gifted students || front matter

Front MatterSource: The Mathematics Teacher, Vol. 76, No. 4, Gifted Students (April 1983)Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963446 .

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the malhematic

teacher April 1983 Volume 76 Number 4

CHARACTERISTICS AND SPECIAL NEEDS OF THE GIFTED STUDENT IN MATHEMATICS M. Kathleen Heid

Mathematics and the Imagination Harold R. Jacobs

An Account of a Mathematician's Career An Interview with Martin Gardner

national council of teachers of mathematics



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Please have a Merrill representative contact me. Please send full-color brochures on the programs checked below. MATHEMATICS: ESSENTIALS AND APPLICATIONS (Grades 7-8) MATHEMATICS FOR THE REAL WORLD ? 1982 MATHEMATICS FOR EVERYDAY LIFE ? 1982 MATHEMATICS FOR TODAY'S CONSUMER ? 1982

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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.

EDPRESS

Member of the

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of America

The Mathematics Teacher (ISSN 0025-5769), an official journal of the National Council of Teachers of Mathematics, is published monthly, September through May, at 1906 Association Drive, Reston, VA 22091. Dues for individual membership in the Council are $30.00 ($15.00 for students). For an additional $10.00 ($5.00 for students) an individual member can also receive the Arithmetic Teacher, the other official journal of the Council. For mailing outside the United States, add $5.00 for the first journal per member ship and $2.50 for each additional one. The institutional membership rate for one jour

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Copyright ? 1983 The National Council of Teachers of

Mathematics, Inc.

EDITORIAL PANEL

CAROLE E. GREENES, Boston University, Boston, MA 02215; Chairman PHILIP L. COX, Walled Lake Central High School, Walled Lake, Ml 48088 KENNETH P. GOLDBERG, New York University, New York, NY 10003 JONATHAN JAY GREENWOOD, Multnomah County Education Service

District, Portland, OR 97216 BRUCE C Burt, West Chester Area School District, West Chester, PA

19380; Board of Directors liaison HARRY B. TUNIS, 1906 Association Drive, Reston, VA 22091; Managing

Editor

STAFF

HARRY B. TUNIS, Managing Editor

CHARLES R. HUCKA, Director of Publication Services ROWENA G. MARTELINO, Advertising Manager ANN M. BUTTERFIELD, Editorial Assistant DOROTHY WELCH ONUF, Editorial Aide

ROBERT MURPHY, Circulation 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 on 8^-by-l 1-inch paper, with figures on separate sheets. No author identification^should appear on the manuscript. Five copies are required. Priority areas are listed in the editorial that appeared in the January 1981 issue.

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. Use 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.

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

The inclusion of advertising and reviews of materials does not imply endorsement of these products by the Council. The Mathematics Teacher will not participate in the unauthorized reproduction of any computerized courseware that bears an explicit or implicit copyright claim.

NCTM BOARD OF DIRECTORS

STEPHEN S. WILLOUGHBY, New York University, New York, NY 10003; President

MAX A. SOBEL, Montclair State College, Upper Montclair, NJ 07043; Past President

JAMES D. GATES, NCTM, Reston, VA 22091; Executive Director BRUCE C. BURT, West Chester Area School District, West Chester, PA

19380 IRIS M. CARL, Houston Independent School District, Houston, TX 77087

THERESA I. DENMAN, Detroit Board of Education, Detroit, Ml 48202 JOHN A. DOSSEY, Illinois State University, Normal, IL 61761 PATRICIA M. HESS, Albuquerque Public Schools, Albuquerque, NM 87125 BETTY K. LICHTENBERG, University of South Florida, Tampa, FL 33620 BOB ROBINSON, Hamilton Board of Education, Hamilton, ON L8N 3L1 WALLACE D. ROGELSTAD, Rex Putnam High School, Milwaukie, OR

97222 LINDA SILVEY, Sepulveda Junior High School, Sepulveda, CA 91343 MARILYN N. SUYDAM, Ohio State University, Columbus, OH 43212 HAROLD D. TAYLOR, Hillsdale High School, San Mateo, CA 94403 JACK D. WILKINSON, University of Northern Iowa, Cedar Falls, IA 50614

HONORARY PRESIDENT

JOHN R. CLARK, Professor Emeritus, Columbia University, New York, NY 10027



Nie mathematics teacher ISSN 0025-5769

VOLUME 76 NUMBER 4 APRIL 1983

ARTICLES 220 Editorial: Challenge of the Gifted Carole Greenes

221 Characteristics and Special Needs of the Gifted Student in Mathematics M. Kathleen Heid

228 An Account of a Mathematician's Education Charles Fefferman

229 Alternative Education Programs for Gifted Students in Mathematics Peggy A. House

234 Contests and Competitions Martin J. Badoian

236 Personal Glimpses from Two Gifted Students Jeremy Primer and Susan Staples

238 Mathematical Research in the Honors Classroom Henry Borenson

245 Mathematics and the Imagination Harold R. Jacobs

250 Challenges for Enriching the Curriculum: Arithmetic and Number Theory Stanley J. Bezuszka and Margaret J. Kenney

253 Sharing Teaching Ideas An Interesting Application of Series and Sequences, Nancy S.

Rosenberg 262 Challenges for Enriching the Curriculum: Algebra

Tom M. Giambrone 264 Enrichment Activities for Geometry

Zalman Usiskin 268 Challenges for Enriching the Curriculum: Statistics and

Probability Jim Swift

270 Computers and the Mathematically Gifted Walter Koetke

274 Challenging Applications: Problems in the "Raw" Jeanne Agnew, Marvin S. Keener, and Ross L Finney

276 An Account of a Mathematician's Career Scot Morris

219 Problems of the Month 256 Activities

Manipulating Numbers, John Firkins 284 NEW Products 285 NEW Projects

Program for Mathematically Precocious Youth

SPATS?Special Projects for Academically Talented Students

Project MEGSSS North Carolina's Special School for Science and Mathematics Students

287 NEW Publications 292 National Council of Teachers of Mathematics

NCTM Affiliated Group Officers

DEPARTMENTS 218 Reader Reflections



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Resources for the Gifted THE Specialists in PROBLEM-SOLVING Materials for Gifted Students

For help meeting their needs, turn to the leader in the field. Thinking skills are easy to teach with our classroom-tested activities emphasizing logic, reasoning, and the ability to analyze, synthesize and evaluate. That's why so many teachers of the gifted depend on our expertise. That's why we think our products belong in your classroom.

lumber Senio: Concept and Process by Dr. Gary Bitter, Dr. Dennis Nelson

Hands-on math exercises guaran teed to challenge students to think problems through to logk^ oondu^ sions. They'll explore formula design, measurement, probability, patterning, charting and computers. Includes 77 fthaiimfla cards, 100 oentacubes, geoboard, styroboard, pegs, dice and graph paper. Grades M M0735 148.00

Mind Over Hath tyDr.EdnaBazik.Dr. Barbara Wilmot

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Unas, Points, ft Patterns An inexhaustible source tor the

myriad of mathematical variations using nature's circular patterning fractured shapes, Piffiorm and colora tions. Demonstrates the beauty in numerical tagte. Reproducible. Grades 6-12 MO 379 19.95

Computer Think hy Ken Florence

No prior expertise is required wit^ this step-by-step guide for problem solving with a computer. Cleverly written, it develops an understanding of principles behind computer logic. Grades 6-12 M1103 18.95

Probability Kit by Dr. Gary Bitter, Dr. Dennis Nelson, Wflnnni* yillftlparirin

These thougutprovrjkingexew^ get kids estimating, predicting and making intelligent guesses?all the while learning the odds behind risk-taking in everyday situations.

Students will incorporate these into a lifetime of practical problem-solving. Includes 8 skill cards, 32 "possibil ity" cards, dice, marbles, chips, charts and graph paper. Grades 6-12 M076X 134.00

fflsulMatk Investigate! Calculate! by Dr. Gary Bitter, Sonia Farseth

Students investigate line, texture and design while calculating with logic, elemente and abstract models. Gives visual representation to mathematical structures. Contains 76 cards for individualizing, teacher guida Two posters and hands-on

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DroidO Dilemmas by Dr. Roger Hufford

Logic gunes with a space-age theme. A chance to decipher intergar lactic (?des and solve mathematical mini-mysteries. 37 intriguing problems with detailed solutions. Reprod?cele. Grades 5-12 M0514 17.98

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THE MATHEMATICAL EDUCATION OF EXCEPTIONAL CHILDREN AND YOUTH

EDITED BY VINCENT GLENNON A Special Reference for Teaching Special Children

A unique interdisciplinary approach to the mathematical education of exceptional children, this reference is intended for professional groups that include classroom teachers, special educators, special education support personnel and teacher educators. The contents represent the cooperative efforts between these mathematics educators and special educators:

Exceptional Children in Changing Times HOWARD H. SPICKER, Department of Special Education, Indiana University, Bloomington, Indiana JAMES McLESKEY, Department of Special Education, Indiana University, Bloomington, Indiana

Variables in a Theory of Mathematics Instruction for Children and Youth VINCENT J. GLENNON, University of Connecticut, Storrs, Connecticut

Teaching Mathematics to Children and Youth with Perceptual and Cognitive Processing Deficits VINCENT J. GLENNON, University of Connecticut, Storrs, Connecticut WILLIAM M. CRUICKSHANK, Director, Institute for the Study of Mental Retardation and Related Disabilities,! University of Michigan, Ann Arbor,. Michigan

Teaching Mathematics to Socially and Emotionally Impaired Pupils J.F. WEAVER, University of Wisconsin-Madison, Department of Curriculum and Instruction, Madison, Wisconsin I WILLIAM C. MORSE, Chairman, Combined Programs in Psychology and Education, School of Education, Universi-1 ty of Michigan, Ann Arbor, Michigan

Teaching Mathematics to Slow-Learning and Mentally Retarded Children LEROY G. CALLAHAN, Department of Elementary and Remedial Education, Faculty of Educational Studies, State| University of New York at Buffalo, Amherst, New York DONALD L. MacMILLAN, University of California at Riverside, Riverside, California

Teaching Mathematics to the Talented and Gifted H. LAURENCE RIDGE, Faculty of Education, University of Toronto, Toronto, Ontario JOSEPH S. RENZULLI, Department of Educational Psychology, School of Education, University of Connecticut, | ' Storrs, Connecticut

Teaching Mathematics to the Visually Impaired JOSEPH N. PAYNE, School of Education, University of Michigan, Ann Arbor, Michigan GERALDINE T. SCHOLL, School of Education, University of Michigan, Ann Arbor, Michigan

Teaching Mathematics to the Deaf and Hard of Hearing CHARLES H. DI ETZ, Model Secondary School for the Deaf, Gallaudet College, Washington, D.C. CLARENCE M. WILLIAMS, Coordinator of Faculty and Graduate Research, Gallaudet College, Washington, D.C

Teaching Mathematics to Children and Youth with Physical and Health Impairments STEPHEN S. WILL0UGHBY, Professor of Mathematics and Mathematics Education, New York University, New| York, New York JEROME SILLER, Educational Psychology Department, New York University, New York, New York

Improving Preservice and In-Service Programs for Teaching Mathematics to the Exceptional JASPER HARVEY, U.S. Department of Education, Washington, D.C.

1981 416 pp. ISBN 0-87353-171-X #49 $28.00

NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS 1906 Association Drive, Reston, Virginia 22091 MasterCard and VISA orders: 703/620-9840 Virginians add 4% sales tax.



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