Effective Strategies in the Teaching of Mathematics: A Light from Mathematics toTechnology by Velta ClarkeReview by: Kayana HoaglandThe Mathematics Teacher, Vol. 98, No. 2 (SEPTEMBER 2004), pp. 142-143Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27971649 .

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PUBLICATIONS

Dr. Math Explains Alqebra: Learning Algebra Is Easy! Just Ask Dr. Math! The Math Forum, 2003.192 pp., $14.95 paper. ISBN: 0-471-22555-X. John Wiley &

Sons, 111 River St., Hoboken, NJ 07030;

www.wiley.com.

For years, students have been writing questions to Dr. Math at the mathforum

.org Web site. At the Math Forum, a team of experts answers all kinds of mathemat ics questions. This book is a collection of

algebra 1 questions posed to Dr. Math, along with answers and helpful hints.

I was skeptical at first about the value of this book, so I gave it to some of my algebra 1 students. I asked them to re

view the sections in the book that dis cussed the topics that we were currently studying in class. All those students in dicated that the book would be a helpful resource for algebra 1. They noted that the explanations given are very clear and that the book offers alternative explana tions of algebra 1 topics.

After my students looked through the

book, I decided to take a look myself. The first thing that I noticed was that the book is set up in a question-and answer format. The range includes ques tions asking what different terms mean,

asking how to do specific problems, and

asking for applications of algebra 1 top ics. I then noticed the order of the book and its correlation to my algebra 1 cur

riculum. The order of topics has a good flow and corresponds very closely to my own classroom teaching. Elementary subjects are not included but are instead

incorporated as part of the companion book, Dr. Math Gets You Ready for Alge bra. The next feature that I noticed? and the one that stood out the most? was the variety of different explanations given for different types of problems. My initial reaction was that since the way subjects were explained in the book

differed from the way that I explained them in class, my students would be come confused. On further review, though, I realized that the alternative ex

planations are exactly what a struggling algebra 1 student needs to help him or

her better understand the subject. The more that I looked through this

book, the more features I found that I liked. It includes historical references, such as that the Vedic Indians geometri cally completed the square years before

Euclid; real-world applications for

everything from linear expressions to

quadratics; and explanations of termi

nology, such as describing why an ex

pression with a power of two is called

quadratic, when quad means four. Also included at the end of each chapter are

Internet resources that direct readers to

expand their knowledge of the topic at hand. A glossary at the end of the book

explains terms in language that high school students can easily understand, and an index helps direct students to

specific topics. After using this book with my stu

dents and looking through it myself, I am convinced that it is a good resource

for students of algebra 1. -David Ebert, Oregon High School,

Oregon, Wl 53575

Effective Strategies in the Teaching of Mathematics: A Light from Mathematics to Technology, Velta

Clarke, 2003. 386 pp., $54 paper. ISBN 0-7618-2602-5. University Press of

America, 4720 Boston Way, Lanham, MD

20706, (301) 459-3366.

This publication is designed to provide a

historical and educational background in

pedagogy, as well as expertise and expo sure to various methods for preservice junior high and high school teachers. The author's preface stresses the need

for utility in mathematics education and

professes to impart a wealth of teaching

142 MATHEMATICS TEACHER | Vol. 98, No. 2 ? September 2004

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strategies to the beginning-level teacher. The table of contents pleased me be cause it includes a broad range of cul tural history, historical influences on

content, national curriculum compar

isons, comprehensive teaching strategies, learning theory, brain function and re

search, approaches to teaching, planning for instruction, classroom research, and

testing and assessment.

As I started reading the text, I was dis

appointed. Chapters 1 through 4 of part 1 seemed like an extended version of the table of contents. The sentences and ideas presented seemed disconnected.

Although I have taught mathematics for almost seventeen years, my histori cal background was not strong enough to make sense of the brief way that the author pulled together her perspective on the history of mathematics. I looked for references to the parts that I did not

understand; many times I could not find a reference to fill in my background with further research. A new teacher would probably find the material ex

tremely confusing. Part 2 of the book deals with theories

of learning and principles of teaching. Some of the author's statements seemed abrasive and subjective, and most of the

figures in the book did not seem to be re lated to the text.

In the chapters dealing with the "nuts and bolts" of teaching, I became frus trated with the many typographical er rors. Some errors are so substantial that

the very foundation of the lessons that the author is trying to present is flawed.

The text has so many errors that I cannot recommend this publication as a reference book, especially for inexperi enced teachers.

-Kayana Hoagland, South Puget Sound

Community College, Olympia, WA 98512

Gene's Corner and Other Nooks and Crannies: Perspectives on Math Education, Eugene A. Maier, 2003. xviii +

291 pp., $24.95 paper. ISBN 1-886131-59-7. The Math Learning Center, P.O. Box 3226, Salem, OR 97302-1442, (800) 575-8130; www.mathlearningcenter.org.

Gene's Corner is an interesting and

provocative collection of personal reflec tions blending one individual's passages

with current trends and issues in mathe matics teaching and learning. The essays provide easy-to-read thoughts and views that span more than a half-century of

Eugene Maier's experiences in teaching mathematics. These reflections grew out of his sense of dissatisfaction with the

way that he was teaching mathematics, characterized by filling blackboards with

proofs and procedures that the students

dutifully copied. A primary theme of the collection is changing mathematics

teaching from practices that promote procedures and skills to developing stu dents' mathematical sense and under

standing. Maier's reflections on his expe riences show mathematics as a vibrant

discipline that involves making conjec tures, seeking relationships, validating theories, searching for solutions, verify ing results, and communicating findings.

The author's ideas provide a context for thinking about such important peda gogical issues as the role of manipula tives and technology. His ideas about the nature of mathematics and why students should study it are likely to stir some de bate. The essays give productive entry points for discussing and thinking about

important issues in mathematics teach

ing and learning. As with any personal reflections, readers will find essays that excite feelings of affinity, as well as dif ferences of opinion; however, the per spectives presented deal with significant issues that will both challenge and au thenticate readers' thinking.

-David K. Pugalee, University of North Carolina-Charlotte, Charlotte, NC

28223-0001

Origami Design Secrets: Mathematical Methods for an Ancient Art, Robert J. Lang, 2003. 594 pp., $48 paper. ISBN

1-56881-194-2, A Peters, 63 South

Ave., Natick, MA 01760-4626; www

.akpeters.com.

This book is large, highly original, ex

tremely complex, and rich. For example, the first figure in the book is a display of

thirty-two different origami elephants, each of which is labeled with the name of its creator. The author, an applied physi cist and an expert in "technical folding," has designed more than 400 origami fig ures in his career. His primary goal is to

Origami Design Secrets Mathematical Methods for an Ancient Art

I ROBERT J. LANG

S

share with the reader his bag of tricks for

creating original designs. He begins by discussing basic origami symbols and terms and gives folding diagrams for stan dard bases. He then explains how to mod

ify standard bases to design origami struc tures. Some of his design techniques involve such mathematics as circle pack ing. Another technique, grafting, involves

"modifying a crease pattern as if you had

spliced into it additional paper for the

purpose of adding structural elements to an existing form." The author expands on these basic design techniques to create even more complex ones. The author also

shares folding diagrams and schemes for

complicated structures, including his in credible Black Forest cuckoo clock, which

requires 215 steps. A chapter discusses some of the higher mathematics that un derlies origami techniques.

The book is clearly and elegantly pre sented and illustrated; it has wide mar

gins for figure numbers and comments. It is definitely not a book for beginning origami enthusiasts, but it is appropriate after students know how to fold standard

origami bases and basic designs and can follow folding diagrams. The book is also valuable because it shows students that

complicated subjects can be beautifully explained and illustrated. This book is a fine addition to any origami library.

-Beth Schlesinger, Mission Bay High School, San Diego, CA 92109

Simple Continued Fractions: An

Elementary to Research Level

Approach, Harry Liberman, 2003. 200

(Continued on page 144)

Vol. 98, No. 2 ? September 2004 | MATHEMATICS TEACHER 143

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