Mathematical Imagining: A Routine for Secondary Classrooms
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""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. 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 examplesmodifications to implement the routine in your classroom, even with varying time constraints37 exercises broken into four categories: constructions, problem-solving, reasoning, and paradoxesdiscussions of the mathematics involved in each exercise, including possible follow-up questionsinstructions 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. Cover Half Title Title Copyright Contents Foreword Preface to the English Edition Acknowledgments An Invitation into My Classroom Introduction 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 Exercises in Mathematical Imagining References Index A B C D E F G H I J K L M N O P Q R S T V W
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