Mathematics for Elementary School Teachers: A Problem Solving Approach by JosephNewmarkReview by: George NattrassThe Arithmetic Teacher, Vol. 39, No. 4 (DECEMBER 1991), p. 44Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41195013 .

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instead, researchers have learned that children can be quite sophisticated in their thinking. Although the book stresses the importance of mathematical lan- guage, the emphasis seems to be on students' using correct mathematical terms rather than on the lan- guage that they naturally use to describe mathematics concepts. For these important reasons this book serves to restrict rather than expand a teacher's vision of children 's potentials. -David J. Whitin.

Mathematics for Elementary School Teachers: A Problem Solving Approach, Joseph Newmark. 1991, xvii + 983 pp., cloth. ISBN 0-201 -58281-3. Addison-Wesley Publishing Co., One Jacob Way, Reading, MA 01867-9984.

This seems like the year to write textbooks for pro- spective elementary school mathematics teachers and for those persons who are already teachers. Al- though this textbook resembles others in content, readers will find such subtle differences as the use of Polya's four-step problem-solving approach, the emphasis placed on the van Hiele model of geometry development in children, and pedagogical considera- tions that one sees in Addison-Wesley' s elementary- and secondary-level textbooks. Another plus is the availability of the Solutions Manual, which gives stepwise solutions and not just answers. Problem solving is stressed throughout the textbook, as is the use of technology (calculators, Logo on a computer) as a tool. The author has even gone to the extent of asking questions that are frequently asked in the classroom.

The chapters include "Problem Solving," "Sets and Logic," "Numeration Systems and Whole Numbers," "Integers," "Number Theory," "Rational Numbers," "Real Numbers," "Probability," "Statistics," "Intro- duction to Geometry," "Coordinate Geometry," "Measurement," "Similar and Congruent Figures," and "Computers and Their Uses." This group of topics represents a wealth of mathematical content.

Examples are documented well and thoroughly explained. The follow-up problem sets are of the proper length, are set in ascending order of difficulty, appropriate for the content, and thorough in coverage of the content. The problem solving involved in the exercises is excellent, and the illustrations are adequate. This textbook does have a few more illus- trations than do others. Like other college textbooks, this work has a lot of black print on white paper.

The content was supposedly chosen on the basis of current elementary school mathematics programs. However, such content as set operations, logic, inte- gral operations, irrational numbers, matrices, and so on, do not strike me as appropriate for elementary school teachers. However, most comparable text- books that deal with the teaching of elementary school mathematics include these topics.

This textbook seems to be "different" from others of the same intent in that it might be more easily understood by those who are not majoring in mathe- matics. Users will like the "real-worldiness" of its problems. - George Ifattrass.

Problem-solving Situations: A Teacher's Resource Book, Vol. i,joei Greenberg. 1990, 149 pp., $15 paper. ISBN 0- 931011-14-0. Grapevine Publications, 626 N.W. Fourth St., P.O. Box 2449, Corvallis, OR 97339.

This booklet is a nice collection of ptafelepréolving activities that involve both mathematics and science. The forty-seven activities are what the author calls "encounters with real-world problems that require students to make testable predictions." The problems are meant to be solved in a discovery-based format using cooperative groups.

These problems seem appropriate for grades 5-8. However, according to the suggestions in the booklet, the level of difficulty of the activities can be raised or the activities can be used as enrichment.

The manual begins with an introduction that justi- fies the author's approach. Following are units on defining problem-solving situations, who can use the booklet, how to use the situations, and getting your "stuff together.

The chapter titles and the respective number of activities are these: "Length, Number, and Weight" -

7; "Speed and Distance" - 5; "Circumference and Area" - 4; "Area and Weight" - 7; "Density, Weight, and Volume" - 7; "Density and Identity" -

3; "Triangulation" - 2; "Flotation and Displace- ment" - 4; and "Odds and Ends" - 8. As readers might predict, scaling principles (ratios) are used extensively.

The activities are strongly science oriented but make extensive use of mathematical operations. The problem solving depends heavily on the use of scien- tific apparatus. This booklet would make a great resource bank of activities for the self-contained classroom or when used with a team-teaching approach. - George Nattrass.

REVIEWING AND VIEWING

Etcetera

The Wonder Number Learning System. 1988, $96.75. Includes the basic teacher's kit (marking pens, poster, miniboard, over- head transparency, and lesson-plan book for grades K-3); the Wonder Number Game (game board, 100 colored chips in 4 colors, spinner, and instructions); lesson-plan books for grades 3-6 and 6-8; a skills- inventory sheet; and a Chip Art and Graph and Game Kit (300 chips in 11 colors). Interactive Dimensions, 1852 E. Gaviota Ct., Simi Valley, CA 93065.

The Wonder Number Game is basically a hundred chart enhanced to illustrate many commonly taught objectives in mathematics. The activities are primar- ily written as games for two to as many as eight players and employ a game board, colored chips, and a spinner.

The game board, modeled after a hundred chart, is coded for odd, even, square, and prime numbers, with factors listed in the square for each composite number and columnar color coding that is used for some of the activities.

The basic idea is to use the chips to indicate the numbers involved in whatever concept is being

Edited by Ann Neaves Doling Mississippi College Clinton, MS 39058

taught by a particular game. For instance, prime numbers may be covered in some fashion, or mul- tiples of five or numbers with a given common factor or multiple or some other relationship may be the key to reveal the squares to be covered. Many other such activities as measuring objects using the squares on the board to find the longest or shortest object or stacking chips to represent fractions or to form graphs are suggested in the teacher's lesson books that ac- company the game set. Masters for students' work- sheets and a transparency of the board are also sup- plied. Three such resource sets are available, one each for grades K-3, 3-6, and 6-8.

If properly used, the Wonder Number Game can promote the learning of basic skills through discovery and group involvement. Teachers will have to com- mit themselves, however, to spending a little time learning how to use the set to carry out effectively the activities in the lesson-plan books. Also, enough boards would need to be made available for every group of about four students with which a teacher would like to use the game.

Students' interest in games and the wide range of grade levels and mathematical concepts that can be taught or reinforced by the use of this resource make the Wonder Number Game worth considering for use in the classroom.

The Wonder Number Learning System Chip Art and Graph and Game Kit is a set of 300 full-sized playing chips matched to the colors of the Wonder Number Game's board. Eleven colors of chips are included. Using these extra chips allows more flexi- bility in conducting activities with the Wonder Number Game board. - Ann N. Boling. Щ

44 ARITHMETIC TEACHER

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