Savings and Investment Information for Teens by Kathryn R. DeeringReview by: Jason MutfordThe Mathematics Teacher, Vol. 101, No. 4, Mathematical Discourse (NOVEMBER 2007), pp. 319-320Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20876126 .

Accessed: 24/04/2014 12:06

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Mathematics Teacher.

http://www.jstor.org

This content downloaded from 85.166.233.236 on Thu, 24 Apr 2014 12:06:04 PMAll use subject to JSTOR Terms and Conditions

1 ^MptH|i|||j

treat f?r the reader i S^*i?^jl| with a solid back ! (j^HH^^BI ground in mathemat

J^^^^^^n i?s history. It consists

|1H^^^H|| of four chapters fol I iH^^Hftij lowed by an appendix i^l^BmB and biographies of the authors. The publication contains beau tiful illustrations of manuscripts, books, and other historical items.

The first chapter introduces various materials and objects that historically have been used as "pages" for written mathematics. The author describes such

landscapes for mathematical writing as the Sumerian clay tablet, Egyptian papyri, and the famous Codex Vigilanus. The second chapter, written by a dif ferent author, explains how significant natural events, scientific exploration, and

everyday practical occurrences led civili zations to the discovery and meaningful use of numbers. In the third chapter, still another author takes us on a journey through the creation and development of numeration systems from the origin of humans up to the Renaissance period. The final chapter takes the reader into the Renaissance period and the advent of the printing press. The book concludes

with a discussion of the printing press's monumental impact on the dissemination of mathematics throughout the world.

This book will challenge advanced students and educators. One minor drawback is its lack of an index; as a

result, readers cannot quickly find spe cific items of interest.

?Scott H. Brown Auburn University

Montgomery, AL 36109

dining with him, you go home perhaps unsatisfied that a particular question has not been answered but much bet ter informed about a variety of topics you did not even know existed a few hours earlier! These topics include how

Asperger's Syndrome may be meaning fully described as a region of rc-dimen sional space with n unknown but proba bly quite large and how gerrymandering can be recast as a branch of mathemat

ics?that is, as political geometry. The book is a loose-knit collection

of brief essays that actually reads bet ter if one ignores the supposed com

mon thread of the title: the relationship between mathematics and common

sense. Davis works hard to return to the theme in most of the essays, but the effort is needless, for most of Davis's

insights stand on their own merit. The preface to Davis's book indicates

that it was inspired by a series of let ters he exchanged with a friend who knows little mathematics. The friend's

questions and Davis's answers open the

book, and it is clear that the friend is an

academic. (She asks, for example, "What can you say about the militarization, centralization, regionalization, and polit icization of mathematics?") Yet much of the book assumes a familiarity with mathematics and mathematical language that would likely be difficult reading for someone without an undergraduate mathematics background (e.g., a region of n-dimensional space above). Fans of Davis's classic text written with Reuben

Hersh, The Mathematical Experience, will find plenty more to chew on here.

?Christopher Danielson Minnesota State University, Mankato

Mankato, MN 56001

triangle's concurrent lines. The group leader poses questions that are new but accessible to the group and directs the students' explorations, giving them as little help as possible. Working in this

way, the children are able to do some rather sophisticated mathematical think

ing. The book's last two chapters provide useful information for workshop leaders, including a list of suggested topics. Sam

ple teachers' journal entries effectively convey the flavor of the class discussions.

The authors devote most of the book to explaining why all school mathematics should follow their program and assert that "this will surely happen one day." They begin with a discussion of the nature of mathematics and then make the dubious claim that mathematical tal ent is a myth. Two interesting chapters discuss the way that mathematical ideas

develop. The chapter "How Math Has Been Taught" does not acknowledge that

cooperative learning and mathemati cal exploration are now a part of many school mathematics classes. However, the

authors' greater concern is that schools focus too much on practical mathemat ics. In the closing chapter, the authors

make the unsupported claim that, with their approach, "[njothing is memorized because it is understood." For example,

they say that no one in their group who

figures out the area formula for a triangle will ever forget it. Although the mathe matics circle approach is worthy of being given more school time, it does not offer a viable way to educate future citizens, consumers, and workers, who require more than a series of explorations in pure mathematics.

? Thomas Sonnabend

Montgomery College Rockville, MD 20850

Mathematics and Common Sense: A Case of Creative Tension, Phillip J.

Davis, 2006. 250 pp., $34.95 cloth. ISBN 978-1-56881-270-0. A K Peters; (781) 416

2888; www.akpeters.com.

xi athkm vrics Reading Davis's Math

*Sense is a bit like having dinner with a fascinat

highly knowledgeable uncle who is not par

ticularly focused but whose musings are

often insightful and informative. After

Out of the Labyrinth: Setting Mathematics Free, Robert Kaplan and Ellen Kaplan, 2007. 244 pp., $25.00 cloth. ISBN 10 0-19-514744-8. Oxford University Press; (800) 451-7756; www.oup.com/us.

The authors conduct wonderful after school enrichment workshops in pure

mathematics for elementary and second

ary school children. In the workshops, five to fifteen children work together on a series of mathematical explorations about a topic such as infinite sets or a

Savings and Investment Information for Teens, edited by Kathryn R. Deering, 2005. ix + 370 pp., $65.00 cloth. ISBN 0-7808-0781-2. Omnigraphics; (800) 234

1340; www.omnigraphics.com.

Although the title suggests that this book is for teens in general, it seems geared

more for younger teens than for older teens. Overall, the coverage and the vari

ety of material are excellent. Both issues and concepts are accurate and are often

Vol. 101, No. 4 November 2007 | MATHEMATICS TEACHER 319

This content downloaded from 85.166.233.236 on Thu, 24 Apr 2014 12:06:04 PMAll use subject to JSTOR Terms and Conditions

clearly accessible to the reader. After I shared passages with certain students and

we discussed their impressions, I came to the opinion that the teen readers whom this book engages to explore concepts deeply are the teens who are already inclined to do so in all their studies.

The book is almost wholly without

exercises, and the explorations included seem to need additional, external moti vation for the intended audience. The book requires an explanatory preface

about how to use it, so that the explora tions and motivations may more easily occur. This book could serve as a primary resource in the hands of a master teacher.

?Jason Mutford Coxsackie-Athens CSD

Coxsackie, NY 12051

Symmetry: The Ordering Principle, David Wade, 2006. 64 pp., $10.00 cloth. ISBN 0-8027-1538-9. The Golden Section:

Nature's Greatest Secret, Scott Olsen,

2006. 64 pp., $10.00 cloth. ISBN 0-8027 1539-7. Published by Walker and Company, distrib. by VHPS Distribution Center; (888) 330-8477; www.walkerbooks.com.

These two books? with their charming design and graphics, appealing titles, and

engaging format?are

delightful in almost

every way. The

authors write with

genuine appreciation of mathematics and

convey a sense of

wonder to the reader. Each book is

designed to introduce the layperson to a

specific topic. There are about thirty sections in each book, consisting of one page of text opposite a page with detailed black-and-white

drawings. This format allows for the

presentation of a variety of ideas and makes for easy reading but also gives the

impression that some topics have been cut short.

There is a lot to like about these

books, but there are also problems, such as many instances of sloppy and inac curate mathematics and cases of what I can only call "gee whiz" mathematics. In Symmetry, the angle 109? 28' 16' is called "magic," apparently because it occurs in nature where two interior sur

faces of a cluster of soap bubbles meet, but it is also the angle "formed by a line from the center to the corner of a tetra hedron." But what is the other leg? The reader is left guessing (it is another such

line, not an edge of the tetrahedron). These books can genuinely stimulate

interest?but need to be used carefully. ?Catherine A. Gorini

Maharishi University of Management Fairfieid, IA 52557 oo

Let NCTM's Resourcls an individual NCTM member, you'll have many resources

liable at your fingertips online.Join and logon today to tak| vantage of these and other time-saving resources:

Online Journal Archives (including ^ ^ thousands of articles) i Lessons and Activities

>;

A Problems Database

Member-Only Grants

Member Update E-mails

Math Standards

work fil

pin todB at

l% get back tj^nj<

(XX NCTM

NATIONAL COUNCIL OF

TEACHERS OF MATHEMATICS

320 MATHEMATICS TEACHER | Vol. 101, No. 4 November 2007

This content downloaded from 85.166.233.236 on Thu, 24 Apr 2014 12:06:04 PMAll use subject to JSTOR Terms and Conditions