Necessary Conditions

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

Math instruction in middle and high school is often something of a grab bag, with schools jumping from curriculum to curriculum, lacking a guiding vision or continuity between years. No wonder so many students conclude, “I’m not a math person.”

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Math instruction in high school is often something of a grab bag, with schools jumping from curriculum to curriculum, lacking a guiding vision or continuity between years.  No wonder so many students conclude, “I’m not a math person."

Geoff Krall thinks that’s a problem, and he’s devoted his career to fixing it. Necessary Conditions posits for the first time a coherent approach to secondary math pedagogy. Krall identifies three essential elements that will open the door to math for all of your students: academic safety, quality tasks, and effective facilitation.

The book discusses each of the three “necessary conditions” in-depth, giving concrete examples and describing the interplay among them. Krall’s guidance equips teachers to:

  • design classroom experiences that increase engagement and build all students’ identities as mathematicians;

  • create dynamic, high-quality lessons that include meaningful, efficient assessment; and

  • implement structures, routines, and facilitation that result in high-quality learning.

With Krall’s guidance, you can help every student come to recognize that they are indeed a “math person.”


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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



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