1st Edition

Mathematical Imagining A Routine for Secondary Classrooms

By Christof Weber Copyright 2020

    Imagine a plastic cup lying on the floor. Give the cup a nudge so that it begins to roll. What does the path it takes look like? So begins the journey that Christof Weber takes you on in Mathematical Imagining: A Routine for Secondary Classrooms . Along the way, he makes the case that the ability to imagine, manipulate, and explain mathematical images and situations is fundamental to all mathematics and particularly important to higher level study. Most importantly, drawing on years of experiments in his own classroom, Weber shows that mathematical imagining is a skill that can be taught efficiently and effectively. Mathematical Imagining describes an original routine that gives students space and time to imagine a mathematical situation and then revise, discuss, and act upon the mental images they create. You can use this creative routine to glimpse into your students' thinking and discover teaching opportunities, while empowering them to create their own mathematics.Inside you’ll find the following:

    • An introduction to the routine including the rationale behind it, facilitation guidance, and classroom examples
    • Modifications to implement the routine in your classroom, even with varying time constraints 37 exercises broken into four categories: constructions, problem-solving, reasoning, and paradoxes
    • Discussions of the mathematics involved in each exercise, including possible follow-up questions
    • Instructions on how to create your own exercises beyond the book

    This one-of-a-kind resource is for secondary teachers looking to inspire student creativity and curiosity, deepen their own subject matter knowledge and pedagogical content knowledge, and invite all students to access the power of their own mathematical imaginations.

    Part 1: The Mathematical Imagining Routine: Background and Guidelines; Chapter 1: What Is the Mathematical Imagining Routine?; Chapter 2: Implementing the Mathematical Imagining Routine; Chapter 3: Developing Your Own Exercises in Mathematical Imagining; Part 2: Exercises in Mathematical Imagining: A Collection of Example Tasks; Chapter 4: About Using the Example Tasks; Chapter 5: Construction Exercises in Mathematical Imagining; Chapter 6: Problem-Solving Exercises in Mathematical Imagining; Chapter 7: Reasoning Exercises in Mathematical Imagining; Chapter 8: Paradox Exercise in Mathematical Imagining


    Christof Weber is a professor in the School of Education at the University of Applied Sciences Northwestern Switzerland. He taught mathematics for twenty-five years at a "Gymnasium" in Switzerland, a post-compulsory public high school preparing students for tertiary education. He currently studies the teaching and learning of mathematics, with a particular focus on algorithms. When not working, Christof and his wife enjoy being outdoors, hiking long treks or traveling to observe eclipses.