and incomplete mathematical thinking often go undetected, as teachers are rarely trained to consider why or how an answer was generated. They often respond to incorrect answers by re-teaching the correct processes, and the underlying problem persists. Unrecognized misconceptions then become permanent ways of thinking; each new layer of mathematics knowledge builds upon on flawed foundations. This book addresses that problem head on. By covering the essential content or "big ideas" of K-2 mathematics, it turns elementary teachers into experts in diagnosis, intervention, and evaluation, and delivers the tasks and tools to use in the classroom day-to-day.

Guiding teachers through six specific actions-including valuing, fostering, building, planning, supporting, and reflecting on struggle-this book provides an essential plan for embracing productive perseverance in mathematics.


Give math practice routines a makeover in your elementary classroom with these 20 energizing warmups designed to jump-start reasoning, reinforce learning, and instill math confidence in students!

This bank of carefully selected tasks to discover what students know - and don't quite grasp - about big ideas in grades 3-5 mathematics. 180 in all, downloadable, standards-aligned, and augmented with sample student work, commentary on strengths and gaps, and next instructional steps so teachers can swiftly spot the teachable moments in students' misunderstandings.

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students' responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students' misconceptions and incomplete understandings as much as their correct ones-because it's the gap in their understanding today that holds the secrets to planning tomorrow's best teaching.



Offering a year's worth of daily instructional material that you can use each class period to promote student reasoning and number sense, this resource will help students:
  • Frequently revisit essential mathematical concepts
  • Foster and shore up conceptual understanding
  • Engage in mental mathematics, leading to efficiency and fluency
  • Engage in mathematical discourse by constructing viable arguments and critiquing the reasoning of others
  • Reason mathematically, which can improve performance on high-stakes assessments
  • Move learning beyond "correctness" by valuing mistakes and discourse to encourage a growth mindset

Teach your students to become decision makers who rely on their own mathematical thinking.

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand.

Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes:

  • "Seven Significant Strategies" to teach to students as they work toward procedural fluency.
  • Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency.
  • Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency.
  • Suggestions for engaging families in understanding and supporting fluency.

Fluency is more than a toolbox of strategies to choose from; it's also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.


Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.


Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.