Number Concepts and Operations in the Middle Grades by Merlyn Behr; James HiebertReview by: Betty PeckThe Arithmetic Teacher, Vol. 37, No. 3 (NOVEMBER 1989), p. 45Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193793 .

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CHARACTER) have optional "timers." • Enhanced debugging tools (TRACEBACK) • A COPYDEF (copy definitions) command • A large set of utilities, tools, and sample pro- grams that illustrate the use of these and other Logo PLUS features

• An accessories file provides a readily avail- able set of tools for formatting disks, convert- ing files from Terrapin Logo to Logo PLUS (I used this extremely convenient feature to translate several complicated programs from older versions of Terrapin Logo; they ran perfectly), and editing fonts (e.g., to create mathematical symbols). The manual for the " PLU Ses" in Logo

PLUS is of the same high quality as previous Terrapin manuals - complete, clear, and illus- trative. The second and larger manual, while of high quality, is basically the same as that for previous versions of Logo. Although this obser- vation may be nitpicking, a synthesis might have been somewhat easier to use.

From a mathematics education perspective, one might prefer that the "PLUSes" include more geometric and other mathematics- oriented primitives, as opposed to additional features related to color and fine-tuned (bit-by- bit) editing. Also missed are such error-trapping primitives as CATCH and THROW and com- mands, such as WINDOW, that are not uncom- mon in other versions. However, others might disagree, and certainly the new features make it easier to add similar pseudoprimitives to the usual Logo commands.

Logo PLUS is a well-designed implementa- tion that invites mathematical explorations by students of all ages. It deserves close examina- tion by anyone interested in using Logo to en- hance mathematics education. - Douglas H. Clements.

Football Fractions . . . Activity Sheet Generator, Frank Herendeen. 1988, 48K, Apple ¡I series; $49.95. Friend Lee Software, 6041 West View Dr., S te. A-l, Orange, CA 92669.

This program generates drill-and-practice activ- ity sheets in game format for the computation of fractional numbers (addition, subtraction, mul- tiplication, and division with proper fractions, whole numbers and fractions, and mixed num- bers). Another part of the program generates drill-and-practice problems, in the same game format, that focus on reducing fractions, chang- ing mixed numbers to improper fractions, changing fractions to decimals, and changing fractions to percents.

A printer is necessary to run the program. To generate worksheets, teachers identify the type of computational problem desired and the type of printer and optionally enter a heading or title for the program. A prompt allows for rules of playing the football game (the same for all ac- tivity sheets generated) to be printed with the activity sheets. A four-page manual accompa- nying the program disk gives directions for booting the disk, a listing of types of problems that can be generated with the program, rules of the game, and some trouble-shooting sugges- tions for printers.

It is suggested that the same activity sheets

NOVEMBER 1989

(duplicated by copy machine) could be used by many students because no two students will play the game the same way. Each game se- lected generates a football game board with fractional values and another sheet with four groups of twenty-six drill-and-practice exam- ples.

To play a game, each player circles ten an- swers on the football field and draws a box around any ten remaining answers. The object of the game is to score the most points by find- ing and marking off an answer behind an oppo- nent's goal line. The game begins with a player reading the first problem aloud, giving the cor- rect answer, and finding it on the football field. The rules describe scoring points and keeping score. Answers to the computation problems are not to be reduced to lowest terms (and are not given in reduced form on the game board).

Overall, I would not recommend this pro- gram because of its emphasis on drill and prac- tice with computation of fractional numbers. What is to be gained by students' practice with repeated examples, such as

3£ + 23- = ^ * * 8 8 152

*

Is this the best use of a student's time? Does extensive use of this type of drill and practice expand or extend students' thinking about frac- tional values? Students are not encouraged to think about relationships, such as equivalent fractions, or to apply what they know about the factors of fraction terms and the relationships between them.

Each activity sheet is in the same format and practices the same type of problem. For exam- ple, by selecting "Subtraction: [D] mixed num- ber - mixed number (no reducing)," 104 exam- ples like

8i-liand3l-l| are generated. This type of drilling does not en- courage students' understanding of the pro- cesses of operating with fractional numbers, but instead encourages rote performance of opera- tions. - Mary Ellen Terranova, State University of New York at Buffalo, Buffalo, NY 14260.

I REVIEWING AND VIEWING

1 New Books

For Teachers

From NCTM

Number Concepts and Operations in the Middle Grades, Merlyn Behr and James Hiebert, eds. 1988, 271 pp., $15. ISBN

Edited by Grace M. Burton University of North Carolina

at Wilmington Wilmington, NC 28403 Hilde Howden Mathematics Consultant Albuquerque, NM 87114

0-87353-265-1. National Council of Teachers of Mathematics, 1906 Association Dr., Reston, VA 22091.

This book is a collection of papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three sections. The first deals with the analyses of subject matter, the second with the growth in student competence, and the third with the effects of current instruction and possible effects of experimental forms of in- struction. Its premise is that conventional in- struction is fundamentally inadequate.

The book should be of great interest to re- searchers in the learning and teaching of math- ematics. The middle school teacher of mathe- matics would find it worth scanning.

I fail to follow the reasoning of Wearne and Hiebert where they consider solving (jc + 4)/5 < 0 to be in the same category as determining the measure of an angle whose sine function is greater than 1 . Do they mean that both are im- possible, or is this statement an error? Are both of these proper concerns for the middle school student?

The papers contain much of value, but if they are meant for the middle school mathematics teacher, much of the "educationese" and com- plex notation is a bit overwhelming. They speak to the misconceptions students develop as they move from the elementary school into the mid- dle grades. They do not, however, offer specific techniques for correcting these misconceptions. Nesher's paper on multiplicative school word problems speaks to an area that needs much attention. Sowder's paper on mental computa- tion is practical and usable. - Betty Peck, 101 Moray Court, Cary, NC 27511.

REVIEWING AND VIEWING

Etcetera

History of Pi. 1988, $9.95. The cartoons on the poster depict several interesting events in pi's long and varied history. An accompanying 12-page booklet contains further information about each cartoon, problems, and a bibliogra- phy. Cabisco Mathematics, Carolina Biological Supply Co., 2700 York Rd., Burlington, NC 27215.

"History of Pi" is a poster that gives a unique overview of the origins of, and little-known facts about, pl. Cartoons on the poster illustrate the varied history of pi from the times of the Babylonians and the Hindus, the Egyptians and the Chinese, dating to 2000 b.c. The theory of Archimedes is shown, as is Euler's standardi- zation of the symbol tt. Drawings of coins are

Edited by Ann Neaves Boling Jackson Public Schools Jackson MS 39225-2338 Donald E. VanOstrand Howard County Public School System Ellicott City, MD 21043

45

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