A Problem Solving Approach to Mathematics for Elementary School Teachers, 2d ed. by RickBillstein; Shlomo Libeskind; Johnny W. LottReview by: David BarnesThe Arithmetic Teacher, Vol. 34, No. 3 (November 1986), p. 42Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193021 .

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New Books

For Teachers

Practical BASIC for Teachers. Jim Thompson. 1985. $14.95. ISBN 0-675-20340-6. Charles E. Merrill Publishing Co., Columbus, OH 43216.

According to the foreword, the primary goal of this book is to present the elements of BASIC to "anyone with a nonmath background in a readable, nonmathematical way." This goal is pursued in a series of sample programs that the reader is encouraged to read, copy by hand onto paper, enter into the computer, run, and analyze. Versions of each program are given for Apple and IBM computers, and an appendix shows how to adapt the programs for Commo- dore and TRS-80 computers. Topics include program entry and editing, PRINT statements and screen formatting, numeric and string vari- ables and operations, flow of control and flow- charting, FOR-NEXT loops (including nested loops), subroutines, and random numbers. A chapter titled "Where Do You Go from Here?" mentions graphics in BASIC, Logo, and word processing as three possibilities for further study but does not cover these topics in great detail. The programs mainly demonstrate pro- cesses used in writing simple CAI programs, such as asking for the student's name, asking questions, checking input for correctness, and branching to various responses.

The author's style is chatty, cute, and non- threatening; he seems to assume that the reader will want or need his or her hand held every step of the way. For example, at the end of the chapter on FOR-NEXT loops, the reader is told, "You have learned some extremely diffi- cult material." Although the scope of the book represents what many elementary and junior high school students have taught themselves in a week or so of spare time, the author calls this "a significant accomplishment." Unfortunate- ly, he sometimes gives advice of dubious value, often fails to mention items that would aid learning, and makes a large number of factual errors.

An example of the questionable advice is the suggestion that it is valuable to recopy each program on paper before entering it at the keyboard. Two examples of helpful hints not included are (1) the failure to suggest issuing direct (immediate mode) commands or running parts of programs by specifying starting line numbers and (2) the failure to mention the concept of reserved words and to warn the reader not to use variable names with reserved words imbedded in them.

The book contains many factual errors. Most are merely annoying, imprecise statements, but

Edited by A. Dean Hendrickson University of Minnesota, Duluth Duluth, MN 55812

others will probably cause the reader real diffi- culty in trying to follow the book's directions. Examples in the first category include the claim that a string consisting of one blank is a null string, the reference to AND and OR as "modi- fiers" rather than "logical operators," and the claim that in BASIC you must write a program and then RUN it, whereas Logo has no equiva- lent to RUN and so "things happen on the screen the moment you tell them to happen." This last error is especially curious, since the chapter goes on to introduce the concept of using TO to define procedures. Examples of "fatal errors" include the suggestion that BRONSON$ is an acceptable variable name (it is not because it contains the reserved word ON), a missing space in the START procedure on page 162, and a missing line (START) in the FLOWCHART procedure on page 163.

As the foreword states, this book is obviously not written for mathematics teachers, but I believe that even "nonmath" teachers will be disappointed that they learn so little that is useful to them as teachers. Anyone wanting to learn BASIC (whether teacher or not) could surely find a better way to do so than by using this book. - Thomas L. Schroeder, University of Calgary, Calgary, AB T2N 1N4.

A Problem Solving Approach to Mathematics for Elementary School Teachers, 2d ed. Rick Billstein, Shlomo Libeskind, and Johnny W. Lott. 1984, 744 pp., $26.95. ISBN 0-8053-0853-3. BenjaminlCum- mings Publishing Co., 2727 Sand Hill Rd., Menlo Park, CA 94025.

This textbook is designed for use in an elemen- tary education mathematics content class.

The first chapter is a brief introduction to problem solving using Polya's four-phase proc- ess. This chapter also includes examples of various strategies, a discussion of ways of breaking mind sets, and a variety of puzzle problems. Chapter 2 explores sets, set opera- tions, relations, and functions.

Chapters 3 and 4 develop the standard opera- tions and properties with whole numbers and integers. Included are visual models and manip- ulative activities to develop concepts and stan- dard algorithms. The topics covered include other numeration systems, computation in oth- er number bases, and the solution of equations and inequalities. Chapter 5, "Number The- ory," presents divisibility tests, primes, com- posites, GCDs, LCMs, and an optional section on modular arithmetic. Chapters 6 and 7 focus on the operations and properties of rational numbers. One section covers negative expo- nents, and another deals with real numbers, with optional sections on radical expressions and the computation of interest.

Chapters 8-12 cover probability and statis- tics, an introduction to geometry, construc- tions, and motions in geometry, measurement using the metric system, and coordinate geome- try. Chapter 13 gives a brief overview of BASIC and turtle graphics in Logo. The final chapter reviews problem solving.

Some added features include laboratory ac- tivities and review and calculator problems.

Computer activities and brain teasers are pre- sent in most chapters. The appendix consists of sections on informal logic, calculator use, and examples of basic geometric constructions. An- swers to odd-numbered problems are included.

Major changes in this edition include devot- ing two chapters to rational numbers, combin- ing probability and statistics, placing measure- ment entirely in one chapter, adding a computer chapter, and offering more practice problems at the end of each section.

In using this book as a text, I have found it to be quite adequate. The students feel comfort- able with the examples and find the problem sets very helpful. The mathematics content focuses on concept development by using a variety of models, manipulatives, and enrich- ment activities.

I am uneasy, however, with the approach to process or nonroutine problem solving. To be successful, one must make a substantial effort to develop the students' problem-solving abili- ty. Minimal effort is devoted to presenting and teaching various problem-solving skills and strategies - problems are merely presented with solutions given later. The solutions often focus on finding an equation or formula rather than on such strategies such as guess and check, work backward, make an organized list, and so forth.

This book does a fine job in developing an understanding of mathematical concepts but does little with the development of problem- solving skills. - David Barnes, Illinois State University, Normal, IL 61761.

42 Arithmetic Teacher

Whole Numbers Decimals I'ercents GeometrY

24 ready-to-use activities dedicated to the proposition that calculators free children to think out problem solutions. 42 pp 1981 ISBN 0-87353-175-2 $400

Individual NCTM Members -Discount 20%

See NCTM Educational Materials Order Form in the back of this issue

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