Front MatterSource: The Mathematics Teacher, Vol. 84, No. 5 (MAY 1991)Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27967174 .

Accessed: 09/06/2014 12:35

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 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

NIC MATHEMATICS

MAY l!t!M

VOI.I MK XI NI M I! ICK

NATIONAL COUNCIL OF TEACHERS OF

MATHEMATICS

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

Two new

equations

from HP:

32+1

And HP has the only calculators that provide the proof! Do your most effective teaching with the best graphic calculators from HE The HP 48SX Scientific Expandable and the HP 28S Scientific calculators are

recognized by educators* as "unique in their symbolic manipulation capabilities and facility with calculus techniques." The HP 48SX is described as "an impressive device that would make Newton and Leibnitz proud"

Buy HP's best and spend less.

And, now, if your high school buys either three HP 48SX or three HP 28S calculators, the fourth one is free from Hewlett-Packard So 3 = 4!

And there's another opportunity to stretch your school's dollars. Calculators received as free units can help your school qualify for the Educator Overhead Display Offer (a free classroom overhead display device with 30 proofs of purchase to HP)

By purchasing 24 HP 48SX or HP 28S calculators, your high school will qualify for 8 free units plus a free HP 48SX classroom display (an $850 retail value) or a free classroom display version of the HP 28S (a $500 retail value) That's how 24=32+1!

Offer available to high school teachers and administrators in the US. and Canada only. In the U.S., call (503) 750-2897 between 8:00 am and 3:00 pm (Pacific time) for more details. Or write: Calculator Support, Hewlett-Packard, 1000 NE Circle Blvd, CorvalMs, OR 97330, Attention: High School Program. In Canada, call (800) 387-3867, Dept 128. Offer ends December 31,1991. HP calculators. The best for your success.

*The Computing Ibacher, April 1990, Graphing Calculators: Comparisons and Recommendations Note: There is no limit to the number of units your school may purchase. ? 1990 Hewlett-Packard Company PG120UB

HEWLETT PACKARD

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

MATHEMATICS TEACHER VOLUME 84 NUMBER 5 MAY 1991 ISSN 0025-5769

ARTICLES

344 Digits Count: Significant Digits and Calculators Joseph Browne

347 Put Some POW in Your First-Year Algebra Classes Martha L. Frank

352 Mathematics Education in Britain: An American Viewpoint Mark H. Meuser

366 Sharing Teaching Ideas Algebra Tic-Tac-Times, Richard J. Croase and Marilyn J. Sweeney Calculating Surface Area, Ray A. Krenek

370 Tips for Beginners Bingo in the Mathematics Classroom, Jeffrey A, Catlett

387 A Monte Carlo Application to Approximate Pi Kenneth Easterday and Tommy Smith

392 Estimating the Volumes of Solid Figures with Curved Surfaces Donald Cohen

396 Inscribing an "Approximate" Nonagon in a Circle John F, Lamb, Jr., Farhad Asian, Ramona Chance, and Jerry D. Lowe

399 Pick's Theorem Extended and Generalized Christopher Polis

402 A Probability Problem Involving Calculus Roger D. Cox

DKPARTM FONTS

342 Reader Reflections

358 Implementing the Standards Incorporating Mathematical Modeling into the Curriculum, Frank Swetz

374 May Calendar

379 Activities Activities to Introduce Maxima-Minima Problems, David Pleacher

406 Technologg Reviews

406 Publications

408 Products

409 Projects AIM-HI Oklahoma

410 Guide to Advertisers

The Mathematics Teacher (ISSN 0025-5769) is published monthly except June, July, and August at 1906 Association Drive, Reston, VA 22091. Dues for individual membership in the Council are $40.00, which include $15.00 for the journal. Institutional membership rate for one journal is $45.00. Please add $5.00 for mailing outside the United States. POSTMASTER: Send address changes to the Mathematics Teacher, 1906 Association Drive, Reston, VA 22091. Printed in the U.SA. Second class postage paid at Reston, Virginia, and at additional mailing offices.

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

LQ x a

.S

go g?

u v 4M

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

,. a

%.

*

R RN

S t

-om 0*

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

AN OFFICIAL JOURNAL OF THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

The Mathematics Teacher is devoted to the improvement of mathematics instruction in the junior high schools, senior high schools, two

year colleges, and teacher education colleges. The

publications of the National Council of Teachers of

Mathematics present a va

riety of viewpoints. The views expressed or implied in this publication, unless

otherwise noted, should not

be interpreted as official

positions of the Council.

EDFRESs

Member of the Educational Press Association of America

Cover comments: The helical form of a

spiral staircase lends maximum efficiency in a minimum area. As persons ascend

the steps, they engage a 360 degree view of their surroundings. Photograph

? Richard Newman

Information is available from the Headquar ters Office regarding the two other official jour nals, the Arithmetic Teacher: Mathematics Ed ucation through the Middle Grades and the Journal for Research in Mathematics Education. Dues support the development, coordination, and delivery of the Council's services, including $15.00 (Can $17.25) for each Mathematics Teacher subscription and $3.00 (Can $3.45) for an NCTM News Bulletin subscription. Special rates for students, institutions, bulk subscrib ers, life and retired members are available from the Headquarters Office.

The index for each volume appears in the December issue. The Mathematics Teacher is indexed in Biography Index, Current Index to Journals in Education, Education Index, Math ematical Reviews, Media Review Digest, and Zentralblatt f?r Didaktik der Mathematik.

The Mathematics Teacher (ISSN 0025 5769) is published monthly except June, July, and August at 1906 Association Drive, Reston, VA 22091. Dues for individ ual membership in the Council are $40, which includes $15 for one official journal subscription. Second-class postage paid at Reston, Virginia, and at additional mailing offices. POSTMASTER: Send address

changes to the Mathematics Teacher, 1906 Association Drive, Reston, VA 22091. Telephone: (703) 620-9840; Fax: (703) 476-2970; CompuServe: 75445,1161. Copyright ? 1991, The National Council of Teachers of Mathematics, Inc. Printed in the U.S.A.

EDITORIAL PANEL JERRY JOHNSON, Western Washington University, Bellingham, WA

98225; Chair WILLIAM S. BUSH, University of Kentucky, Lexington, KY 40506 EDWIN M. DICKEY, University of South Carolina, Columbia, SC

29208 BRUCE KING, Western Connecticut State University, Danbury, CT

06810 BEVERLY W. NICHOLS, Shawnee Mission Northwest High School,

Shawnee Mission, KS 66216 THERESA OEHMKE, University of Iowa, Iowa City, IA 52242 JENNIFER J. SALLS, State of Nevada Department of Education,

Carson City, NV 89710 GAIL BURRILL, Whitnall High School, Greenfield, Wl 53228, Board

of Directors Liaison HARRY B. TUNIS, 1906 Association Drive, Reston, VA 22091;

Director of Publications

STAFF JAMES D. GATES, Executive Director HARRY B. TUNIS, Director of Publications

CYNTHIA C. ROSSO, Publications Business Manager JOAN ARMISTEAD, Editorial Coordinator ANN M. BUTTERFIELD, Editorial Associate SHEILA C. GORG, Editorial Assistant ROWENA G. MARTELINO, Advertising Manager

JOSEPH R. CARAVELLA, Director of Member Services ROBERT MURPHY, Computer Services Manager STEPHANIE J. MULLIN, Communications Coordinator

BETTY C. RICHARDSON, Director of Convention Services BARBARA J. THODE, Convention Manager

ANTHONY T. FRAGNITO, Controller MARILYN L. HALA, Professional Program Manager

All correspondence should be addressed to the Mathematics Teacher, 1906 Association Drive, Reston, VA 22091. Manuscripts should not exceed ten pages of text and should be typewritten, double-spaced with wide margins, with figures on separate sheets. Manuscripts should be prepared according to the Chicago Manual of Style and the American National Metric Council's Metric Editorial Guide. No author identification should appear on the manuscript. Five copies are required. Priority areas are listed in the editorial that appeared in the January 1990 issue. Guidelines for the publication of computer programs appeared in the January 1990 issue. Three returnable disks for computer programs with more than thirty statements should be furnished.

Permission to photocopy material from the Mathematics Teacher is granted to classroom teachers for instructional use, to authors of scholarly papers, and to librarians who wish to place a limited number of copies of articles on reserve. Permission must be sought for commercial use of content from the journal when the material is quoted in advertising, when articles are included in books of readings, or when charges for copies are made. Uses of material from the Mathematics Teacher, other than those cases described, should be brought to the attention of the National Council of Teachers of Mathematics. The Mathematics Teacher will not participate in the unau thorized reproduction of any computerized courseware that bears an explicit or implicit copyright claim.

For information on reprints or back issues of the Mathematics Teacher, write to Robert Murphy, Circulation Manager, in the Headquarters Office.

NCTM BOARD OF DIRECTORS IRIS M. CARL, Houston Independent School District, Texas; President

SHIRLEY M. FRYE, Scottsdale, Arizona; Past President JAMES D. GATES, NCTM; Executive Director GAIL F. BURRILL, Whitnall High School, Wisconsin CHARLOTTE EVANS COPLEY, Hampton City Schools, Virginia FRED CROUSE, Kings County District School Board, Nova Scotia FRANCES R. CURCIO, Queens College of the City University of New

York HOWARD C. JOHNSON, Syracuse University, New York GLENDA LAPPAN, Michigan State University RICHARD D. LODHOLZ, Parkway School District, Missouri ALAN OSBORNE, Ohio State University CATHY LYNN SEELEY, Texas Education Agency LEE V. STIFF, North Carolina State University JUDY TROWELL, Little Rock School District, Arkansas LEE E. YUNKER, West Chicago Community High School, Illinois

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

gTP tie f " SGyTr 5 ' 56

RIP 514. N a g t f t "? ter 3 ek l :i

dAM,+kedg"IB ,hy'' X N q "+LF 'y a b'", , 1aa 3 Nw .

, + ;4 de wa d t ,, f ya t q m' s hr y nR

IRV

TM, Ol L,

t t 1 pe y,

y'e "r v r,

y' o w 3 qt a #x A''9 C. n ' t

NX,

L 4a.,kla '?nF , f ,nu4' y qk E. t y J, d f+, ' u q

AM yn f\ SS Awd A b'd ."'fib, 1 t V EA i . r.}' . 3 3. eW yk4$ m Yh'..' yw N 9{1! R

9yg x' ?g' l

W A, FRm Yd! . W'r'wre,14 !ry K i S : t f

P r

' : .. 1 ' " maw "' '. Ile,

-Ift

1

gb H

I

u , sv ?' a x, e .a" wa a , N, r F . gra E., , s

to ,P: Fr' n' 4',Y'N _ '1 >VS.rud ... a ! .i.. k . ,t .. ,.. ;.. . "er - - _ .._

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

The joy of learning couldn't be more basic* Presenting the teacher-designed TI Math Mate: The first calculator with correct order of operations specially developed for the young est students* Teachers across the country apee. Young eleirientary students need a calculator that allows them to explore and discover mathematical concepts. The Math Mate Iran Texas Iratruments meets this need as well as all die require

mei^jpath teachers have for

instruaing you^g children. ? rx>#er?uTi^^ and learn

ing tool, the Math Mate can be used to make realistic problem-solving a focus of the mathematics curriculum.

Designed with educators With the input of leading educators

throughout the United States, the Math Mate was specially designed to meet requests for a simple calculator

with the correct order of operations. Math Mate has an Algebraic Operat ing System (AOS ) that multiplies and divides before adding and sub tracting (M-D-A-S). What's more, students can override the cader of opmtions and develop conceptual understanding through the use of built-in parentheses.

The Math Mate is easy to use for even the smallest hands, with extra

large keys that are functionally grouped and color-coded. And the

big display makes entries easy to read. Math Mate offers all the stand

ard functions, plus a change sign key, constants for all four basic operations and easy-to-use memory keys.

The brighdy colored Math Mate is

designed to appeal to children. But even more irnportant, Math Mate is

Trademark of Texas Instruments Incorporated 1991 IH00095 04-1047A

rugged enough to take on the daily demands of young learners. The plas tic keys are tough and tampe^oof, and an impact-resistant sliding case offers extra protection.

Free 3(kky evaluation The Math Mate is available for a free 30-day trial as a Preview Kit. Convenient purchase options include a Student Pack and a Teacher's Kit

TT wants to help you help your students learn the value of mathe

matics. With the Math Mate, it's never been easier for you. Or more fun for them.

For more information, call 1-800 CARES.

Texas Instruments

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

Teachers and Texas mstruments

Helping students develop jratterns

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

calculators:

for success.

Because our newest generation must be our smartest generation.

Each of our classroom models contains featuies to make math education more interesting and effective. For example, the features on our Math Explorer were chosen

by teachers to provide assistance in

teaching concepts of fraction and division. And our TI-81 is the first

graphics calculator developed with

leading educators to meet the special needs of mathematics instruction. Each classroom calculator in our line has unique features that resulted from the requests of educators and the difficulties they had with pre vious models available.

Throughout society, technol ogy is continually changing the way we work, learn and

live. But as society changes, there is one constant: A thorough education is Vitalin helping students develop patterns for success.

Our classroom calculators are

designed for the special needs of schools. ?T Calculators are now accepted as effective and cost-efficierfl: tools for use in math education.

Correctly designed products used by teachers with the proper support materials and training promote achievement, improve problem-solving skills and enhance the understanding of math ematical concepts.

For 17 years, has worked

closely with educators to design calculators that enhance classroom instruction. With the collaboration of hundreds of teachers throughout the country, we've developed a series of six products that

support the National Council of Teachers of Mathematics (NCTM)

Cmrkx?mm?d Evdm?mStffl??mk

CMOJLATOR m INCLUDES CA?CULATORS? POSTER AND ?NSTRUCTfONALMATERIALS.

Presentir^ oiir new

teacher-designed Math Mate? Ulis year we introduce the Math Mate, the first AOS calculator with correct order of operations designed for the youngest students. A powerful teaching and learning cool, the Math

Mate meets all the requirements math teachers have for instructing young children.

Toas Instruments wants to help you help your students succeed m irath*

We're mmitted to mamtaining a

working relationship with education. We welcome your input. Together, we can continue exploring needs and developing products to help prepare today's students to take their

places in tomorrow's high-technology world.

For more information, use our toll-free number - - -CARES

(842-2737).

IHex?s Instruments

Trademark of Texas Instrumente Incorporated ? 1991 TI IH00096 14-10470

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

Career

Information

from the

MAA

MATHEMATICAL SCIENTISTS AT WORK

If you have difficulty clarifying career op

portunities in the mathematical sciences for

your students, then let these 14 practition ers speak for you. This attractive book let provides career information about statis

tics, actuarial science, operations research, and computer science as well about math

ematics. Each essay is accompanied by a photograph of the author and by addi tional information relevant to the occupa tion. The booklet also contains general in

formation about careers in mathematics and sources where additional information may be obtained.

This is what some of our writers have to say to students:

...when seeking a mathematical posi tion, doni be put off the trail by ti tles of jobs or work units that may not seem mathematical. Mathematicians can pop up, and do mathematical work, all over the place. Michael Weiss, Agricultural Economist

The attempts to build expert systems, which can perform tasks such as med ical diagnosis or operating a computer, show the need for mathematical mod els of how computer systems can store

data and "reason" about knowledge.

Maria Klawe, Computer Scientist

This valuable booklet should find its way into every mathematics department and

guidance office in the country. Be sure that

your students get their hands on a copy.

32 pp., 1990, ISBN 0-88385-452-X

Price: 1-9 copies $5.00 each

Price: 10-49 copies $4.50 each

Price 50 or more copies, $4.00 each

Price 100 or more copies, $3.00

Cataiog Number MSW

CAREERS IN THE MATHEMATICAL SCIENCES

This pamphlet contains condensations of

six of the essays in "Mathematical Scien

tists at Work" plus sources for additional in

formation. It is ideally suited for distribu

tion to high school or college mathematics

classes and to mathematics clubs. Take some with you when giving a talk to student

groups and make them available to students who visit your college campus?you will find

many uses for these handy pamphlets.

Price: 1-99 copies 25 cents each

Price: 100 or more copies 20 cents each

Catalog Number CMS

Order From

Mathematical Association of America 1529 18th Street, N.W.

Washington, D.C. 20036

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

DISCI??T?

doss

THE

m THE 1991 YEARBOOK Edited by Margaret J. Kenney

A BOOK YOU HAVE TO HAVE! Learn why discrete mathematics is important, what it comprises at various grade levels, and where it belongs in the curriculum. There is something in this yearbook for everyone. Read it and you will find?

many instructional options for your classroom;

topics, activities, and problems specifically appropriate for K-8; discourses on graph theory, matrices, counting methods, recursion,

algorithms, and so on;

teaching units and activities designed specifically for secondary students; and other suggestions for making mathematics come alive for your students.

Order your copy now! $18* 1991,256 pp., #450, ISBN 0-87353-305-4

mm NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

1906 Association Drive, Resten, VA 22091 ?yuo Association jjnve, Kesion, va ??vvi ^wms. Tel. (703) 620-9840 ? Fax (703) 476-2970 flg^

To order, call (800) 235-7566 *20% discount to individual members. See the NCTM Materials Order Form in this issue.

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

Order copies for your schools!

As an individual member of the NCTM, you necentty received a copy of the PROFESSIONAL STANDARDS FOR TEACHING MATHEMATICS.

Together with the CURRICULUM AND EVALUATION STANDARDS FOR SCHOOL MATHEMATICS, you now have a pack

age that will help improve the teaching and learning of mathematics in the

1990s.

Be a "5 3 3 ^|8 8^ and

spread the news?to your principal, colleagues, state

supervisors, parents,

buiness leaders, and others.

With these _ ^Itapardsai a ; ';; guide, you can chart the

programs that will help you and your schools achieve a brighter future for

all students.

Special price for the two-book set, $42 JO ISBN 0-87353-308-9, #481

Professional Standards for Teaching Mathematics 200 pp., ISBN 0-87353-307-0, #439. $85*

Curriculum and Evaluation Standards for School Mathematics 258 pp., ISBN 0-87353-273-2, #396, $25 ($20 for individual members)

(Quantity discounts for each book are also available.)

NATIONAL COUNCIL OP TEACHERS OF MATHEMATICS 1Q?? Association Drive, Restos, VA 22(381

Tel. CT?33 6?O-S&40-?r- fax 7033 ?T78-297O To ? order, call

' CSOO) -230-7588

* ?S 10 fbr mil now NCTM individual members and for mtt NOTM tnetfcutional members until 1 Au^uets 1 1.

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions

ORDER FORM MEMBERSHIP APPLICATION

Educational Materials* Stock # Quantity Unit Price

20% Discount: Individual members, bookstores, or quantity orders for 10 or more copies of a single title shipped to one address. Prices subject to change without notice. Shipping and handling charges will be added to all billed orders.

Membership #

Special Products*

Subtotal Less 20% Subtotal

Total Price

$_ $_ $_ $_

$.

Stock # Quantity Unit Price

$. $.

Membership Application* Dues support the development, coordination, and delivery of Council services for one year, including $15 for each subscription to the Arithmetic Teacher and Mathematics Teacher, $20 for the Journal for Research in Mathematics Education, and $3 for five issues of the NCTM News Bulletin, including Math Student Notes. Full-time student dues are 1/2 regular dues.

$.

$.

$.

$.

$.

Arithmetic Teacher (AT) Individuals $40; Institutions* $45. 9-issues September-May for elementary grades K-8.

Mathematics Teacher (MT) individuals $40; institutions $45. 9-issues September-May for secondary grades 7-14.

Journal for Research In Mathematics Education (JRME) 5-issues November, January, March, May, & July. Individuals $45.

Periodical Combinations (Select one option) O AT & MT: $55; O AT & JRME: $60; O MT & JRME: $60; O AT, MT & JRME: $75.

Additions and Information Special Product orders must be prepaid and Include $2 for shipping and handling. Sales tax on materials and products (not membership) for Virginia residents 4.5%. Additional >47copies, for institutions only, mailed to the same address $15/order/year. For mailing outside the U.S., add $5 for the first AT or MTan $2.50 for each additional AT or MT; add $1.50 for JRME.

MasterCard VISA Total payment to NCTM in $ U.S.enclosed. $_

Credit Card #_,_ Expires_/_

Signature_ Canadians enter "U.S." after the dollar amount on your personal checks.

Other international orders must be paid by MasterCard, VISA, or a U.S. check drawn on a U.S. bank.

Home Phone (.

Name_

Work Phone (.

Address.

City_ State Postal, Code or Province uode 789 a2

NCTM 1906 Association Drive Reston, VA 22091 703 620 9840 FAX 703 476 2970

This content downloaded from 95.47.162.2 on Mon, 9 Jun 2014 12:35:08 PMAll use subject to JSTOR Terms and Conditions