By Julia Brodsky, March 2016, 119 pages, ISBN 978-0-9776939-8-6

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What’s Inside the Book?

I will share with you what I have learned as I tinkered with teaching problem solving to curious young children, ages six to eight. The purpose of this book is to invite you to experiment with your own children or students, without any preconceived notions of how the outcome will look. Instead, allow your personal taste and the children’s feedback to guide you. Julia Brodsky, author, in the book introduction

It is a commonplace of teaching that you first try to teach the way you were taught. And so people pioneering math circles or informal learning situations often start out in the wrong direction, trying to apply to these situations the teaching methodologies that they experienced in formal classrooms. Julia Brodsky does a wonderful job describing other ways to teach. And maybe ‘teach’ is the wrong verb: other ways to guide students in learning from and enjoying mathematics. The mathematical examples are tailored to encourage children’s exploration. Mark Saul, Director, Center for Mathematical Talent, Courant Institute, NYU

What I loved about this book is that it gave me a chance to impart so much more than information to my children – I soon understood that the underlying purpose was not necessarily mastery of facts, but an opportunity to teach them how to think, that it is acceptable to be wrong, and that sometimes there is more than one answer to a problem. Angela Harris, co-founder of Mosaic Freeschool, a homeschooling mom Print this Parent Bingo to play as you observe children’s mathematical inquiry.

About the Author

Julia Brodsky is a homeschooling mom with three naughty and curious kids. When she is not with her family, she works as a rocket scientist for NASA Goddard, runs a weekly Art of Inquiry math circle for elementary school students, organizes the annual Math Kangaroo Olympiad for Montgomery County kids—and still keeps some sanity. She is constantly fascinated by the way children learn and solve problems. Julia grew up in Russia, where she was a mediocre student in one

of the best math magnet schools of St. Petersburg. Later, she had a lot of fun working as an International Space Station astronauts’ instructor at Johnson Space Center. Julia also enjoys writing poetry, hiking, and watching somebody else working instead of her.

Table of Contents

Foreword 1 My math circle values 5 Secrets of the trade 9 Topics 14 Introduction to thinking 15 Strange statements 32 Tiling puzzles 41 Infinity 63 Symmetry 76 Lateral thinking 87 Festival 99 Some advice for parents 107 Grown-up participants 109 Appendix A: Debate rules 111 Appendix B: Stuck? 113 Appendix C: Parent Bingo 114 Appendix D: Resources 116 Extra resources per topic 117 Summary 119

And One More Thing

Our book will be published under Creative Commons license. It means that people all over the world will be able to access its content, translate it into different languages – and share their ideas based on the book with you. The Creative Commons site Team Open features Natural Math in its celebration of innovative projects in education.