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Front Matter Source: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987) Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41193082 . Accessed: 18/06/2014 09:57 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 185.2.32.24 on Wed, 18 Jun 2014 09:57:12 AM All use subject to JSTOR Terms and Conditions

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Page 1: FOCUS ISSUE: CALCULATORS || Front Matter

Front MatterSource: The Arithmetic Teacher, Vol. 34, No. 6, FOCUS ISSUE: CALCULATORS (February 1987)Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193082 .

Accessed: 18/06/2014 09:57

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

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Page 2: FOCUS ISSUE: CALCULATORS || Front Matter

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Page 3: FOCUS ISSUE: CALCULATORS || Front Matter

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Page 4: FOCUS ISSUE: CALCULATORS || Front Matter

The ARITHMETIC TEACHER Is an official journal of the National Council of Teachers of Mathemat- ics. It is a forum for the exchange of ideas and a source of techniques for teaching mathematics in grades kindergarten through eight. It presents new developments in curriculum, instruction, learning, and teacher education; interprets the re- sults of research; and in general provides informa- tion on any aspect of thebroad spectrum of math- ematics education appropriate for preservice and in-service teachers. The publications of the Coun- cil present a variety of viewpoints. The views expressed or implied in this publication, unless otherwise noted, should not be interpreted as offi- cial positions of the Council.

EDITORIAL PANEL Joan E. Worth, University of Alberta, Edmonton, AB T6G

2G5; Chairman Francis (Skip) Fennell, Western Maryland College, West-

minister, MD 21157 Marsha W. Lilly, Alief Independent School District, Alief,

TX 77411 Edward Rathmell, University of Northern Iowa, Cedar

Falls, IA 50614 Jean M. Shaw, University of Mississippi, University, MS

38677 Charles S. Thompson, University of Louisville, Louisville,

KY 40292 Henry S. Kepner, Jr., University of Wisconsin-Milwau-

kee, Milwaukee, Wl 53201; Board of Directors liaison Harry B. Tunis, 1906 Association Drive, Reston, VA

22091 ; Managing Editor

STAFF James D. Gates, Executive Director Harry B. Tunis. Managing Editor

Joan Armistead, Editorial Coordinator Ann M. Butterfieki, Program Assistant Lynn Westenberq, Editorial Assistant

Charles R. Hucka, Director of Publication Services Rowena Q. Marteiino, Advertising Manager

Robert Murphy, Computer Services Manager Joseph R. Caravella, Director of Membership Services Betty C. Richardson, Director of Convention Services Art direction by William J. Kircher and Associates

Correspond«*» should be addressed to the Arithmetic Teacher, 190$ Association Drive, Reston. VA 22091. Manuscripts should be typed doubte-spaoed throughout, with wide margins, on 81¿ x 11 paper and with figures on separate sheets. No author identification should appear on the manuscript Five copies are required. See the October 1966 issue for underrepresented topics. Follow the Chicago Manual of Style in the preparation of manuscripts.

Pewnlaaioii to photocopy material from the Arithmetic 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 tor commercial use of content from the Journal when the material is quoted in advertising, anides are included in books of readings, or charges for copies are made or profit is intended. Use of material from the Arithmetic Teacher» other than those cases described, should be brought to the attention of the National Coun- cil of Teachers of Mathematics. The Arithmetic Teacher will not participate in the unauthorized reproduction of any computerized courseware that bears an explicit or jmofidt copyright «aim.

The Arithmetic Teacher (ISSN 004-1 36X), an official Journal of the National Council of Teachers of Mathematics, is published monthly, September through May, at 1906 Association Drive, Res- ton, VA 22091. Dues for individual membership in the Council are $35.00, which includes one Journal subscription. For an additional $13.00 an individual member can also receive the Mathematica Teacher, the other official Journal of the Council. Rates for student members are one-half the regular rates. For mailing outside the United States, add $5.00 for trie first Journal per membershto and $2.50 for the second official journal ($1.50 for Journal for Re- search In Mathematics Education). The institutional membership rate for one journal is $40.00. Multicopy subscribers pay $13.00 for each additional copy going to one address. For mailing outside the United States, addi

copy $5Ü00 for the first copy and $2.50 for each addi-

tional copy per membership. Airmail rates for institutional and indi- vidual membership are available on request Ufo and retired mem- bership information is available from the NCTM Headquarters Office. Dues support the development, coordination, and delivery of the Council's services, including $13.00 for each Arithmetic Teacher and Mathematics Teacher subscription and $2.00 for an NCTM News Bulletin subscription.

The index for each volume appears in the May issue. The Arithmetic Teacher is indexed in the Current Index to Journals in Education w& Education Index. Second-class postage paid at Reston, Virginia, and at additional mailing offices. PCÄTTÖlASimSerid address crianges to the Arithmetic Teacher, 1906 Association Drive, Reston. VA

Serve: 75446J161. Copyright © 1967, The National Council of Teachers of Mathematics, Inc. Printed in the U.SA

Cover story: The photographs appear through the courtesy of Ray Kurtz and Joan Spier, authors ¿fan article in this issue.

i w^^^^^^^^^ w M0TWD0f or tne V"^ w * Educational Près« EDPRE88 Association of America

HI Arithmetic ^^^^■m^^Bj ^m ^L^ ^mm ̂ b Volume 34 I ff#nf I mmWm ^mm ̂ b Number 6 ■ ^M^I^BI I^mI February 1987

Content} By Way of Introduction, Marsha W. Lilly 2

One Point of View: The Calculator-based Curriculum: Deceased or Just in "Suspended Automation"? Bob Kansky 4

Readers' Dialogue 5

From the File Celestine Wyatt; Ann Bol ing; William R. Hastings 6,66,68

A Calculator-integrated Curriculum: The Time Is Now, David E. Williams 8

Calculators in the Classroom: How Can We Make It Happen? Barbara J. Rey s and Robert E. Rey s 12

A Compelling Case for Calculators, Bernard R. Yvon 16

Research Report: What Are Calculators Good For? Marilyn N. Suydam 22

Teaching Primary-Grade Mathematics Skills with Calculators, Joan Spiker and Ray Kurtz. 24

Estimation and Mental Computation, Harold L. Schoen 28

IDEAS, Terrence G. Coburn 31

Guide to Advertisers 32

Activities for Calculators, Arthur A. Hiatt 38

Problem Solving: Tips for Teachers, Joan Duea and Earl Ockenga 44

The Calculator Is a Problem-solving Concept Developer, Margaret Comstock and Franklin Demana 48

An Instructional Model for Integrating the Calculator, Donna F. Berlin and Arthur L. White 52

Calculators and Connecticut's Eighth-Grade Mastery Test, Betsy Y. Carter and Steven J. Leinwand 55

Calculators and the Mathematics Curriculum, James H. Wiebe 57

NCTM Position Statement on Calculators in the Mathematics Classroom 61

Computer Corner, Don E. Ryoti 62

Mathematics Framework for California Public Schools K-12: Calculator Technology 64

Reviewing and Viewing Computer Materials, Douglas H. Clements, Peter Kloosterman, and Barbara Signer; New Books, A. Dean Hendrickson; Etcetera, Carol Novillis Larson 65

^^^HMHjjjjj^gjjj^gjjjj^ggjjj^^gg^ggi ISSN004-136X

NCTM Board of Directors: John A. Dossey, Illinois State University, Normal, IL 61761, President. F. Joe Crosswhite, Northern Arizona University, Flagstaff, AZ 86011, Past President. James D. Gates, NCTM, Reston, VA 22091. Executive Director Joan L. Akers, San Diego County Office of Education, San Diego, CA 92111. Albina S. Cannavaciolo, Hamden Hall Country Day School, Hamden, CT06517. Philip L. Cox, Walled Lake Central High School, Walled Lake, Ml 48088. David J. Glatzer West Orange High School, West Orange, NJ 07052. Marilyn L. Hala, South Dakota Department of Education, Pierre SD 57501-2281 . Donald W. Hight, Pittsburg State University, Pittsburg, KS 66762. Henry S. Kepner, Jr., University of Wisconsin- Milwaukee, Milwaukee, Wl 53201. Mary Harley Kruter, Thomas Jefferson High School for Science and Technology, Alexandria, VA 22312. Katherine P. Layton, Beverly Hills High School, Beverly Hills, CA 90212. Mary M. Lindquist Columbus College, Columbus, GA 31993. Bonnie H. Litwiller, University of Northern Iowa, Cedar Falls, IA 50614. Ronald Wittner, Lakeview School, Regina, SK S4S 0N8.

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Page 5: FOCUS ISSUE: CALCULATORS || Front Matter

Silver Burdett Mathematics grades k s

Establishing the new pattern of excellence in mathematics.

Silver Burdett & Ginn 191 Spring Street, Lexington, Massachusetts 02173-8087 250 James Street, CN-1918, Morristown, NJ 07960-1918

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Page 6: FOCUS ISSUE: CALCULATORS || Front Matter

^

An Alternative Basal Math Series From MCP

TEACH MATH SKILLS WITHIN THE CONTEXT OF PROBLEM-SOLVING SITUATIONS!

Curriculum Press is proud to announce a new alternative basal math series for students in grades K-6.

This unique alternative program is perfect for providing the flexibility you need for ability grouping. Highlights of Modern Curriculum Press Mathematics include: ■ Teaching math skills within the context of problem-solving situations ■ Adequate practice to master those skills ■ Developed models students actively work with to solve problems ■ Reinforcement of problem-solving thinking skills.

With Modern Curriculum Press Mathematics, your students think, actively participate, and develop an understanding of math skills.

The developmental sequence of Modern Curriculum Press Mathematics introduces and extends skills taught in the normal basal curriculum - such as statistics, logic, and probability. Teachers can then choose what is most appropriate for the needs of their students ... that's flexibility!

Other features include: abundant practice of math skills, practice in estimation, mental math, calculator use, and computer activities. Comprehensive Teacher's Editions provide you with plenty of additional enrichment, reteaching, and application activities and contain a complete Error Pattern Analysis.

You have come to expect quality materials at reasonable prices from Modern Curriculum Press. Our new math series continues that tradition. Remember Modern Curriculum Press Mathematics... it's brand new for 1987!

ORDER TOU-FREE 1-800-3^06 In Ohio, call collect 216-238-2222. A / Q^ / / / / C^<o^c^°

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Page 7: FOCUS ISSUE: CALCULATORS || Front Matter

Mathematics Unlimited Celebrate the possibilities!

We've raised mathematics success to new heights correcting common errors, the possibilities are endless, with the program that wins hands down. Mathematics Students become active, involved decision-makers, Unlimited gets students enthusiastic about computation, totally confident with numbers and able to experiment r problem solving, and estimation strategies and skills. in self-assured, individual ways. So they can appreciate the logical, elegant power of ^ We'd like you to see how well Mathematics numbers- and gain confidence in their own power of ^^^^Ê^L Unlimited lives up to its name, and to mathematical ¿bAce. ^^^^^^^^^^^^L our expectations.

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Page 8: FOCUS ISSUE: CALCULATORS || Front Matter

I VT7C7 IVI lîlro Please have a sales representative contact me. The last time we adopted | IEi3. 1U 11KC Mathematics was

tO p get HIV handS ame The grades wewiU adopt are_üü

J p ". « . Position

on Mathematics .

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School approximately students. T

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in ■ Other ~i people i to contact about k this k • adoption j ♦• are:

City/State/Zip XT

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j Gl We are planning to adopt Mathematics in 1 98 7. ""

I The decision deadline is , Name ■ (month) 4^ate) ■ D We are not adopting Pndtinn I - * Mathematics in 1^7, but in ̂__

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HC*T, RINEHART AND WINSTON L We are currently using 383 Madison Avenue, New York, New York 1001 7

f i ^V S %itle and/or publisher)

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Page 9: FOCUS ISSUE: CALCULATORS || Front Matter

Advertisement

WHY SAXON ELEMENTARY BOOKS SAY NO TO CALCULATORS

In December of 1985, a report was issued that com- pared the mathematics skills of students in 26 nations. The 500 classes of American students who participated scored at the bottom of the civilized nations and just above Swaziland. More frightening was the fact that the top 5 percent of the Americans had an average score that was at the 25th percentile of the scores of the Japanese. This means that 75 percent of the Japanese students outscored the top 5 percent of their American peers.

American students are not genetically inferior. American society is not sick and our teachers of mathematics are totally competent. I believe that these unbelievably poor scores are the direct result of trying to teach advanced concepts too early and of neglecting the emphasis of fundamental concepts that can be taught and whose use can be automated by students. The December, 1981 issue of The Mathematics Teacher reported that the most recent NAEP area and volume test showed that 82 percent of American 17- year-olds do not know what the word area means. In the September, 1986 issue of The Arithmetic Teacher, Barbara Reys quoted from a report in December 1983 that ' 'poor concept development of fractions, decimals, and percents inhibits application of estimation to prob- lems containing these numbers."

When I look at the history of elementary and high school mathematics for the last 30 years, I note a distinct pattern. There has been a search for a panacea, for a magic elixir, for some wonderful way to "teach higher order thought processes'

' (whatever that means) and a neglect, almost to the point of overt disdain, of trying to automate the fundamental concepts and skills that are necessary for any intelligent application of mathematics. I think it began with the so-called "new math. ' ' The students already knew that the green Chev- rolets were also Chevrolets, but there was a drive to teach them about the ' 'higher order concept of subsets' ' which they already understood. We gave them big names to discuss the fact that the sums and products of 3 and 4 were not altered if the numbers were inter- changed. This is not an advanced concept, but a very simple concept to which a complicated name was given. Now that this fad has faded, there is a new drive to teach concepts from probability and statistics before the students have the maturity to understand and there is

also an effort to teach logic prematurely. To this we add the requirement that students should become adept at 4 'estimating.

' ' I believe that estimating is a higher order skill that is developed only when it is necessary. As a graduate student in electrical engineering, my class- mates and I were often berated because our answers were not reasonable. I am still a poor estimator and while I have no objection to acquainting students with the idea of estimation, I hold little hope for measurable success in this area.

In contrast to our search for the magic solution, the Japanese concentrate on teaching fundamentals and do not allow calculators in their elementary schools. The famous meta-analysis on the results of using calcula- tors in American elementary schools reported that the use of calculators in the fourth grade was detrimental to average students and that insufficient evidence was available for grades K-3 to make a recommendation for these grades. In spite of this, there has been a big push to force calculators into every elementary classroom in America. I believe that this is a great mistake and I am writing and publishing a K-8 series that does not en- courage the use of calculators. These books concentrate on giving the students the fundamental skills that will enable them to use calculators intelligently when the time comes. I ask each reader to carefully evaluate what I have said and not to use calculators in the elementary classrooms until their use has been proved to help all of the students and to hurt none. We do not have this proof now and I do not believe we ever will because I believe these machines will cause great damage to a significant number of students if these machines are introduced while arithmetic is still being learned.

I have books in print now for grades 6-11 and plan to have a full K-12 series available in about 2 years. Look at these books carefully before you decide to use books that encourage the use of calculators before Algebra I. Talk to teachers who use my books and you will be amazed at what they will tell you about the success that my philosophy and my books have made possible.

John Saxon Order Samples From: Saxon Publishers, Inc. Thompson's 1002 Lincoln Green P.O. Box 53158 Norman, OK 73072 Oklahoma City, OK 73152

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Page 10: FOCUS ISSUE: CALCULATORS || Front Matter

Advertisement

SAY NO TO CALCULATORS IN ELEMENTARY SCHOOLS

I disagree with the decision of the NCTM to encour- age the use of calculators in elementary schools because I believe the use of calculators at the elementary school level will cause great damage to many children and will provide only marginal benefits to a few. I have dis- cussed my views on calculators with hundreds of elementary school teachers and almost all of them agree with me.

We have only a few short years to prepare students for algebra, geometry, and trigonometry. The fifth, sixth, seventh, and eighth grades are crucial grades. If we use these grades properly we can give the students a solid foundation in arithmetic skills that will permit success in high school mathematics. If students do not get a solid foundation during these four grades, they are programed for failure. I believe that there is a time for everything and if some things are not done at the proper time, then they never will be done. I believe that there is a time for students to assimilate, internalize and auto- mate the use of the fundamental concepts and skills of arithmetic and this time is in the upper elementary grades. And then there is a time in high school mathematics for reaping the benefits of having taught fundamentals when the time was right for teaching fundamentals. If we permit ourselves to be distracted from the teaching of fundamentals by the pursuit of lesser and possibly chimerical goals, we will be doing a disservice to the students with whose mathematics edu- cation we have been entrusted.

I have written a mathematics series that permits the use of calculators in Àlgebra I. These books rely heavi- ly on calculators for computational purposes in Algebra II, and in the Geometry-Trigonometry- Algebra III book. Many schools that have used this series report that they have doubled fourth-year mathematics enroll- ment, have had huge gains in chemistry and physics enrollment, and have increased college board scores over 20 percent. At Ponderosa High School in Parker, Colorado, the 108 students who took the ACT in the spring of 1986 had an average mathematics score of 25 . 2 and no student had a score below 20. Next year we will have college board scores from over 1 ,000 students in 10 major school systems and we predict that these students will also have scores that are unbelievably high.

In the 3-book Saxon high school mathematics series, we practice estimation using scientific notation for almost two years before problems with difficult num- bers are attempted on calculators. Since the Saxon students have internalized the fundamental concepts and have automated the fundamental skills, they are competent estimators and can use the scientific calcula- tor intelligently and can tell if the answers to problems are reasonable answers.

I contend that our goal is keeping students in mathematics and having them proficient in all possible areas by the time they finish high school. Our goal is a long-term goal and there is nothing, absolutely nothing, to be gained by trying to teach advanced concepts and advanced thought processes too early. I believe that introducing calculators in elementary schools will con- vince many students that the calculator is a magic box that can be used as a substitute for understanding, and these students will resist the arduous mental effort that is required to develop a feel for numbers and the ability to estimate. If the presence of calculators will cause this reaction in only 5 to 10 percent of our elementary school students, then the loss to these students will far outweigh the temporary gains that a few other students might experience.

I am writing and publishing a full K-8 series that concentrates on insuring that all of the students master the fundamental concepts and skills through the repeti- tive completion of carefully designed problems. The numerical problems provide the long term practice that will instill a sense of confidence in basic skills and will carefully and patiently work at automating the thought processes necessary to be successful problem solvers. The book for average 7th and bright 6th graders is called Math 76. The next book is called Algebra Vi and prepares students totally for Algebra I which is also in print. I will give you 15 of any of these books for a pilot if you buy at least 16 more. I can afford the pilot but since there are over 50,000 schools K-8, 1 request that you order your samples from Thompson's. I will be happy to refund if you return the books within a reason- able time.

John Saxon Order Samples From: Saxon Publishers, Inc. Thompson's 1002 Lincoln Green P.O. Box 53158 Norman, OK 73072 Oklahoma City, OK 73152

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Page 11: FOCUS ISSUE: CALCULATORS || Front Matter

Presenting a math show kids can count on for fun.

^^^&. #L l 1 ^^^^m fvTv * / ̂ ^"- .-» jV . y •* • ^^^^^^^^^^^f^W M - ■ B^^v

Presenting "Square One TV!' rmvr^ "^ 1 ^H^ Its new. Its different. It's a series jßSd^^, Í ■ <4 ^ J ™"T*^ for children 8 to 12 that makes ÄjT ^ M^' Sim *^L : J « ̂«^ -

math fun and interesting. ffl^x^^^L äJEm&jßi^f* ^¿¿WmlH^ìÈ ̂ Ü^HMÍt ^«^ -

Television Workshop, the creators ̂BÊ^^^ÈÊ^F*v *' ^f ^¿L ^^^^''^^^^^B

of "Sesame Street r And it makes ^^{^^1 '^i¿^- ^^f ^Eu^^ novel use of entertainment forms

Square One TV. It s another f^ SW ]■■ ^S ï -^i ^^^'rffe^HÏ example of our commitment to 1 (jV S| ■ fl^L íV^V-^JIÉi^íPÍ

January 26 and will run every

Funding for"SquareOneTV" provided |m^B^K ^^^^^^fc^H Z*^« ^ by IBM as corporate underwriter, the U.S. WÜH STUFF ír ^1 ^BI^^^^^B ■ _1¿*'- ^P ' t^É^^M^^.^.^Ìfll Department of Education, The National LJHHÉ^^ 1^^^ 1 S

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Public BroadcastingiTheAndreiv W.Mellon ^^^^^f^^'^i^Bl J I JUBBBl^^^K A ̂^^F% ~ ff**'** Foundation, and the Carnegie Corporation w^^^r ^»4 jSÍ^^ ~ ÊË li ^S«S^^^^^^| ^^^^^3 ~^A of New York. ^^^i^^^Sm

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Page 12: FOCUS ISSUE: CALCULATORS || Front Matter

8-11 APRIL

65TH ANNUAL MEETING

NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

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Page 13: FOCUS ISSUE: CALCULATORS || Front Matter

ö To help you teach lôuâl V mathematics better ... W

Books on COMPUTERS and CALCULATORS Written and produced by mathematics education personnel-

Computers In Mathematics HM Math Study Skills Program, Computing and Mathomatlcs: The Education (1984 Yearbook). by Catherine D. Tobin. Features a program for Impact on Secondary School Discusses computing from the standpoints of its reinforcing study skills that can be integrated Curricula, challenge, impact, and perspective and as a with the regular prealgebra curriculum. Skill edited by James Fey. Reports on a conference diagnostic tool. Also explains how programming areas include problem solving, study habits, esti- sponsored by the NSF where a group of well- can be used as a means of teaching mathemat- mating, calculators, and test taking. A joint known mathematics educators made a concen- ics. Annotated bibliography. 244 pp.; #328; NCTM/NASSP publication. Teacher's Guide, 60 trated effort to rethink traditional curricula in light $16.tK). pp.; #318; $4.40. Student Text, 95 pp.; #319; of electronic technology. Deals with the effect of ActivitUft from ^^ Mia mamemauc» ii*th*mütio.* $5-60- computing technology on school mathematics, Teacher

^^ mamemauc» the prospeCts for change, and its specific impact

»ä^ sässb^ 8olvlng ^^"^TMS^r^^ and ÄÄ SjSiSSi S^'SSSSSf^ Calculators: Reading, from the grades 7 through 12. 140 pp., #55, $8.50. ^ to used wjth elementary grades Shv^mci C B?rt F^uses on classroom Guidelines for

Instructional Evaluating through high school. Dedicated to the proposition ^^^

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on classroom Guidelines Computerized

for Instructional Evaluating

that calculators free children to think out problem SgSoo r¿y4' *lum Materials (2d ed.)v solutions. 40 pp.; #112; $4.00. r¿y4' *lum

by William P. Heck, Jerry Johnson, Robert J. Developing Computational Skills Kansky, and Dick Dennis. An up-to-date revision "Calculators,9,1 February 1987 (1978 Yearbook). of the popular guidelines that have given thou- Arithmetic Teacher. Digs deeply into the subject of computation, giv- sands of teachers and administrators concise, Ideas from cover to cover on teaching mathemat- ing a fresh view of teaching the basic facts, . practical help for slicing through the maze of ics with the help of calculators. Discusses how algorithms, and mental arithmetic, along with materials in the software jungle. Usefulness not the calculator is a problem-concept developer, ideas on teaching learning disabled children, confined to mathematics: valuable for evaluating gives activities for their use in various grade inspiring junior highs, and teaching skills with a software in any discipline. Contains reproducible levels, and presents the current thinking of calculator. 245 pp.; #98; $16.00 evaluation instruments and outlines for using mathematics education personnel concerning the them. 32 pp.; #122; $3.00. classroom use of calculators. #368; $4.00

National Council of Teachers of Mathomatlcs See the NCTM Materials Order Form in the back of this issue. 1906 Association Drive, Reston, VA 22091

Professional Development for Teachers of Mathematics:

A HANDBOOK Edited by Ross Taylor

Excellent guide for mathematics teachers, super- visors, administrators, and college mathematics educators in charge of designing and imple- menting professional development programs for teachers of mathematics. Co-published with the National Council of Supervisors of Mathe- matics.

Because mathematics and education are disci- plines that grow and change, teachers cannot depend on what they learned as undergradu- ates to carry them through their entire careers. They require ongoing professional development to maintain and enhance their teaching skills and knowledge.

This handbook will help you decide what kind of activity will be most beneficial to your teachers- peer-group meetings, workshops, seminars, observing demonstration classes, individual research and planning, and so on. You will find out how to organize, implement, and evaluate a program once it has been selected, as well as how to get funding and other support for your chosen professional development activity. 1986; 66 pp.; #352; $7.50.

I I National Council of d B Teachers of Mathematics Q EJ 1906 Association Drive ^JP? Reston, VA 22091

See the NCTM Materials Order Form in the back of this issue

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Page 14: FOCUS ISSUE: CALCULATORS || Front Matter

Our difference is mathematics

Something critical is missing in every math program except Houghton Mifflin Mathematics K-8. Word power. Cur- rent research has discovered that when you strengthen students' language and vocabulary skills, you stren^hen their ability to understand word problems. To verbalize during class exercises. To read directions. To score higher on standardized math tests.

Only Houghton Mifflin Mathematics a o has an intense focus on language and li ñ vocabulary. Instruction and support ' jl combine with superior content in every /ZJu&j^

chapter, at every level of our program. fflßjS* £ a And we provide every teacher with a ^K^^g^ ü#0 £ a

free Language and Vocabulary Activi- ̂ ^^^^ ¿jjtt ties Manual packed with ideas. ^¿fÛII I IK»' So if you're ready for a program ¿glff 1 4M^ 'ß^ with a difference, mail the cou- vÖn LI rrSfu M pon on the opposite page. You'll i-m eLT* jJ [ find out all the good news about ^■j Mg Houghton Mifflin Mathematics K-8. |P"i wWr

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Page 15: FOCUS ISSUE: CALCULATORS || Front Matter

Copyright © 1987 by Houghton Miff lin Company. All rights reserved.

*-**»«*? - - - LANGUAGE and VOCABULARY I Ä^Ä^rfS^

*-**»«*? - - / REVIEW |

" JÜ2-- WING ^ VTise the words to complete the sentence. Write the word on K

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^ M^^% tfUMß your paper. | K ' ^^^^^a^^^^^^P rytj^p^'P^ ^f tenths hundredths factors common factors round K

' ^^^^^^ ^^^^HH decimal number sentence ordinal numbers Br

' A 'tip'y4*298' .^^^^B a if ' | ^en VoU ^t 10 hundred ̂̂ ^^^^ ^

a L One tenth can be written as a 1 P

' 1 retnernj^ ^t nd. **r^^^^Ft' M 2. Five ? (or 0.5) is greater than five 1 (or H

' lequa^tn 7^ ^^V

VH 0.05).

M ' 1 jS^ ^^^^ 3. You can ? 5.81 up to 6 when you estimate. ■§

' ' /S 8 es MuVt^V ^ I Snl^1 4- ̂ 2' 4' 5' 10» and 20 are - ^- of 20' ■ B ' VlÖh^iP^ the 8 oo

es 6as «^daàdt^ hundreds^1 5. Numbers like first, second, third, and fourth are B

' XAbV 4 ^enatne oo

39 tenS 3. called ? . K

' /^ ' 3tens2ones. 29s 6. 18 + 3 = 21 iscalleda^_. f

' ^^ -^^^^^^^^^^^ r^Ê^ t ^B ^^BIllBBBIBlBBBBI^tBBIlWlBljBBpBBBBBIBpP^

^.^^^^L^ *^~-^ ^^ : ■■' HowmanyofyouhmrthMrdttwword '«vw^«'b^or«to<tey7 t *^~-^

^^ çr FXt^^^ Make a list on the chalkboard of all the ways they have heard the I ' CL^J S63 word used. Ask the students to write two different problems that I ' o u' 86 - ^e need the use of the average to solve. For example: Tim weighs 67 ;; ' îAultVpW-

u' 5

J*3 pounds and Mary weighs 73 pounds. What is their average weight? f

■" -' j I I Please send me a full-color brochure about ^^^^^^^^^^^^^^^^ I

| Houghton Mifflin Mathematics K-8. ^^^^^^^^^^^^^^^^^t v I

I Name ~

Giade Level 1^^^^^^^^^^^^^^^^^^^^^^^^ ° 1 ^^ ■

I school ^^^Ê^^^^^^^^^^m ' ■ '" x

* School Address

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^ ^^

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'''V ^

. , ^^^^fl~ , '

I Program I now use ' « ' '- ^^^dLIL^L^L^L^BË^.: I Our school will adopt a new math program in 19 ^ « • «' ^g^j^^^^^^^^^HHH^ I I will be on the adoption committee. ^^^^ÊÊÊÊ^^^^^^K/f^^^ ■

¡

TiiE All-New ^^Ê^^^^^ ' ■

' Houghton Mifflin Mathematics K-8 ¡ i Mail coupon to: Houghton Mifflin, Dept. J, One Beacon St. , Boston, MA 02108 i

^4 Houghton Mifflin Atlanta, GA 30360 / Dallas, TX 75244 /Geneva, IL 60134 / LawrencevUle, NJ 08648 / Pialo Alto, CA 94303 /Toronto, ONT UR1B2/ Boston, MA 02108

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