Can You Believe What You See? by Louis Grant Brandes; Mary Ellen NicosiaReview by: David J. WhitinThe Arithmetic Teacher, Vol. 36, No. 5 (January 1989), p. 40Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194434 .

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asks the viewer to use arrow keys to cross out pictures not in the initial set.

Lessons and materials for three readiness and supplementary activities are included in an ac- companying three-ring notebook. Card Sorting introduces regrouping through "hands-on" work. Thirty Days Has September uses rhymes or jingles to assist students in remembering lists of objects. Tray Game presents a number of objects to be remembered.

Of the three original memory strategies that this disk attempts to promote, none is actively cultivated through documentation on the screen as lessons progress. Repeated reminders by the teacher would be necessary to reinforce these strategies. For example, the auditory strategy is only supported by the accompanying lesson plans. No sound is produced by the software, nor is the rhyme strategy suggested on screen.

What's in a Frame? does offer practice and draw attention to useful memory strategies. Even eighth graders were challenged in re- sponding to What Did You See? within a ten- second period. Elementary school teachers were enthusiastic about the software. - Glenn D. Attinger.

Writing Numbers II. 1987, Apple II fami- ly, 1 disk drive, 48K; $39.95. Dynamic Auto- mated Teaching Aids, P.O. Box 1485, Bolingbrook, IL 60439.

Writing Numbers II has four components. The first is the tutorial. A spotty explanation of place value is offered, and then the student enters a three-digit number that the computer displays in expanded notation:

526 5 in the

hundreds place =500 5 x 100 2 in the

tens place =20 2 x 20 6 in the

ones place = 6 6 x 1 526

Following this activity, the number

1 000 000 000 000 000 000 000.000 000

(one sextillion) is displayed. The student can move the cursor left or right, and the computer will name the place.

The second item offers practice in writing numbers at three levels of difficulty. Level 1 uses numbers less than 100 000. Level 2 uses numbers between 1000 and 1 billion. Level 3 uses numbers between 100 000 and 1 trillion. Numbers at each level are randomly generated. The computer expresses a number in word form (one period to a line), and the student enters the number numerically. Commas are accepted but not necessary. If the numerical entry is incor- rect, the student can try again, continue, or quit. Incorrect responses can be given to the same item indefinitely with no additional feed- back. After a correct answer, the student can continue or quit.

The third menu item is a drill section consist- ing of fifteen level-3 problems. The computer

reports the number correct (first and second tries) and the number incorrect.

In the final section, Watch Me Count, the student simply watches while the computer counts by ones. The computer also calculates the time it would take, in years and days, to reach 1 trillion. The only input available to the student is to change the factor by which the computer counts to any number less than 100 000. The computer will change its 1 trillion calculation accordingly.

This program is narrowly conceived, lacks variety, and requires little mental activity. Some second graders found it interesting and challenging; however, any student who cannot read numbers in word form would be unable to use the program independently. Fourth-grade students found it either too simplistic or too boring, and students who could not use it independently needed additional traditional in- struction in which oral and written drill were combined. - Susan Phillips.

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New Books For Teachers

Can You Believe What You See? Louis Grant Brandes and Mary Ellen Nicosia. 1988, 64 pp., $10 paper. Activity Resources Co., P.O. Box 4875, Hayward, CA 94540.

Have you ever been fascinated by optical illu- sions and wondered why they work? If so, then this book is for you. It consists of forty-five illusions drawn in black and white. In each drawing a question is posed to direct attention to the illusion. Each drawing is explained and classified.

This book, which is best suited for interme- diate-grade children, not only addresses the question of why these illusions deceive us but also explains how these optical tricks are used in everyday life. For instance, after explaining the common height- width illusion, the authors assert that architects use the same principle to make buildings look longer or wider. Even interior decorators use wallpaper with horizon- tal patterns so that a room with high ceilings appears lower; conversely, wallpaper with ver- tical designs is used to make a room with low ceilings appear higher. Advertising artists use various illusionary devices. Lines on packages are used to focus the buyer's eyes to the name of the product or to a list of its desirable benefits. After explaining another illusion of black-and-white contrast, the authors give an

Edited by Grace M. Burton University of North Carolina Wilmington, NC 28403

example of how advertisers capitalize on this principle: a brightly colored box of cereal on a store shelf appears to be larger than a darkly colored box of equal size. Explanations such as these make this book more than a listing of optical illusions; the explanations highlight the use of these principles in various situations. The examples invite children to look more closely at the world around them to find in- stances of the illusions discussed. This book would be an excellent resource for teachers who wish to integrate mathematics into the fields of science, social studies, and consumer awareness. - David J. Whitin, University of South Carolina, Columbia, SC 29208.

Mathematics in Primary Education, Contemporary Analysis in Education Series, Michael Preston, ed. 1987, viii + 175 pp., $18 paper. ISBN 1-85000-197-9. Palmer Press, 242 Cherry St., Philadelphia, PA 19106-1906.

Michael Preston has edited a thought-provoking collection of articles by British educators about mathematics education at the primary school level. Throughout the ten articles, the reader is reminded of the complexity and interrelated- ness of such factors as language, teacher atti- tude and preparation, technology, the role of activity-based lessons and applications, paren- tal involvement, and assessment in mathemat- ics for young children. Chapters on mathemat- ics advisors, resources, and calculators and computers, as well as appropriate content, fo- cus attention on current trends.

Whereas the articles do not provide a road- map for change, they definitely stimulate an examination of the complexity of the topic. College students, staffs involved in curricular changes, and persons responsible for support- ing change in school systems will find the book helpful in clarifying issues and concerns. Class- room examples in most articles illustrate the writers' ideas in practical ways. The overall tone of the book is positive, but many articles leave the reader wishing that the writers had included more specific suggestions in their sound discussions of the issues.

One problem might be the reader's lack of familiarity with the specific content of Mathe- matics Counts (Cockcroft Report 1982) and Mathematics from 5 to 16 (1985), both pub- lished in England and heavily referenced throughout the book. Although the gist of the documents is obvious from quotations, readers who have not studied these works will wonder about the entire content of the referenced pas- sages.

Teachers of mathematics for young children should consider including this book on their professional reading lists. No matter their na- tionality, mathematics educators will recognize similar issues and appreciate the variety of discussion. - Jeane M. Joy пег, Department of Public Instruction, Raleigh, NC 27603-1712.

Multiplying and Dividing, Annabel Thomas. 1985, 32 pp., $3.95 paper. ISBN 0- 86020-919-9. Usborne Publishing, 20 Garrick St., London WC2E 9BJ, England.

40 Arithmetic Teacher

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