Developments in School Mathematics Education around the World Vol. 2 by Izaak Wirszup;Robert StreitReview by: George NattrassThe Arithmetic Teacher, Vol. 39, No. 3 (NOVEMBER 1991), p. 58Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41195125 .

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What Do You Do with a Broken Calculator? is a

problem-solving program for students grade 3

through adult. The main objectives of this software

package are to -

• gain a deeper understanding of basic operations, • formulate rules for solving similar types of prob-

lems, • develop estimation skills, and

• improve mental arithmetic skills.

The software package accomplishes these aims by presenting the students with a goal or answer to derive on a calculator displayed on the computer monitor. Users can set their own goals and disable certain calculator keys or let the computer create the prob- lems. The more keys disabled, the harder the prob- lems.

This program is very user-friendly. It comes with

precise instructions, along with ideas for extra class- room activities. I experimented with this program at the seventh- and eighth-grade levels in a large class with the students divided into groups of four. It was

simple to select a range of problems that involve

single or multiple strategies. The students' interest was easy to maintain for approximately twenty min- utes.

The students and I judge this program to be good. It is easy to use, and students of all ability levels can be challenged. Its most important quality is that it

strengthens a student's problem-solving ability. -

Tom Mitchell, Townsend Junior High School, Townsend, MT 59644. Insert

REVIEWING AND VIEWING

New Books

For Pupils Annofe Math Games III, MitsumasaAmo. 1991 103 pp., $19.95 cloth. ISBN 0-399-22274-X. Philomel Books, 200 Madison Ave., New York, NY 10016.

Anno has written a third volume to this captivating series of books that address a variety of mathematical concepts. In this third volume the author presents the reader with four unique explorations:

Edited by Hilde How den Mathematics Consultant Albuquerque, NM 871 14 George Nattrass Northside Independent School District San Antonio, TX 78238 Rosamond Tischler Brooklyn College of CUNY Brooklyn, NY 11210 David J. Whitin University of South Carolina Columbia, SC 29208

(1) Changing shapes with magic liquid. The familiar characters of Kriss and Kross develop a special liquid that stretches or shrinks objects horizontally and vertically. The faces of these two characters, as well as the bodies of

lions, monkeys, and crabs, are stretched into unusual

shapes. In his afterword Anno discusses the mathematical

significance of this section by emphasizing that even

though the original shape shrinks or expands, the correla- tion of its position points remains constant, an important concept in the area of mathematics known as topology.

(2) Exploring triangles. Readers view a series of

squares pushed together to create triangular shapes and then observe the use of triangles in baskets, kaleidoscopes, and quilts. Anno also presentsa series of paper-folding experiences that highlight the use of triangles to create a

variety of figures and designs.

(3) Mazes. Anno presents the well-known seven-bridge puzzle of Königsberg for readers to solve. In his afterword he discusses Euler's mathematical explanation of this

topologici puzzle. Teachers might share this explanation with their students and encourage them to test out this

theory with some of their own bridge problems. Anno

presents other mazes constructed of two lines and also of one continuous line and describes the applicability of these mazes to today's circuit theory. This combination of the actual puzzles to solve and the explanatory notes in the afterword constitutes a rich resource for the classroom teacher.

(4) Left and right. Anno invites readers to explore the

positional relation of left and right by describing the

position of certain animals on the left and right sides of a

page and then describing them again once the book is turned upside down. Left and right are also used to describe the movement of gears and the directions along a series of roadways. The maps that Anno draws encour-

age readers to discuss positional relations and serve as a familiar precursor to the more abstract x- and ̂ -coordi- nates.

This book would be a welcomed resource for any classroom. The combination of the puzzles and the mathe- matical notes in the afterword makes it suitable for use

throughout K-6 classrooms. The illustrations are clear and inviting, and the text encourages readers to participate actively in many different explorations. - David J. Whitin.

HOW Many Feel ¡n the Bed? Diane Johnston Hamm, illustrated by Kate Salley Palmer. 1991, 27 pp., $13.95 cloth. ISBN 0-671-72638-2. Simon & Schuster Boob for Young Readers, Simon & Schuster Bldg., 1230 Ave. of the Americas, New York, NY 10020.

The author presents a delightful counting book in which readers count the feet of five family members as they tumble in and out of bed on a Sunday morning. Dad begins the count with "two" and is joined successively by his

daughter, son, infant, and wife. However, a series of incidents force people to leave the bed one by one (or two

by two if you are counting by feet!): Dad jumps out of bed to answer the phone; Mom runs to stop water from

overflowing in the bathtub; the baby leaves to get her

diaper changed; and so forth. Soon all the feet are gone, and only a sleepy teddy bear remains.

The illustrations are particularly effective in showing sets of two. As the story progresses, the feet of the family members are usually shown sticking through the slats at the end of the bed, inviting young readers to count by twos. This counting book is unusual because it involves count-

ing by multiples of 2. Readers might enjoy comparing this

book with Ruby Dee's Liberian folktale titled Two Ways to Count to Ten, one of the few other counting books that

emphasize this pattern of twos. Another unique feature is its illustration of the multiples of 2 in ascending and

descending sequences. Again, readers might enjoy com-

paring this descending sequence to the one found in Molly Bang's counting book Ten, Nine, Eight. Lastly, this story about feet could be a springboard for students to do some

counting of other sets of two, such as elbows, knees, wrists, and eyes, as well as sets of other multiples by using fingers, toes, or knuckles. Challenge them to count even

freckles, and see what strategies they use! - David J. Whitin.

For Teachers

FromNCTM 20 percent discount for individual NCTM members on NCTM publications

Developments in School Mathematics Education around lhe Worid Vd. 2, /^ Wirszup and Robert Streit, eds. 1990, xiv + 475 pp., $20

paper. ISBN 0-87353-302-X. National Council of Teach- ers of Mathematics, 1906 Association Dr., Reston, VA 22091.

This collection of articles has been compiled from papers presented at the Second International Conference on Mathematics Education held in conjunction with the

University of Chicago School Mathematics Project's (UCSMP) conference and at the National Council of Teachers of Mathematics's (NCTM) 66th Annual Meet-

ing held in Chicago in April 1988, along with other papers submitted by worldwide leaders in education. As these

papers reflect the world's current perception of curricula, reform, and research in mathematics, this volume repre- sents a significant work, which should be placed on one's

must-reading list. Part 1 of this three-part collection examines mathemat-

ics curricula and reform measures. Included are articles from Japan, Czechoslovakia, the German Democratic

Republic, England, Belgium, and the United States. The wealth of information included in these papers is enormous.

Part 2 examines current international research covering a variety of subjects. Topics include the role of calculators and computers in mathematics instruction (Sweden), a child's maturity and learning (Poland), statistics (Hun- gary), teaching fractions (Mexico), middle school stu- dents and proof processes (France), mathematics in Po-

land, and computer-based and -managed instruction and its effect on teachers (U.S.).

Finally, part 3 offers an overview of UCSMP, evalu- ations of UCSMP, and uses of technology in UCSMP. The section ends with articles that examine innovative curricu- lum projects and international perspectives and national

progress in education. John Dossey, one of the authors, mentions the "grow-

ing awareness of the fundamental role that mathematics education plays in social stability, economic security, and

strategic positioning." This volume affixes an interna- tional stamp on that perception. - George Nattrass.

Developing Graph Comprehension* Ele* mentory and rVudcIle School Activities/ Frances R. Curdo. 1989, Hi + 85 pp., $11 SO paper. ISBN 0-87353-277-5. National Council of Teachers of Mathe- matics, 1906 Association Dr., Reston, VA 22091.

58 ARITHMETIC TEACHER

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