1st Edition

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

By Geoff Krall Copyright 2018

    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.

    Chapter 1: Introduction; Academic Safety

    Chapter 2: Math and the Mathematician

    Chapter 3: Math and Academic Safety; Quality Tasks

    Chapter 4: Defining Quality Tasks

    Chapter 5: Task Models and Designing, Finding, and Adapting Tasks; Effective Facilitation

    Chapter 6: Norms, Structures, and Routines

    Chapter 7: Facilitation Within a Task; Putting the Pieces Together

    Chapter 8: Planning the Lesson

    Chapter 9: Problem Solving and Pedagogy

    Chapter 10: Assessment

    Chapter 11: The Physical Environment; Zooming Out

    Chapter 12: Structuring the Year

    Chapter 13: Aligning the System, Crafting the Story


    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. He lives in Colorado, where he and his wife, two kids, three cats, and varying numbers of chickens live and play in the mountains. He also has a calculator tattoo—a permanent commitment to math.