Elementary School Mathematics: Teaching Developmentally by John A. Van de WalleReview by: Hilde HowdenThe Arithmetic Teacher, Vol. 39, No. 8 (APRIL 1992), pp. 58-59Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41195179 .

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REVIEWING AND VIEWING ■ COMPUTER MATERIALS ■ NEW BOOKS

FOR TEACHERS

■ ETCETERA

REVIEWING AND VIEWING

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Geometry Workshop, Grades 3-8. 1991 , Apple family, 128K; activity book, refer- ence guide, reference stickers, workshop, projects, Teacher Utilities disks (525"), and Workshop and Projects disk (3.5"), $89.95. Scott, Foresman & Co., 1900 E. Lake Ave., Glenview, IL 60025

Six Geometry Workshop activities per grade level, third through eighth grade are included in this package. The activity pages are repro- ducible black-line masters. The software al- lows students to draw, measure, and modify geometric shapes. Each activity is supple- mented by suggestions for extending the activ- ity and making cross-curricular connections. The program's uses are mainly demonstration, instructional support, and problem solving. The user must exhibit flexibility for appropri- ate thought development to occur.

From the student's point of view, the direc- tions are unclear regarding the use of the various keys for the activity, leaving the stu- dent the option of trial and error to determine the correct key to accomplish the task at hand.

The instructional focus is enhanced by the inclusion of professional articles and sugges- tions for introducing the program to students and parents, as well as guidelines for home improvement.

The program really needs a color monitor for maximum effectiveness. With the availability of graphing tools and figure-manipulation

Edited by Glenn D. Attinger Montana State University Bozeman,MT 59717 Jane F. Schielack Texas A &M University College Station, TX 77843

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. The comments reflect the reviewers' opinions and do not imply endorsement by the National Council of Teachers of Mathematics.

58

capability, the student can make decisions and experiment with the figures on an expanded basis. The most frustrating aspect of the soft- ware is the use of the measure menu. When the table is superimposed on the grid to supply the area, perimeter, or other information, it covers the figure. This problem could be solved sim- ply by placing the figure on the right side of the screen only. If the table could be removed or shifted at will, this feature might help the student deal with the problem of the lost pic- ture. I found the capabilities to be very useful and easy to follow. However, the keystrokes needed to accomplish one simple task are often a lot of work for a little bit of satisfaction.

In my view, if the parent or teacher has limited computer expertise, this program would be a good beginning to enhance discovery geometry - a wonderful way to make math- ematics come alive, especially in the topic of dimension. The activity in which the students create a hypercube in the planetary-planning lesson may be the most valuable aspect of the software. It is one topic that is truly enhanced by the use of the computer. - Bonita Gibson McMullen, Texas A & M University, College Station, TX 77843-4232.

Primary Geometry Workshop, Grades K-2. 1991, Apple family, 128K; activity book, reference guide, reference stick- ers, workshop, projects, Teacher Utilities disks (5.25"),andWorkshopandProjectsdisk(3.5"), $89.95. Scott, Foresman & Co., 1900 E. Lake Ave., Glenview, IL 60025.

This package contains six Primary Geometry Workshop activities per grade level, kinder- garten through second grade. The activities employ software tools that allow students in kindergarten through second grade to make, use, and measure geometric shapes. Each activity is supplemented by suggestions for extending the activity and making cross- curricular connections. The program's uses are mainly demonstration, instructional sup- port, and problem solving. The user must exhibit flexibility for appropriate thought de- velopment to occur.

From the student's point of view, the direc- tions do not specify the use of the various keys for the activity but simply illustrate what hap-

pens if the student uses the correct key. The instructional focus is enhanced by the

inclusion of professional articles and sugges- tions for introducing the program to students and parents, as well as guidelines for home involvement.

The program really needs a color monitor for maximum effectiveness. Having graphing tools and figure-manipulation capability avail- able permits the student to make decisions and experiment with the figures on a limited basis. The reinforcement of verbal instructions with graphic diagrams is very useful with younger students, since it also helps to teach terms. However, the keystrokes needed to accom- plish one simple task are often a lot of work for a little bit of satisfaction.

In my view, if the parent or teacher has limited computer expertise, this program is a good beginning to enhance discovery geom- etry and a wonderful way to make mathemat- ics come alive. - Bonita Gibson McMullen.

REVIEWING AND VIEWING

New Books

For Teachers Elementary School Mathematics: Teaching Developmentdlly, John A. Van de Walle. 1990, ix + 465 pp., $29.56 paper. ISBN 0-801 3 -0203 -X. Longman, 95 Church St., White Plains, NY 10601-1505.

Elementary School Mathematics: Teaching De- velopmentally is more than a textbook to be used in a mathematics-education course; it is a

Edited by Hilde Howden Mathematics Consultant Albuquerque, NM 87114 Rosamond Welchman-Tischler Brooklyn College of the City University of New York Brooklyn, NY 11210 David J. Whitin University of South Carolina Columbia, SC 29208

ARITHMETIC TEACHER

This content downloaded from 195.34.79.228 on Thu, 12 Jun 2014 21:36:34 PMAll use subject to JSTOR Terms and Conditions

comprehensive resource book. Its twenty-three chapters and three appendixes not only address the different areas of the elementary school curriculum but reflect on what it means to teach mathematics; describe the general philosophy behind the subtitle "Teaching Developmen- tally"; make recommendations for lesson plan- ning, classroom management, assessment, and homework; and supply black-line masters for the many activities described throughout.

Also discussed are the roles of the basal textbook, calculator, and computer in a devel- opmental program. The last chapter, "Math- ematics and Children with Special Needs," considers specific perceptual and cognitive- processing deficits and ways to adapt instruc- tion for students who have them, as well as mathematics instruction for gifted-and-talented students.

Its frequent references to, and quotes from, the NCTM' s curriculum standards and various position papers serve as a guide for imple- menting them and furnish teachers with vali- dation for doing so. The "For Discussion and Exploration" section at the close of each chap- ter, although intended primarily for the use of students using the volume as a textbook, fre- quently references articles from the Arithmetic Teacher, the Mathematics Teacher, other pro- fessional journals, and supplementary materi- als to raise questions about issues of concern to all mathematics educators.

Although in its preface the author states, "This book is not about mathematics but about children learning mathematics," it is packed with mathematical insights and connections that will delight mathematics educators at all levels. For example, using metric blocks or paper squares to continue the growing pattern in figure 1 produces a model of the golden rectangle in which the lengths of the sides of successive squares gives the Fibonacci se- quenceO, 1,2,3,5,8, 13,21, ...)and defines the chambered-nautilus spiral.

I highly recommend Elementary School Mathematics: Teaching Developmental for use in preservice and in-service instruction. In addition, I strongly recommend that it be in- cluded in the libraries of individual teachers and schools. Its 378 activities alone make it a wise purchase. - Hilde Howden.

Mathematics for Young Children: An Active Thinking Approach, Marion H Bird. 1991 ,xii + 183 pp. $15.95 paper. 1SBN- 0-415-05951-8. Routledge, Chapman & Hall, 29 W. 35th St., New York, NY WOOL

This book presents a detailed view and analy- sis of young students engaged in active math- ematical thinking and is highly recommended for anyone concerned with mathematics learn- ing in early childhood. In the first part, "Set- ting the Scene," the author raises questions

APRIL 1992

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about young students' mathematical thinking and describes her classroom work with four- and five-year-old English students. The sec- ond part contains six case studies - narrative descriptions of mathematical activities done by small groups of students, including copies of students' work and conversations among students and author. The third part analyzes the case studies in terms of mathematics used by students, students' initiatives in the learn- ing process, and the teacher's role.

The book does not intend to present "direct recipes for action of the tips for teachers sort" but achieves its goal, that it will "serve to intensify some perceptions and challenge oth- ers whilst all the time increasing sensitivity to possibilities in the classroom." The case stud- ies furnish a fascinating set of examples of young students' thinking and of the interac- tions of a sensitive teacher with students en- gaged in active learning. The analysis of the teacher's role raises many important issues, including planning in a way that doesn't pre- vent spontaneity, covering a set syllabus with- out inhibiting students' ideas, and finding and adapting ideas for activities that spark stu- dents' thinking. Many open-ended questions that encourage readers to extend and apply the ideas to their own experience make the book especially suitable for group discussion by teachers, for example, in advanced preservice or in-service courses.- Rosamond Welchman- Tischler

Multiplication and Division Made Easy, Catherine F. DeBie. 1990, 63 pp., $10.95 paper. ISBN 0-9627585-0-7. M. andD. Made Easy, P.O. Box521,Artesia, CA 90701.

This book presents a method for teaching whole- number multiplication and division with and without remainders. Intended to supplement a textbook, it presents eight units that go through the tables, first 2s, then 3s, and so on. In a consistent structure using minimal chalkboard space for directions, students are taught to fill pages with up to forty computational examples, relating multiplication to division from the start. Additional reinforcement is suggested through whole-class drill-and- practice games, dependent only on memory with no role for

strategy. Eggs in egg cartons are the only visual aids, and these are used only by the teacher for demonstration and only in the first three units. The only reference to story problems is in the preface, which states that "they can best be made up by the teacher who is acquainted with local customs and terminology."

Although a lot of space is given to generat- ing pages of exercises, little attention is paid to fundamental concepts. For example, when introducing multiplication by 10, the only explanation given is "when 10's number is multiplied, write the zero out to the side, bring down to the answer and multiply the 1." The stress is on the algorithm, not on why it works. Thinking strategies for multiplication and di- vision are barely discussed. In summary the techniques advocated are inconsistent with the vision of mathematics teaching of the curricu- lum standards - lacking are experiences related to mathematics as problem solving, communication, reasoning, and making con- nections, and the development contradicts most of the recommendations concerning concepts of whole-number operations and whole- numbercomputation.- Rosamond Welchman- Tischler.

REVIEWING AND VIEWING

Eiccicra Junior Genius' Common Denomina- tor. 1986, challenging game for up to 4 play- ers, aged 6 years and up; 2 special "Professor Thoth" spinners, playing board, 144 colored counters, and case, $7. 50. Junior Genius, 4865 Hunters Way, Boca Raton, FL 33434.

Junior Genius' Common Denominator is a game played on a multiplication chart. Players each have thirty-six markers that they use to cover a product obtained by spinning a wheel. The player must cite all multiplication facts that relate to the product before covering all

Edited by Mary Kay Tornrose Mathematics Coordinator Newtonville, MA 02160

59

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