Necessary Conditions

Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation

In this practical and inspirational book, Geoff Krall articulates a clear vision of what secondary math classrooms should look, sound, and feel like. Through classroom stories, research, advice from his wide experience as a math coach, and the sharing of rich resources, Geoff provides the Necessary Conditions for secondary math students and teachers to thrive.

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During his years working as an instructional coach for a national network of schools, Geoff Krall had the chance to witness several inspirational moments when math class comes alive for middle or high school students—when it is challenging but also fun, creative, and interactive. In Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation, Krall documents the essential ingredients that produce these sorts of moments on a regular basis and for all students. They are Academic Safety, Quality Tasks, and Effective Facilitation.


  • Academic Safety: Krall implements equitable classroom experiences that help fight stigmas associated with race and gender in schools. This allows students to feel socially and emotionally secure while nurturing their identities as mathematicians and increasing engagement during classroom discussions

  • Quality Tasks: Teachers can adapt or create dynamic, student-centered lessons that break down math into small, manageable sections, removing the frustrations felt by students who aren't considered "math people"

  • Effective Facilitation: This book shows how to incorporate teaching moves and math routines designed for engagement, persistence, and interactivity. Teachers can allow students to explore safely while maintaining consistent classroom expectations

"My work as a math instructional coach for a network of schools has afforded me the unique opportunity to visit exceptional teachers across the country, documenting their tasks, teaching moves, and academically safe learning environments. You’ll experience dispatches from these effective classrooms in which we’ll observe how teachers attend to all three elements that make up the ecosystem.”
— Geoff Krall from his book, Necessary Conditions


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Geoff Krall's valuable new book Necessary Conditions gets down to the ‘nuts and bolts.’ It’s not just about theory. It offers detailed strategies and ideas to create the three conditions teachers need to establish before students to begin to see themselves as mathematicians.

Michelle Russell

About the Author(s)

Geoff Krall is a math coach for the New Tech Network, supporting teachers and administrators. He taught high school math in Texas, the last few years of which were under the New Tech model, which emphasizes inquiry, collaboration, communication, and real-world connections.


Table of Contents

  • Acknowledgments
  • Preface: I Keep My Math Everywhere
  • CHAPTER 1: Introduction - Welcome to Math Class
  • CHAPTER 2: Math and the Mathematician
  • CHAPTER 3: Math and Academic Safety
  • CHAPTER 4: Defining Quality Tasks
  • CHAPTER 5: Task Models and Designing, Finding, and Adapting Tasks
  • CHAPTER 6: Norms, Structures and Routines
  • CHAPTER 7: Facilitation Within a Task
  • CHAPTER 8: Planning the Lesson
  • CHAPTER 9: Problem Solving and Pedagogy
  • CHAPTER 10: Assessment
  • CHAPTER 11: The Physical Environment
  • CHAPTER 12: Structuring the Year
  • CHAPTER 13: Aligning the System, Crafting the Story
  • References
  • Index


Product Details

Grades: 6, 7, 8, 9, 10, 11, 12
Media: 368 pp/paper
Year: 2018
Item No: 1145Item No: 1434-5
ISBN: 978-1-62531-145-0ISBN: 978-1-62531-434-5
Hashtag: #NecessaryConditions