Table Of ContentWriting Math Research Papers
A Guide for High School Students and Instructors
Fourth Edition
Writing Math Research Papers
A Guide for High School Students and Instructors
Fourth Edition
Robert Gerver, PhD
Cover and illustrations by Michael Gerver
Edited by Julianne Gerver, MA
INFORMATION AGE PUBLISHING, INC.
Charlotte, NC • www.infoagepub.com
About the Cover
A treasure map was chosen as the cover theme. Why? The math research journey involves
exploration. It involves charting new territory and overcoming obstacles. It involves looking
for clues in the mathematics, interpreting those clues, and doing lots of digging to uncover
something very rewarding—a new mathematical result!
Library of Congress Cataloging-in-Publication Data
For the reasons I’ve got sunshine on a cloudy day; Linda, Julianne,
A CIP record for this book is available from the Library of Congress
http://www.loc.gov and Michael
ISBN: 978-1-62396-863-2 (Paperback)
978-1-62396-864-9 (Hardcover)
978-1-62396-865-6 (ebook)
Copyright © 2014 Information Age Publishing Inc.
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, microfilming, recording or otherwise, without written permission
from the publisher.
Printed in the United States of America
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For the reasons I’ve got sunshine on a cloudy day; Linda, Julianne,
and Michael
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Acknowledgments
Without the help, encouragement, and support of the following people, this book would
not have been possible:
Elaine Boyrer Joan Fowler Regina Newman William Wagner
Everyone who benefits from Writing Math Research Papers can join me in thanking the
North Shore School District and these fine young scholars from North Shore High
School, Cold Spring Harbor Junior-Senior High School, and Smithtown High School
West:
Sara Abbondondolo Logan Kupferman Simran Bagga
Stephanie Bazan Aidan Lewis Dalita Balassanian
Allison Black Liz Lucas Tim Bramfeld
Andrew Carnevale Max Moore Jeff Chew
Claire Castellano Aidan Murray Jocelyn Chua
Cecilia Castellano Alexandra Osman Gabrielle De Rosa
Nicole Ciotoli Pam Otis Nancy Friedlander
Stephen Davis Talia Pelts Michael Gerbush
Jill DeDona Miranda Purcell Blake Gilson
Jeanne DiSimone Julia Reilly Parisa Golestaneh
Alexia Efstathiadis Molly Reilly Robin Hadley
Andrew Fierstein Will Rosencrans Laura Henning
Fossett Mike Rovner Tiffany Indence
Farb Danielle Sacco Kim Martini
Raquel
Fossett Charlie Schubach Vandana Minnal
Gabrielle
Ganasoulis Erin Sheerin Nicole Miritello
AMyiachnaneal
Gerver Dylan Smith Dan Moadel
KJualtiaenrinnea G
erver Christian Van Pak Sharon Poczter
Stephen Grudman Diana Vizza Daniele Rottkamp
Meghan Henneberger Sunaina Vohra Shikha Singhvi
Sarah Ivanovic Stephanie Zelenetz Alexis Soterakis
Olivia Jacome Lauren Adelman
Stephen Johansen
Special thanks also to Joseph Quarteraro and family, Jeff Lesser, and the entire Al Kalfus
Long Island Math Fair organization, for giving tens of thousands of Long Island students
the chance to write math papers, exchange presentations, and meet like-minded students
from other high schools. This book would not exist without this forum for exploration.
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Table of Contents
Introduction ...........................................................................................ix
Chapter 1
Mathematics: Shouting Questions and Whispering Answers ..................1
Chapter 2
Finding a Topic.......................................................................................17
Chapter 3
Problem Solving: A Prerequisite for Research……………………...……31
Chapter 4
The Importance of Clear Communication..............................................56
Chapter 5
The Notes You Take in Math Class ......................................................63
Chapter 6
Technical Writing Techniques................................................................84
Chapter 7
Conjectures, Theorems, and Proofs……………..................................118
Chapter 8
Reading and Keeping a Research Journal .........................................146
Chapter 9
Components of Your Research Paper ................................................160
Chapter 10
Oral Presentations ..............................................................................171
Chapter 11
Sample Pages from Actual Papers......................................................194
Chapter 12
Some Suggested Resources ..............................................................229
Chapter 13
A Guide for Instructors and Administrators .........................................243
References .........................................................................................277
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Introduction
As an avid fan of writing and mathematics, I began giving my students writing
assignments as a new teacher in 1977. The initial reaction was “This is math— why are
we doing English?” As the students completed their math writing projects on varied
topics such as automobile insurance, income taxes, stocks and bonds, consumer credit,
and more, they began to realize the value of being able to communicate the powerful
results mathematics can provide. Students who wrote about surface area, parabolas, the
Pythagorean theorem, and other mathematics topics were quick to point out that they
internalized the material so much better because in order to explain it they really had to
understand it. Students concluded that writing is an essential component of any
discipline, not just humanities courses. Based on the successes of these early writing
experiences, I began to incorporate writing in my mathematics classes on a daily basis.
Needless to say, I was very excited when the National Council of Teachers of
Mathematics (NCTM), an organization of educators dedicated to the improvement of
mathematics instruction, recommended the integration of writing across the mathematics
curriculum. Mathematics and writing, to me, have always complemented each other
naturally.
Since problem solving is a central focus of math classes, it is clear that writing must be
integrated with mathematics courses. Problem solvers have to be able to explain the
procedures they used and the solutions they found.
Have you ever been absent from a class and asked a fellow student, “What did we do in
math yesterday?” only to hear the response “I know it but I can’t explain it”? How did
you react? Imagine a detective telling a superior, “I’ve solved the case but I can’t explain
my solution”!
Mathematicians must be able to communicate their findings to others so their important
results can be used to solve future problems. This is not the only value of writing in
mathematics. Writing will also help you understand mathematical concepts. As you
construct written explanations, you will need to explore and review mathematical
concepts in your mind. Writing Math Research Papers will help you expand your ability
to read about mathematics, explore mathematics, and write about your mathematical
experiences. Writing in mathematics also aligns beautifully with the recently
implemented Common Core State Standards for Mathematical Practice.
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