Rowman & Littlefield Publishers

Pages: 346
•
Trim: 6⅜ x 9¼

978-1-4422-1874-1 • Hardback • April 2013 • $78.00 • (£60.00)

978-1-4422-1876-5 • eBook • April 2013 • $74.00 • (£57.00)

**G. Arnell Williams** (MS Yale) is an associate professor of mathematics at San Juan College in New Mexico. He has won numerous teaching awards for helping people to overcome their fear of math.

Acknowledgements

Introduction

Part I: The Relevance of the Past

1. Tools of the Intellect

2. The World in Symbols

3. An Ancient Tool Gives Rise to Modern Mathematics

4. The Ancients Perform Miracles with Numbers

Part II: The Spectacular Fusion of Calculation with Writing

5. Numeral Formations Come to Arithmetic

6. The Symmetry of Repetition

7. Dance of the Digits

8. The Highest Mathematical Faculties

9. The Powder Keg of Arithmetic Education

Part III: Beautiful Dreams and Horrible Nightmares

10. Triumph of the Numerals

11. From the Frontier to the Classroom

Part IV. Illuminations

12. Symbolic Illumination

13. General Resumé

Notes

Appendices

Bibliography

Index

*How Math Works* delivers exactly what it promises: an extremely thorough explanation of numeration and the four basic operations. It’s completely fascinating, but information-dense and academic. It could serve as a text for a graduate-level course in the history of arithmetic...All explanations are accompanied by detailed diagrams and multiple methods: a “coin system” (basically enhanced tally marks), an abacus, and written out in Arabic numerals (though you’ll learn about Roman numerals, too). Learn how ancient Egyptians multiplied using doubling charts. It’s pretty amazing. If you’ve always wanted to understand math but never quite grasped it, this book can help you see how the numbers dance.

**— ****Tulsa Book Review**

Williams is a huge fan of using diagrams and pictures along with step-by-step breakdowns of each concept he discusses. Williams sets the stage by beginning with the 'coin system,' which is basically the method of tally marks, the abacus, and Arabic numerals. The reader will also obtain an understanding of how the Romans had a difficult time coming to grips with the number zero, negative numbers, and how the Egyptians used doubling charts to multiply numbers. The examples in the book are simple to understand yet the history is more complex. When reading the book, the reader is sent on a journey through history that is compelling and downright fun.

**— ****Mathematical Association of America**

I don’t know about you but I honestly have to admit that Math confuses me at times! As a Homeschool parent, I find that often it seems like Greek language to me. I have struggled with Math since high school and now that my son is 10, I feel that I need to have a better understanding of Math. Thanks to *How Math Works *by G. Arnell Williams I do feel like I at least have a better understanding of Math. I love that the book explains the history of arithmetic and the author connects it to other areas such as language which is a subject I love. My son enjoyed learning more about numbers and how they came about and I honestly feel that I now am more capable of explaining Math to my son. I’m still not an expert in the subject, but it would take a lot for me to accomplish that goal. I do like that this book was also interesting to read and I highly recommend it to all parents and teachers. Math no longer seems like a complicated and boring subject to me. This book truly has helped me to see the beauty in Math and that is a big accomplishment!

**— ****Home Education Magazine**

This guide outlines the rich history of math by answering how it formed and how it functions. Williams clearly articulates how math was founded through relationship patterns using symbols such as tally marks, abacus tables, and Hindu - Arabic (numeral) methods. He writes about how necessary these methods are when teaching foundational algorithms in elementary school classrooms. As an elementary school math teacher, I recommend this book for those who are curious about math and are interested in knowing more about its history and how it works.

**— ****Teaching Children Mathematics**

What are numbers? Where did our numbers come from? And why do we calculate with them the way we do? This entertaining, well-written, and instructively illustrated book is a mine of information for anyone (children, parents, teachers, etc.) fascinated by such questions.

**— ****Robin Wilson, emeritus professor of pure mathematics, Open University Pembroke College, Oxford**