journal for research in mathematics education

ISSN 0021-825 1

JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION VOLUME 23

NUMBER 1

JANUARY 1992 National Council of Teachers of Mathematics

The journal for R~search in Math~matics Education, an official journal of the National Council of Teachers of Mathematics. 1> devoted to the interests of teacher~ of mathematics and mMhematic• education at all levels--pre· .choolthrough adult. The JRME ~~a forum for dt&e1plined 1nqu1ry into the teaching and leammg of mathematics .. It encourages the ~ubmiSsion of a vancty of types of h1gh-quality mnnuscrip~>:

Reports of re,earch. including c:C\penments. case ,tudies, ,urveys, plulo..oplucal stud1e!>. and ht>!oncal stud1es • An1cles about research. tncludtng literature rev1ews and theoreticnl unnly>e> Brief repons of rc.carch • Cntiques of an1des nnd bool.> • Bnef com~ntanes on ISSUes penauung to ~arch The Index for each volume appetln

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the November ~r Rrs~arr/r in /11atl,moucs £dut·anon (ISSN 0021·8251) "pubhshc:d five ume' a year. l\o•ember. JanuQry, March. May. and July, at 1906 Associa· lion Drive, Reston. VA 220Cil, by the National Cou nc1l of Teachen< of M:uhcmatics. An 1ndividual NCTM membership lirolh a JRM£ 'ub>enption costs S45 a year. Dues include S20 fur the JRME Criber:, and hfe and reured member:. as well a> tnformation about the other IWO official JOUrnals. Artthmnu r~aclt~r and MutiiMIOIIeholarly p~pc:r>. and to libranan> "'ho wish 10 pi~~• a limued number of eopoc5 of ankles on re>crve. Permission must be sought for commercial use of content from the JOurnal "hen the mu1erial is quoted in udvenmng. anicles 31\' 111dudcd in book~ or n:ading:.. or ch:trges for copoe' are mode or profi1 is mtc:ndcd. The use of matenal from the JRM E other than Ill those of MathematiCS. gr.~nted

EDITORIAL BOARD Editor THOMAS P. CARPENTER, Univen.ity of Wiscon~~nMadison Editor-elect FRANK K. LESTER . JR.. Indiana University nt Bloomingto Associate Editors MARGARET R. MEYER. University of WisconsinMadison WALTER G. SECADA. Univer.~tyofWisconsin-Madison Review Editor DOUGLAS B. McLEOD, San Diego Stme University Editorial Panel CATHERINE BROWN, Virginia Polytcchmc Institute and State Unive /991 IAEP Assessmem· Objectil•ts for Mathematics. Scirnce, and Gl'ograplry. Cemer for the Assessment of Educational Progress. Princeton. NJ: Educational Testing Service, 1991 .63 pp. $9.00. The first International Assessment of Educational Progress was conducted in 1988 and involved 6 countries: the second was held in 1991 , and 20 countries panicipated. The~ assessments are based mainly on the National Assessment of Educational Progress, aho conducted by ETS. All countries included IJ-year-olds in the mathematics assessment; most also gathered data on 9-year-olds. Watch for your "repon card'' in the newspapers. EDTALK: What We Know abo111 Mathematics Teaching and Learning N. Kober. Ponland. OR: NonhweM Regional Educational Laboratory, 1991. iv + 71 pp. $11.00. Brief summaries of research suggest ways 10 improve mathematics teaching and learning in both the classroom and the home. Eachof23topics(e.g.,calculal0rs, cooperative learning. homework) is covered in terms suitable for the general reader. The comments are generally very u~eful. Toward tire Practice ofTireory-Based lnstrtlction: C11rre111 Cogmti11e Tlreortes and Therr Ed11Cotional Promise. A. McKeough & J. L. Lupnn (Eds.). Hillsdale. NJ: Erlbaum, 1991. xvii + 189 pp. $32.50. Three theoretical fmmeworks are emphasized in this volume: culruml tran\mission in the sense of Vygotsky. strategic learning from an information-processing per pective. and developmental p~ychology. The six contributors (0. Olson. J. Wensch, A. Palincsar. B. Wong, R. Sternberg, and R. Case) discuss cognition and learning in terms of their own theoretical perspectives, and the editors and comributors make recommendations on how the different theories might inOuenee educational practice. Toward a Logic ofMeamngs. J. Piaget & R. Garcia. (P.M. Davidson & J. Ea~ley. Eels.) Hillsdale, NJ: Erlbaum. 1991. xiii + 178 pp. $32.50. This volume. Piaget's last. repons investigations carried out by Piuger and his collaborators in 197879. It focuses on the root~ of logic. going back 10 implications between ~cnsorimotor actions. The mathematical topics under discussion include tessellations and !>ymmetries. a~ well aJ. counting and cl:t!>sification. As usual. the mterviews with the children are very enlightening. In his pan of the book. Garcia highlights Piaget's contributions 10 the logic of meanings and provides an interpretation of the discoveries reponed in the book. Fractions in Realistic Mathematics £d11cation: A Paradigm ofDl'l'rlopmemal Restarclr L. Streenand. Norwell, MA: Kluwer. 1991. ix + 355 pp. $99.00. A prototype of a new course of instn1c1ion on fractions is presented in thiS volume. 11 describes the development and evaluation of the course. along with a theory of teaching and learning fractions and a more general theory of realistic mathematics education. The work empha~ites the role of student construction~ and intemctions in the analysis of problems involving frac110n5 and proportional reasoning. 8l'ing N11merate: Wlrat Counts? S. Willis (Ed.). Hawthorn, Victoria. Australia: Australian Council for Educational Research. 1990. (Available from ASHE, Box 31576. Richmond. VA 23294.) viii+ 199 pp. A$29.95. Conceptualiting numeracy means reconceptualizing mathematics, and th:u b the task taken up by the contributors to this volume. 111e authors discuss number sense. problem solving. assessment, and other topics from an Australian perspective. The book. which will be of panicular Interest to policy makers and researcher;,. includes an annotated bibliography for reform effons in mathematics educauon around the world. Visualization in Teaching and Learning Mathematics. W. Zimmermann & S. Cunningham (Eds.). Washington. DC: Mathematical A~sociation of America, 1991. viii+ 224 pp. S20.00. This volume provides an overview of research, analysis, practical experience, and informed opinion about visualit.ation and its role in teaching and leaming. The focus is on undergraduate mathematics. including calculus, geometry. differential equations. and other topics. In the spirit of the times. the contributors emphasize mathematics as the science of panems and the development of imuuion rather than logical arguments.

Telegraphic Reviews

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Needed: An Agendafor Equity in Mathematics Education. W. G. Secada & M. R. Meyer (Eds.). Special Issue of Peabody Journal of Education. Vol. 66. No.2. July 1991. (Avai lable from George Peabody College, 113 Payne Hall. P. 0 . Box 41, Nashville, TN 37203.) 160 pp. $ 14.00. The purpose of this special issue is to help bring issues of equity to the fore of the current mathematics education refonn movement. The authors are concerned that equity has frequently been ignored, transfonned, or submerged in the rapidly rising tide of refonn documentS. Major contributors include G. Stanic. P. Campbell. N. Kreinberg. the editors. and others.

The California Smdy of Elememary Mathematics. Special Issue of Educational E1·aluation and Policy Analysis. Vol. 12. No.3. Fa111990. (Available from AERA. 1230 17th Street. NW. Washington, DC 20036.) 126 pp. $8.00. This special issue investigates the relationship between instructional policy and c lassroom practice in mathematics. The 1985 California Mathematics Framework representS the policy. and case studies of five elementary teachers provide data on classroom practice. The case studies, conducted by researchers from Michigan State University. provide insightS into factors that help or hinder current refonn effortS. Major contributors include D. Ball, D. Cohen. and P. Peter..on. an1ong others.

The Mathematics Educator. N. Oppong (Ed.). Athens. GA: Department of Mathematics Education. University of Georgia. 1991. This new journal, an official publication of the Mathematics Education Student Association of the University of Georgia, is a delightful addition to the literaiUre in our field. The first issue (Summer 1991) includes anicles related to both research and practice. and even contains problems "From Dr. Wilson's Notebook." The journal is available without charge, but donations are requested.

Statement of ownership, management and circulation (Required by 39 U.S.C. 3685). lA. Title of publication. Journal for Research in Mathematics Education. lB. Publicatoon No .. 0021-8521 . 2. Dmc of filing. II September 1991. 3. Frequency of i>s uc. five times per year: January. March, May, July, November. A. No. of issues published annually. five. B. Annual subscription price, S30. 4. Location of knuwu office of publication, 1906 Association Drive, Reston. VA 22091-1593: Fairfax County. 5. Locatoon oftbe headquancrs or general busine each issue during preceding 12 months. A. Total no. copies printed, 8.920. B 1. Paid circulacion. sales through dealers and carriers. weel vendors and counter >ales. none. 82. Paid circulauon. mail subscriptions, 7,780. C. Total paid circulauon. 7,780. D. Free distribution by mail. carrier or other means, samples. complimentary. Jnd other free copies, 171. E. Total distribution. 7,951. Fl. Copies not dostributcd, office use. left over, unaccounted, spoiled after pnnu.ng. 969. F2. Copie~ not dostnbuled, returns from new> agents, none. G . Total. 8,920. Actual no. copies of songle issue published neares11o lihng date. A. Total no. copoes printed, 10.000. B I. Patd ctrculation. sales through dealers and carriers. ~1rce1 vendors and counter sale,, none. 82. Paid circulallon. mao I subscnpllon>. 8.149. C. Total paid circulation. 8.149. D. Free distributoon by matl, carrier or other mean~. •amples, comph· menmry, and other free copies, 171 . E. Total distribution. 8,320. Fl. Copies not distributed, office use, left over. unnccoumed. spoiled after printing. 1,680. F2. Copies not distrihuteo, returns from news agcncs, none. G. Total. 10.000. ll . I cenify that the statements made by me above nrc correct and complete. J.tmc• D. Gates. Business Manager.

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ANNOUNCEMENTS _ _ _ __ Call for Research Reporting Proposals Program space at the NCTM 71 st Annual Meeting in Seattle, 31 March- 3 April 1993, has been reserved for those interested in research and its implications for classroom teachers and curricul um builders. Proposals are being solicited for Research Reporting presentations. All proposals submitted are reviewed by the Research Advisory Committee of NCTM. The deadline for submiuing proposals is 1

May 1992. Anyone wishing to be considered for a place at one of the Research Reponing sessions should submit four copies of a typewritten, double-spaced abstract or proposal not exceeding 1000 words. The following arc to be included in the mailing: I. The name and professional affiliation of the author. lf more than one person is involved, complete information about the anticipated responsibility of each contributor must be given. The principal presenter must be identified. 2. The preferred mailing address of each contributor. 3. The title of the paper or presentation. 4. An abstract of the paper or an outline of the presentation, clearly describing the purpose and significance of the research; the conceptual framework; and the procedures, design, analysis, findings, and conclusions. 5. Two self-addressed envelopes. One will be used to acknowledge the receipt of the proposal; the other, to notify the sender of the screening committee's decision. All submissions should be sent to Dr. Glendon Blume, The Pennsylvania State University, 145 Chambers Building, University Park, PA 16802. They must be received by I May 1992.

Research Presession in Nashville The NCTM Research Advisory Committee and the AERA Special Interest Group on Research in Mathematics Education are cosponsoring a research presession to the NCTM 70th Annual Meeting in Nashville, Tennessee. The presession will begin at 7:00p.m., Monday, 30 March, and end at 5:30p.m. on Tuesday, 31 March 1992. The opening presentation will be a discussion of JRME. For more information write to Joan Ferrini-Mundy, Department of Mathematics, College of Engineering and Physical Science, Kingsbury Hall, Durham, NH 03824, call (603) 862-2684 or send a request via bitnet [email protected].

New From Our Other Journals Readers of the Journal for Research in Mathematics Education might be interested in the following articles in this month's issues of the other official NCTM journals. In the Mathematics Teacher: • "Implementing the Professional Standards for Teaching Mathematics: Improving Teaching, Not Standardizing It," Deborah Loewen berg Ball and Thomas L. Schroeder. And in the Arithmetic Teacher: • "Promoting Local Change: Models for Implementing NCTM's Curriculum and Evaluation Standards," Mary M. Hatfield and Jack Price.

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MICHIGAN TECHNOLOGICAL UNIVERSITY

Mathematics Education The Mathematical Sciences Department at Michigan Technological University is seeking applications for a tenure-track position beginning September 1992. Applicants should have a Ph.D. or Ed.D. in mathematics education with a strong background in mathematics. The successful candidate is expected to have a sufficient background in mathematics to teach such courses as geometry, calculus, and other selected undergraduate math courses; and a sufficient background in education to teach such courses as math methods, computers in education, and measurement and evaluation. Candidates should have teaching experience at the secondary level (7-12). A commitment to quality teaching and to the development of an active research program in mathematics education is necessary. Send vitae, transcript, and three letters of recommendation to A. H. Baartmans, Head, Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, Ml 49931 -1295. Applications will be accepted until February 3, 1992. MTU is an equal opportunity educational institution/ equal opportunity employer.

Foundation Chair of Mathematics Education Applintoons are invited for appointment to tb~ Foundation Cbair of Mathem21ics Educnion within th~ Institute of Education. The University seeks a leader in the lield of mathematics education, with an outsWldlng research rerord and wide recognition In the field, strong qualifications In mathematics, and an exctllent record as a teacher The appointee will build up a centre for tb- wishing to de\-elop upeni~ or undenake funher ~reb in mathematics education The chair will be located within the School of Science and Mathematics Education in the Institute of Education. The new professor wUJ strengthen CO·Oper:ulve links already es12blished with the Department of Mathematics in the Faculty of Selene~. This is a continuing chair, with an initial sabry of AU0$72,000 rising to AU0$76,000 in July 1992. Further mformation about the position, including de12ils of application procedure, conditions for outside work, superannuation, travel and removal expenses, housing assist2nce and conditions of appointment, is available from the Registrar. All correspondence (marked "PERSONAL AN D CONFIDENTIAL") should be addressed to the Registrar, The University of Melbourne, ParkvUJe, Victoria. 3052, Australia. Telephon~ ~nquiries· (613) 344 7527. Facslmi!t: (613) 344 6897. Applications d-on 31 January, 1992. The Council reserves the right to make no appointment or to lill the position by invit2tion at any s12ge. The University of Melbourne is an equal opponunity employer and bas Implemented a smoke-free workplace policy

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THE UNIVERSI1Y ~ OF MELBOURNE arm51376

THE ADDENDA SERIES "Teacher-friendly" books to translate the STANDARDS into classroom practice lethe first to use the Addenda books. You will be well-equipped with ield-tested teaching examples linked to the CURRICULUM AND NALUATION STANDARDS FOR SCHOOL MATHEMATICS. KINDERGARTEN BOOK (24 pp., ISBN 0-87353-31 0-0, #453, $9.50*); the FIRST-GRADE BOOK (32 pp., ISBN 0-87353-311-9, #454, $9.50*); and the THIRD-GRADE BOOK (32 pp., ISBN 0-87353-313-5, #456, $11.00*). These grade-specific books focus on patterns, number sense and operations, making sense of data, and geometry and spatial sense. The activities have been given a new investigative flavor. DEALING WITH OATA AND CHANCE (Grades 5-8). Considers people's natural understanding and daily use of data and chance and then addresses how to build on these natural abilities. 71 pp., ISBN 0-87353-321-6, #463, $15.00*. DEVELOPING NUMBER SENSE IN THE MIDDLE GRADES (Grades 5-8). Shows how to encourage the meaningful learning of mathematics and lead students to relate new information to previously acquired knowledge. 56 pp., ISBN 0-87353-322-4, #464, $10.50*. PATTERNS AND FUNCTIONS (Grades 5-8). Provides examples for using patterns to deepen understandings of concepts in exponents, number theory, rational numbers, measurement, and other topics. 72 pp., ISBN 0-87353-324-0, #461, $13.00*. CONNECTING MATHEMATICS (Grades 9-12). Focuses on current algebra and geometry programs. The book also reflects the multidimensional aspects of student assessment and the fact that assessment is integral to instruction. 69 pp., ISBN 0-87353-327-5, #466, $9.50*. A CORE CURRICULUM: MAKING MATHEMATICS COUNT FOR EVERYONE (Grades 9-12). Offers several models for organizing mathematics content and gives suggestions for assessment techniques that focus on problem solving, reasoning, and disposition toward mathematics. 152 pp., ISBN 0-87353-328-3, #469, price to be announced. GEOMETRY FROM MULTIPLE PERSPECTIVES (Grades 9-12). Includes classroom-ready activity sheets and helpful instructional suggestions as well as a discussion of the growing use of technology. 80 pp., ISBN 0-87353-330-5, #468, $14.00*.

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National Council of Teachers of Mathematics 1906 Association Drive, Reston, VA 22091

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Mathematics Education Position The University at Buffalo The State University of New York UB is seeking an Associate/Full Professor to assume leadership of a well-established program in Mathematics Education within the Graduate School of Education. The successful candidate will be expected to continue to conduct research and publish in secondary school and college mathematics education; teach courses and graduate seminars related to mathematics instruction; supervise the program and research activities of master's and doctoral students; and pursue funding to support research activities. Mathematics teaching experience at the school o r college level is expected. Consideration of applications will begin January 20, 1992 and will continue until the position is filled. Contact Leroy G. Callahan, Professor & Associate Dean 367 Baldy Hall University at Buffalo (716) 636-2491 Buffalo, New York 14260

State University of New York at Buffalo is an AAEO employer.

NORTHERN ILLINOIS UNIVERSITY Department of Mathematical Sciences 1. Anticipated senior (full or associate) professorship in mathematics education. Ph.D. or equivalent in mathematics education, a background in mathematics at the master's level, an outstanding research and a strong teaching record required. Application (vita) plus three letters of reference, and a description of research program should be sent to: Senior Math Ed Position, c/o Professor William D. Blair, Chair, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115 by January 15, 1992. EO/AEE. 2. Anticipated assistant professorships in mathematics education. Preference will be given to those with interests in secondary school and/ or collegiate mathematics. Ph.D. or equivalent in mathematics education, mathematics at the master's level, and strong potential in research and teaching required. Application (vita) plus three letters of reference and a description of research program should be sent to: Junior Math Ed Position, c/o Professor William D. Blair, Chair, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115 by February 1, 1992. EO/AEE.

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UNIVERSITY OF TEXAS AT SAN ANTONIO The Division of Mathematics, Computer Science, and Statistics is accepting applications for tenure-track position at the assistant professor level in mathematics education. Applicants must have at least 30 hours of graduate mathematics and a doctoral degree in mathematics education or a related area by August 1992. Preference will be given to those candidates with a commitment to research and whose research complements the interests of the current faculty. Responsibilities include teaching, research, and program development. Applicants should submit a resume and arrange to have three letters of recommendation sent to:

OR. SHAIR AHMAD Division of Mathematics, Computer Science, and Statistics The University of Texas at San Antonio San Antonio, TX 78249-0601. The closing date for this position is January 31 , 1992. UTSA is an Equal Opportunity/Affirmative Action Employer. Women and minorities are encouraged to apply.

TOWSON STATE UNIVERSITY Tenure-track assistant or associate professor in mathematics education available fall '92, contingent on state funding. Teach 12 hours/semester of undergraduate courses. A doctorate in mathematics education and a commitment to teaching and research are required. Preference will be given to applicants with three years' teaching/research experience in elementary and /or early childhood education. Minorities are encouraged to apply. Salary and rank are commensurate with experience and background. Send resume, three letters of recommendation, and all undergraduate and graduate transcripts by February 14, 1992, to Robert Hanson, Chairperson, Search Committee, Mathematics Department, Towson State University, Baltimore, MD 21204. An Equal Opportunity, Affirmative Action Employer.

PURDUE UNIVERSITY CALUMET The Department of Mathematics, Computer Science and Statistics announces a tenure-track position in MATHEMATICS EDUCATION for August, 1992. Duties and responsibilities include teaching a range of mathematics courses, content and methods courses for prospective K-12 teachers, supervising field experiences and working collaboratively with public schools. Active involvement in research is expected. A doctorate in Mathematics, or in Mathematics Education with at least a masters degree in Mathematics, is required. Candidates should have a strong commitment to teacher education and to quality teaching at both the undergraduate and graduate levels. Submit a letter of application, curriculum vitae, both graduate and undergraduate transcripts. Also arrange for three (3) letters of recommendation -- at least one addressing your research potential and one addressing your teaching ability. Send all matetjals to: Professor J. Paul McLaughlin, MCSS Department, Purdue University Calumet, Hammond, IN 46323. Review of applications will begin February 1, 1992 and continue until the position is filled. Minorities and women are encouraged to apply. Purdue University is an Equal Opportunity/Affirmative Action employer.

How to Use the Spreadsheet as a Tool in the Secondary School Mathematics Classroom By William J. Masalski This publication (includes two Apple lie diskettes) illustrates how the spreadsheet can be used in the secondary school mathematics classroom. It focuses on the advantages of using a spreadsheet, such as the enhancement of the user's insight into the development and use of algorithms. Students are freed from laborious manipulations of numbers, allowing them to concentrate on the mathematical problem itself. 1990,80 pp., ISBN 087353-303-8, #427, $16.50. fim3l

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VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY MATHEMATICS EDUCATION Tenure-track position, joint appointment, Curriculum and Instruction and Math· ematics, beginning Fall 1992. Assistant Professor level, however, experienced candidates may be consider ed for higher rank . African-American and women candidates encouraged to apply. Requiremen ts: interest and expertise in eiE'rnentary edu-:ation, teaching experience, strong m athematics background, and doctorate. Re • !W of applications will begin January 15, 1992 and continue until position is filled. Please send letter of application, vita and three letters of reference to: Dr. Harold Mick, Mathematics Department, 460 McBryde Hall, Virgini a TE'ch, Blacksburg, VA 24061-0123. Equal Opportunity/Affirmative Action Employer .

Illinois State University Mathematics Education The Mathematics Department seeks applications for tenure track positions at the assistant or associate professor rank for August 1992. Applicants should have a Ph.D. or Ed.D. by August 1992 in Mathematics Education or other comparable degree; the ability to teach a wide range of mathematics education courses including content and methods courses; an active research program; a commitment to teacher education and quality teaching at both the undergraduate and graduate levels; and some K-12 teaching experience. To apply send vita, three letters of recommendation, and official transcripts by February 1 to: Dr. Jane 0. Swafford, Dept. of Mathematics, Illinois State University, Normal, IL 61761. AA/EEO.

Mathematics, Assistant/Associate, tenure-track position beginning fall1992. Teach introductory and advanced undergraduate courses in mathematics (12 credits per semester), serve on committees, review and plan curriculum, advise students. Qualifications: Doctorate .n mathematics or related field, full-time college teaching experience; record of scholarly activity; excellent oral communication skills and strong commitment to teaching required; people with experience in mathematics education encouraged to apply. Rank and salary dependent upon qualifications; minimum for assistant, $28,200; associate, $33,450. Send letter of application, resume, and three letters of recommendation documenting teaching excellence to Gaynelle Pratt, Office of Human Resource Management, Keene State College, Keene, NH 03431. Non-US citizens include current visa status. Review of applications begins January 20, 1992. Keene State College will be represented at the January 1992 AMS/MAA meeting in Baltimore. AA/EOE.

DISCR MATHEMATICS

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THE CURRICULUM, K-1 Z THE 1991 YEARBOOK Edited by Margaret 1. Kenney , BOOK YOU HAVE TO HAVE! Learn why discrete mathematics is nportant, what it comprises at various grade levels, and where it belongs 1 the curriculum. There is something in this yearbook for everyone. ~ead 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, algoritluns, and so on; • teaching units and activities designed specifically for secondary students; • and other suggestions for making mathematics come alive for your students.

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1991,256 pp., N450, ISBN 0-87353-305-4

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IN THIS ISSUE:

ARTICLES

A Constructivist Alternative to the Representational View of Mind in Mathematics Education

Paul Cobb, Erna Yackel. and Terry Wood Bilingualism and Mathematics Learning: Another Perspective Philip C. Clarkson and Peter Galhraith Computational Estimation Strategies of Professional Mathematicians Ann Dowker Secondary School Calculus: Preparation or Pitfall in the Study of College Calculus Joan Ferrini-Mundy and Marie Gaudarcl

BRIEF REPORT

InstructiOn Supporting Children\ Counting On for A?dition and Counting Up for Subtraction Karen C. Fuson and Adrienne M. Fuson

REV IE\\

Two Generations of Feminist Thinking-A revie~ of Gender and Mathematics: An International Perspecti\e, edited by Leone Burton Laurie E. Hart