Front Matter Source: The Arithmetic Teacher, Vol. 39, No. 1 (SEPTEMBER 1991) Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41194892 . Accessed: 12/06/2014 14:46 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 of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PM All use subject to JSTOR Terms and Conditions
Transcript
Front MatterSource: The Arithmetic Teacher, Vol. 39, No. 1 (SEPTEMBER 1991)Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194892 .
Accessed: 12/06/2014 14:46
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 [email protected].
.
National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.
http://www.jstor.org
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PMAll use subject to JSTOR Terms and Conditions
{iiiieisii the ■ future?^ ^ •iWeSit-SiiilliS ■ ^^^^B
Addison-Wesley Mathematics ^^^^^^^^^^^^^^H helps you implement the NCTM Standdrcl5* ̂̂ ^^^^^^HBHPP^^^^^^^I Addison-Wesley Publishing Company |Р|НрР^^|^^^^И provides support and service for educators, !^^|^^%2^|||^^^^^^^^Н in the past, in the present J|t/|M/< J^ttÉBil^^^^^^^^^^H
and in the future. ; r^i|£||á ' 1|^^^^|^^^^^^^^^^^^H '^ ά ^^^^H
Addison-Wesley ^^^^^H Publishing Company ^^^^^^^^^H 2725 Sand Hill Road, Menlo Park, CA. 94025 ^^^^^^^^^^^^^^B
(415) 8540300 ^^^^^^^^^^^^^H
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PMAll use subject to JSTOR Terms and Conditions
STUDENT SURVEY SEE PAGE 26 On the cover: These junior high school students are getting a taste of "realtiy math"; see Linda Moniuszko's article in this issue. Photographs by Terrell Photography; all rights reserved. Readers are encouraged to submit color slides of children involved in mathematics through the middle grades for possible use on the cover.
9 READERS' DIALOGUE
ONE POINT OF VIEW: We Must Have "Designated Math Leaders" in the Elementary School! James V. Bruni
I %0 Linda K. Moniuszko
THE PROFESSIONAL STANDARDS FOR TEACHING MATHEMATICS: Improving, Not Standardizing, Teaching Deborah Loewenberg Ball
AJ CALENDAR MATHEMATICS ^BW Dinah Chancellor
^Ä IDEAS ^^^* Dianne Bankard and Francis (Skip) Fennell
RESEARCH INTO PRACTICE: Enhancing Mathematics Learning through Imagery Grayson H. Wheatley
1Ш FROM THE FILE Щ&ш William R. Hastings; Rebecca B. Barbusca
*M» TEACHING MATHEMATICS WITH TECHNOLOGY: How Big Is a Million? iP^P Janet Parker and Connie Widmer
ЛЖ REVIEWING AND VIEWING: Computer Materials, Glenn D. Allinger and John F. Martin, Jr.; ЩН0 New Books, Hilde Howden, George Nattrass, Rosamond Tischler, and David J. Whitin; Etcetera, Iva
J. McCants and Mary K. Tornrose
COUNCIL OF TEACHERS OF MATHEMATICS: NCTM Officers and Directors Elected in 1991
BA GUIDE TO ADVERTISERS
Ж£% FROM THE FILE ^^Щ0 Lyn D. English; Anthony Standen
ISSN 0004-136X
The Arithmetic Teacher: Mathematics Education through the Middle Grades is an official publication of the National Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, VA 22091 . See the masthead for subscription information.
Editorial Panel: Portia Elliott, University of Massachu- setts, Chair. Anne Bartel, Minneapolis Public Schools. Randall I. Charles, San Jose State University. Linda Gojak, Hawken School, Lyndhurst, Ohio. Michael Hynes, University of Central Florida. Carol A. Thorn- ton, Illinois State University. Ian С deGroot, Sutherland Secondary School, North Vancouver, Board of Directors Liaison. Harry B. Tunis, NCTM, Director of Publications.
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 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 youngest students· Teachers across the country agree. Young elementary students need a calculator that allows them to explore and discover math' ematical concepts. The Math Mate from Texas Instruments meets this need as well as all the requirements math teachers have for instructing young children.
A powerful teaching and learning 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 Operating System (AOS™) that multiplies and divides before adding and subtracting (M-D-A-S). Whaťs more, students can override the order of opera- tions and develop conceptual under- standing through the use of built-in parentheses.
ТЪе 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 standard functions, plus a change sign key, con- stants for all four basic operations and easy-to-use memory keys.
more important, Math Mate is rugged enough to take on the daily demands of young learners. The plastic keys are tough and tamperproof, and an impact-resistant sliding case offers extra protection.
Free 30-day evaluation The Ή Math Mate is available for a free 30-day trial as a Preview Kit. Convenient purchase options include a Student Pack and a Teachers Kit.
Ή wants to help you help your students learn the value of mathematics. With the Math Mate, it's never been easier for you. Or more fun for them.
For more information, call 1-800 Ή CARES.
Texas ^^ Instruments
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PMAll use subject to JSTOR Terms and Conditions
^^^^шЕЕШ^^тш^Еш^В^^^^^ШШ^^М^^^Ш^^^^^^^Яш It was scripts and video cameras instead ^^^^^Р^ШпИИНМ^^^^^БрР ДлЕ<1^Р^^вИН^н1 ofp^^s and paper when Bonnie Dixs math ^^^^Нч^шН^Р^ЯЯ^^^^^^Ж^ 1 ид ш~ *~» Ч^ШЯЯЯШ class studied fractions this year. The seventh ^^№Л11ш^^^ JUUB Τ ЖЛ1 gradeis at Monte Cassino Middle School in ^■ГЖ Ш в2^^^^Ш*Ж'ШШ& ' ДЩД*Щ Ш Tulsa, Oklahoma wrote and starred in their ^^Ш^ЩШШ^ШаЬ^^ШшЕЕЕШЕ&ЙШ l Щ own Fraction Television Video. V^^K '^' I^^K^^^R^^H^K ^^
l The kids went way beyond the math Ψ ^^^A aJI^ ' ̂ ^^^H|^V ^^^^^^rf^É^T^ *X)O'C' writing ^d videotaping a series
^^^|L^RS|l^^t Щ^^^^^Шш&Ш С^1ЕЕЕаЕ^^^Ш^ ofskits that made fractions fun and easy to ИЕИЕИЯ^^ИиШГ^^^^к. ̂ ^^^^^ШВгшшЕ^^Ш^^^^^^ЖШ understand. In one segment, a soap opera ^Е|ЙШ^^^|&^ ^I^H ^^B^^^MI^^^^^^^^^^B I chronicles Miss Numerator's anguish after ^^^^^^В1^В^>'^' ^^^Шк^тШ^^^^^^^^^^Ш I being abandoned by her denominator ^^Н|Ш Д '' ^Шк^^^^^^Ш^^ЛЩ (uNowrmjust...anumberrshewails).News Hf^^^^^^^^^^m ' ' 1^^Л^ЩВ^^^^Ш^^^^Лш bulletins break in with a story of escaped frac- ННН^^^^^В^А W Х^^^^Н^ЭН^^Ш^^^нВ ti°ns(uThreeF°urtb^ ^^^^В^НШ^»-
W '^. ^^^BT ll^H^^^^P One Fourth is still at large") and a report
^^^^^^^^ШшШЁшг<***^*тШ1^^^Ш ЩВшшШЕ^^ on renegade General Two And One Third ^Я^^^^^^Ш^^^ШШЕ^ШМ^^^^^Ш^ -^MJL ' ("He mS1StS heS bigger ЛаП Three")· Fraction ^^■^^^^^^^^K^^^^^^H^H^Bj^^H^^^^ fl^^ ;ïUffjpW^ Television even has its own music videos and ^^^^^^^^^^^■^^^^^HHI^^H^^^BKi.. яГ^^ ^^■t^' commercials, all designed to help fractions ^^B^^^^Hk^^^^^^I^^I^H^^Imí. ^^kSI j^M come alive in the children's imaginations. ■^^^^^^^■Μ^^^^^Η^^^^^^^^^Η^ς^Κ^ 1fl| "My goal is to make math ran and Щ^^^ШШ^Я£щЕ^^^^ш/^^Е^^^^Ш11^ШшЬ^ШЕ1^^ ^^ËjL· exciting to the students so they'll no longer ^^^^^^^^KT ^^^^^^К^^^^^^ЯШ^ИИррР^^^^В^ ^Ш^Ек groan at the thought of math class'/ says ^ШШШ^Ш^^ьтЕЕт?'/!- ^hHB^^^v ^^^0^Ш^ Bonnie. "For me, being enthusiastic about ^ЩГ ^^ШЕШЕШ^^Еи./ 1^:: r^· : ■ ^r-!^^ M r^2të ' "^^r ^И1 mat^ ^ inventing creative ways to teach it VlV^ ^^ШЕ^^Ш^ Н^Ш^^^^В
1^:: r^· V^; ^B are as important as the material itself' ^^^^Q^ ^^^н^|НННШши"^ш ψ ^Hj For her innovative approach to teach- I^^^^^V^^H^^^H^ ШЕ^^^^^^^^^^^Шк ^ш i ^^Ě ing, we at State Farm are delighted to honor ^^^Н^Г Ц^^^^^^^^^^^^^^^^^^^^Нк;^ Щ1 ^^ff Bonnie Spence Dix with our Good Neighbor Н|^^^^Я ^^r _^^^^^^^^^^^Hpà: ^Bk'^^ ^Hfe Award' ^ to contribute $5,000 in her pjidS ^^^&^^^^^^^^^^^Ш"~^Нк^^Р^В name to the Monte Cassino Middle School. B;B^^BI V^^fl^^^^^^^^^^^V"1 '■'''ЯЩРЧВВ Bonnie Spence Dix. A good neighbor ЩШ^^^Ш ^jjr м^^^В^^^^^^^^^^^^^^^Г^ ш^^Е9ш w^° ̂e^Ps ma^e I62117™? a star attraction.
B| ' .ЕЕ^^^^^^^^^^^ЯВ^^^^^^^^^^^^^кк^^^ЕЕ^^^^^^^Шг ^Н STATE FARM
INSURANCE STATE FARM INSURANCE COMPANIES The Good Neighbor Award was developed in cooperation with the National Council of Teachers of Mathematics (NCTM). ^^^^^нн^^^ Home ^^^ Bioomington, Illinois
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PMAll use subject to JSTOR Terms and Conditions
Call for Manuscripts for Focus Issue: Empowering Students through Connections in Mathematics The February 1993 issue of the Arithmetic Teacher: Mathematics Education through the Middle Grades is planned as another in the series of focus issues. The theme of the issue, Empowering Students through Connections in Mathematics, addresses one of four major areas emphasized by the National Council of Teachers of Mathematics in its Curriculum and Evaluation Standards for School Mathematics and its Professional Standards for Teaching Mathematics.
Manuscripts are invited that present ways connections can be emphasized by teachers and made by students as an important part of mathematics teaching and learning. Each manu- script also should specifically emphasize how making connections enhances students' math- ematical power as defined in the aforementioned standards documents.
No author identification should appear in the text of the manuscript. Authors should iden- tify one category from those listed below that represents the major thrust of their manuscript. An article might, however, incorporate components of more than one category. Interdisci- plinary coauthorship is encouraged.
Seven copies of a completed manuscript should be sent for review to the Arithmetic Teacher, 1906 Association Drive, Reston, VA 22091, by I November 1991.
The mathematics connection situations? In investigating and solving prob- What mathematical relationships can and ^J !? How HprediHCting do*s Ι*!"*** ******
and in wh,ch ff"* stu- should be recognized and used by primary, ^f5,7 lea™
How do*s ****** aflfec<
in wh,ch under-
stu-
intermediate, and middle school students? dfnt* Standmg lea™
of mathematIcaI ™<hemf<* concePts? aflfec<
hfr under-
How and when can these relationships be Standmg of mathematIcaI concePts?
developed? How can teachers help students -. The . „. ,. ̂ MM^*:^M connection see mathematics as an -integrated whole" The leamm9 „. ,. ̂ MM^*:^M connection rather than as a series of disjointed concepts How might instruction be structured to allow and skills? How might students be led to use students a more active role in learning math- one mathematical idea to further their un- ematics? How might teachers help students derstanding of other mathematical ideas? make connections between their present un- How can mathematics be presented as a dis- derstanding of a mathematical concept or cipline that has evolved throughout history, topic and extensions or applications of that reflecting the uniqueness of each culture and understanding? How might students be in- language? volved in activities that broaden their aware-
ness of multicultural and multiethnic contribu- Connections with other curriculum tions to mathematics? areas How might students be led to apply mathe- Uses of technology to make matical thinking and modeling to solve prob-
connections lems that arise in such other curricular areas What role does technology play in helping stu- as art; music; physical, life, and social sei- dents make important connections? How ences; language arts; and physical educa- might technology be integrated with other ef- tion? forts to help students make important mathe-
matical connections? The applied connection: Real-world problem solving Connection of teaching and learning to What applications are most appropriate for assessment
key topics at the primary, intermediate, and How can teachers use assessment as a bridge middle school levels? How might teachers between teaching and learning? What assess- help students value mathematics as a real- ment options best inform teachers of impor- world problem-solving tool? tant connections being made by students?
The language connection The home-school connection What is the role of language in concept de- How might the home-school connection be velopment? In extending or applying con- strengthened? What role does homework play cepts to one another? In interpreting and in laying the foundation for or strengthening connecting physical, graphical, numerical, mathematical connections focused on in the or algebraic representations of problematic daily lesson?
Your link to good teaching
MATHEMATICS FOR THE
YOUNG CHILD Edited by Joseph N. Payne . . . will help you introduce the
exciting world of mathematics to young children, ages three through nine.
This book has gathered the most useful ideas and fused them into a resource that will be your link to good teaching. Its sugges- tions are practical, and the activi- ties are easy to follow and effec- tive.
Use this book now and become an outstanding teacher of mathe- matics to young children. It will help you - e find techniques that work espe-
cially well with preschoolers through fourth graders
e update your curriculum confi- dently
e keep up with the latest re- search findings
e teach your students how to use calculators and microcomputers appropriately
Should be used by new teachers, experi- enced teachers, teacher educators, future teachers, and curriculum developers in
states and provinces. 1990, 306 pp., #402, ISBN 0-87353-288-0
$39.50* шв| National Council of Щр Teachers of Mathematics 1906 Association Drive, Reston, VA 22091
(703) 620-9840 · Fax (703) 476-2970 FOR ORDERS ONLY, CALL
(800) 235-7566. *20% discount to individual members.
See the NCTM Materials Order Form in this issue.
SEPTEMBER 1991 23
This content downloaded from 188.72.126.55 on Thu, 12 Jun 2014 14:46:36 PMAll use subject to JSTOR Terms and Conditions
Ä «"ilRRICULUM-rK-i» Ä *■* Ä ·* 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! $ 1 8 * 1991, 256 pp., #450, ISBN 0-87353-305-4
l4^ gg NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS l4^ 1906 Association Drive, Reston, VA 22091 -^^
Because our newest generation must be our smartest generation.
society, technol-
Throughout ogy is continually changing the way we work, learn and
live. But as society changes, there is one constant: A thorough education is vital in helping students develop patterns for success. Our classroom calculators are designed for the special needs of schools« Calculators are now accepted as effective and cost-efficient 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 mathematical concepts.
For 17 years, Ή 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) Cuniculum and Evaluation Standards for School Mathematics.
Each of our classroom models contains features to make math edu- cation 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 Ή-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 previ- ous models available. Presenting our new teacher-designed Math Mate· This year we introduce the Math Mate, the first AOS™ calculator with correct order of operations designed
for the youngest students. A power- ful teaching and learning tool, the Math Mate meets all the requirements math teachers have for instructing young children. Texas Instruments wants to help you help your students succeed in math· We're committed to maintaining 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: 1-800-TI-CARES (842-2737).
¥ύ Texas Instruments
mí ScottForesman A Division of HzrperCollinsPublishers
1900 East Lake Avenue 99 Bauer Drive 1955 Montreal Road 2105 McDaniel Drive P.O. Box 3633 Glenview, IL 60025 Oakland, NJ 07436 Tucker, GA 30084 Carrollton, TX 75006 Sunnyvale, CA 94088
