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Analyze by Eleanor Villalpando; Synthesize by Eleanor Villalpando Review by: Tommie A. West The Arithmetic Teacher, Vol. 28, No. 1 (September 1980), p. 55 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41189352 . Accessed: 12/06/2014 19:13 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 91.229.248.139 on Thu, 12 Jun 2014 19:13:44 PM All use subject to JSTOR Terms and Conditions

Analyzeby Eleanor Villalpando;Synthesizeby Eleanor Villalpando

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Page 1: Analyzeby Eleanor Villalpando;Synthesizeby Eleanor Villalpando

Analyze by Eleanor Villalpando; Synthesize by Eleanor VillalpandoReview by: Tommie A. WestThe Arithmetic Teacher, Vol. 28, No. 1 (September 1980), p. 55Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41189352 .

Accessed: 12/06/2014 19:13

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 91.229.248.139 on Thu, 12 Jun 2014 19:13:44 PMAll use subject to JSTOR Terms and Conditions

Page 2: Analyzeby Eleanor Villalpando;Synthesizeby Eleanor Villalpando

RaviGGDing and '7iaoDing

New Books for Pupils Edited by Tommie A. West Montgomery County Public Schools Rockville, Maryland

Prices on books and materials are included with reviews for general information only. Prices change and actual prices may vary from those listed. Please check with the individual publishers and producers.

Analyze. Eleanor Villalpando. 1979, $6.95. Synthesize. Eleanor Villalpando. 1979, 64

pp., $6.95. Think Ink Publications, 3421 North 44th Street, Phoenix, AZ 85018.

Although Analyze is not a book of mathematics, this collection of reproducible exercises does present clever activities which call upon thinking skills characteristic of mathematical problem solving. The following exercises and activities are included in this group: a family tree exercise, tangram-like exercises, word puzzles, mazes, classification activities, detecting similarities and differences activities, logic puzzles, word plays, patterns, and codes.

The treatment is strictly nonstandard and quite creative. Gifted students of upper elemen- tary and beyond will find this collection enter- taining fare.

Synthesize is an extension of the kinds of exer- cises found in Analyze. There are more analo- gies, classification exercises, word plays, codes, and games. Many of the exercises in this collec- tion, however, are more open-ended and call upon the reader to create something, given the conditions. It is cleverly developed, and will pro- vide a few hours of fun for more able learners.

Brain PleaserS. Marie Masse. 1979, 56 pp., $3.50. Logic and Learning, 260 Ipswich Road, Topsfield, MA 01983.

This booklet joins the host of publications pres- enting problems in logical deduction. Its focus is on the younger student.

Fifty pages of logic problems are contained in the typescript copy; half of the hundred prob- lems are nonnumerical and half are numerical. The clues given are couched in both positive and negative terms - "It is . . ."; "It is not . . ." The problems, varying from quite simple (grades 2-3) to quite complex (high school), are usually framed in a rectangular box on the page. Some

of the problems are illustrated by primitive pen and ink sketches.

Although the format appears to be prepared for limited copy permission, there is no state- ment that such is granted. Whether the book's use is for teacher resource or student workbook is not clear.

Computer Alphabet Book. Elizabeth s. Wall. 1979, $8.95. Bayshore Books, P.O. Box 848, Nokomis, FL 33555.

Computer literacy is the catchword of the 1980s for mathematics curriculum makers. This picture dictionary is an effort at bringing some elemen- tary information about computers to young stu- dents. It is a lexicon of terms occasioned by the initial letters and presented in alphabetical or- der. The problem with this arrangement of terms, however, is that the terms are presented out of a logically sequenced presentation about computers. Whether this alphabetic hodge podge of terms will be comprehensible to the audience for whom it is appropriate, or appropriate for the audience for whom it will be comprehensible is a matter of question.

CryptarithmS. Josephine Andrée and Rich- ard Andrée. 1978, 186 pp., $3.60 (individual member price $2.88).

Instructor's Manual for Cryp- tarithms. Josephine Andrée and Richard Andrée. 1979, 82 pp., $2.50 (individual member price $2). Published by Mu Alpha Theta. Na- tional Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 22091.

Husband and wife team Richard and Josephine Andrée have coauthored a booklet that is certain to become a classic for aficionados of logic puz- zles. Cryptarithms are defined as "puzzles made by substituting letters for digits in a simple arith- metic problem. The puzzle is to discover the original digits."

The authors begin by describing the step-by- step solutions to very simple cryptarithms and proceed to more difficult ones. They describe the logic and trial-and-error solutions to the con- struction and use of the more systematic "possi- bilities table" for more complex puzzles. A most useful chapter tabulates properties of numbers and cites generalizations that are time-savers for the problem solver.

Chapter 5 serves up a smorgasbord of other puzzles and riddles, and develops what for many students could be their first introduction to in- direct proofs using the "let's suppose" strategy for cryparithm solution. In chapter 6, the authors apply the strategy of cryptarithm solution to the problems of everyday life, such as constructing schedules of activities and "goal" charts for deci- sion making. They also supply the solutions to all the puzzles posed in the preceding chapters.

Chapter 7 gives clues for creating cryptarithms with suggestions on how to tell if a puzzle solu- tion is unique. In chapter 8, as an extension of the basic cryptarithm format, the authors discuss hidden cryptarithms, cryptarithms in bases other than ten, and cryptarithms involving square roots. The final chapter discusses the application of computers to solving cryptarithms. A program

for solving the following cryptarithm is given:

one + two + three = seven

A bibliography of related materials is provided at the end of the book, together with a page of grids to use for possibility tables.

The authors' explanatory style is a study in elegance, as they seek to unfold the mysteries of the cryptarithm solution and construction. The book will be of interest to all who are interested in the challenge of logical thinking. It is a "must" for the teacher of the gifted.

In addition to the numerical solutions of the cryptarithms included in the text, the instructor's manual gives in detail the logical steps used in arriving at the solutions. It also identifies useful "chalkboard" cryptarithms for introducing the topic. Newspaper release forms for advertising this minicourse, bulletin board displays, repro- ducible possibility tables, and an extended bibli- ography are included in the manual, too.

Exploring Elementary Mathematics. Julian Weissglass. 1979, 279pp., $14.95. W. H. Freeman and Company, 660 Market Street, San Francisco, CA 94104.

This lab-text is designed as a text or text supple- ment for the college-level mathematics methods class for preservice teachers. It is a laboratory manual for the physical modeling of abstract mathematical concepts and procedures.

Attribute blocks are used to depict sets and set operations. In the chapter on numerations sys- tems, base blocks are used to depict numbers in positional systems. Addition and subtraction are developed through Cuisenaire rods and the Chi- nese abacus. The concept of multiplication is de- veloped through Cuisenaire rods and geoboards, while the multiplication algorithms include the lattice method and the partial products through Cuisenaire rods.

Division is restricted to the measurement con- cept, since the model is the Cuisenaire rod. The algorithm for division is rationalized by the base ten blocks, but the "array" model which the au- thor uses (see p. 69) will be lost on all but the most sophisticated. The two factors (missing and given) and the product are depicted as three-di- mensional base ten blocks. This is inconsistent with either the measurement or the partition in- terpretation of the algorithm.

Number theory (factorization) is depicted by using towers of Cuisenaire rods. These also are used to show odd and even numbers.

The chapter on topology presents the classic Königsburg bridge discussion. The modeling of fractions and operations on fractions is shown through arrays, strips, and Cuisenaire rods. Posi- tive and negative numbers are developed on a numberline and through a pedagogically pow- erful "counter" model. Multiplication is ratio- nalized through the "backward projector" de- vice.

Geometric concepts in chapter 12 are treated in the traditional nonmetric manner: shapes, lines, planes, and inside and outside. Lines, an- gles, and triangles are shown through Mira ma- terials with the usual construction tools used.

The chapter on area, developed by using the geoboard, is an excellent treatment of this topic,

September 1980 55

This content downloaded from 91.229.248.139 on Thu, 12 Jun 2014 19:13:44 PMAll use subject to JSTOR Terms and Conditions