Computers in Teaching Mathematics (P) by Peter KelmanReview by: Richard H. KingThe Mathematics Teacher, Vol. 77, No. 3 (March 1984), pp. 242-243Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963991 .

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NEW PUBLICATIONS Code: Tj = Textbook, junior high L = Library

Ts = Textbook, senior high = Professional Tt = Textbook, two-year college S = Supplementary student reading

Algebra in the Real World: 38 En richment Lessons for Algebra 2

(S), LeRoy C. Dalton. 1983, x + 226 pp., $12.50 paper. ISBN 0-86651-121-0. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303.

The material in this book has been collected from reading books,

magazines, and newspapers ; taking nature walks; collecting seashells;

studying pianos and guitars; ob

serving the growth and decay of

bacteria; and examining heat,

light, sound, radioactive sub

stances, fruits, animals, and stars in fact, all biological and

physical phenomena. This list of sources suggests how teachers and students can develop their own in

vestigations and applications. The author states that students

must learn to look before they see.

Showing teachers how to en

courage students to observe and to

learn how to interpret and analyze situations from the mathematical

point of view is the goal of the teacher's guide. Algebra in the

Real World is a collection of math ematical applications designed to meet the needs of teachers of

second-year algebra. The topics are drawn from the standard algebra two curriculum, including some ge ometry and elementary combi

natorics, quadratic and ex

ponential relations, rational poly nomial expressions, and trig onometry. The first part of the book contains follow-along lessons in seven sections, which can be used in any order. Each lesson has

three main parts: discussions, worksheets, and follow-up exer

cises. The discussions are written in narrative form, as if a teacher

were speaking to students.

Questions guide students to dis cover key ideas for themselves. For

purposes of reference, abridged ver

sions of the worksheets appear on

the discussion pages. At the end of

each lesson are exercises to illumi nate points in the lesson and to

extend it to new ideas. The second part of the book

consists of "

squintproof "

(the author's word) masters for the worksheets and exercises; the

pages are in bold type and are suit

able for in-class work, homework, or transparencies. Permission for

duplication of up to 100 copies for classroom use is given.

Each section is organized around a common theme: Com

puters, Packing Problems, A Very Special Number Called e, Algebraic Functions, The Golden Ratio, The

13th Century Still Lives, and Math ematics and Music. Answers to all

exercises appear on the same page with the narrative. Of course, they are not on the worksheets (which also appear in tiny print on nar

rative pages). This book is well-conceived,

lucid, and challenging set of real world studies, applications, and ex

ercises. Teachers of second-year al

gebra should find it very helpful in

focusing the students' use of math ematics in real-world applications. The book can provide a starting point for research and can stimu late imagination by answering the

question, "When will we ever use

this stuff?" Margaret Holland, 1712 Forestdale Blvd., Birmingham,

AL 35214.

Basic Mathematics: Mastering Skills (Tt), John Konvalina. 1983, xiv + 584 pp., $20.95 paper. ISBN 0-15-504970-4. Harcourt Brace Jovanovich, Publishers, 757 Third Ave., New York, NY 10017.

This text contains some standard definitions and procedures for ar

ithmetical operations, but it does have some interesting features. The layout is spacious and easy to read. Each topic is preceded by a

section detailing necessary pre skills as well as the skills the sec

tion will teach. The book incorpor ates some self-directed learning and evaluation and can be used as a workbook, because the pages are

perforated for easy removal. Mona Fabricant, Queensborough Community College, Bayside, NY

11364.

Challenging Puzzles in Logic (L), Roger Hufford. 1982, xi + 103 pp., $3.50 paper. ISBN 0-486 24224-2. Dover Publications, 180 Varick St., New York, NY 10014.

For day-before-a-holiday classes when you want to give your stu

dents some mathematically rele vant activities, for quick test takers who wait for twenty min utes until the other students are

finished, for a change-of-pace moti vational activity, may I suggest a

logic puzzle from this book. The book contains seventy

eight puzzles in twelve categories, most of which comprise several

puzzles of the same type but of

varying degrees of difficulty. Solu

tions to all the puzzles are includ ed.

The overall level of difficulty of the puzzles ranges from novice to

intermediate. Although the puzzles are of common types, the book pro vides a good source of fun and

motivation! Mark Juliani, Com

munity College of Allegheny County, Pittsburgh, PA 15212.

Competency in College Mathemat ics. 3d ed. (Tt), Jack C. Gill and Robert Blitzer. 1983, viii&495 pp., $17.95 paper. ISBN 0-943202 09-4. H & H Publishing Co., 1117

Webb Dr., Clearwater, FL 3351 5.

The authors claim that this text is

designed to meet the competency requirements for higher education as of summer 1983, as well as the

requirements of a traditional gen eral education course in mathemat ics. The book meets the general ed ucation requirements admirably; it is both easy to teach from and easy to use for independent study. The introductions to the chapters give interesting historical information about the topic and list learning objectives. Clear explanations are

followed closely by problems to test understanding. A few review

problems are included in each sec tion of problems, and the end of the

chapter is followed by a chapter self-test.

The authors' claim that the book would make a suitable text

for a finite mathematics course is difficult to justify. The topics cov

ered are set theory, logic, basic al

gebra, number bases, geometry, probability and statistics, and some

computer topics. Matrices, linear

programming, and the mathematics of finance are not included.

Beverly Mugrage, University of Akron, Akron, OH 44325.

Computers in Teaching Mathemat ics ( ), Peter Kelman, Art Bardige, Jonathan Choate, George Hanify, John Richards, Nancy Roberts,

Mary Kay Tornrose, and Joseph

242- -Mathematics Teacher

This content downloaded from 129.130.252.222 on Wed, 16 Jul 2014 15:29:41 PMAll use subject to JSTOR Terms and Conditions

Walters. 1983, x + 308 pp., $13.95 paper. ISBN 0-201 10565-9. Addison-Wesley Pub lishing Co., Reading, MA 01867.

Computers in Teaching Mathemat ics is one of the truly good books on the market that details the inte

gration of mathematics and com

puters. The book is divided into

eight parts, some of which would be of general interest in other sub

ject areas. For example, the book contains chapters on programming and computer languages, staff de

velopment and training, main tenance of a resource center, and curriculum planning and . devel

opment. An excellent glossary and list

ings of organizations, resource cen

ters, projects, publications, and software sources are included.

The text is a must for the math ematics or computing teacher, but it should not be neglected by others using computers in other in structional areas. Richard H.

King, Essex Junction Educational

Center, Essex Junction, VT 05452.

Creative Problem Solving in School Mathematics (Ts, Tt), George Lenchner. 1983. 295 pp.. $12 paper. ISBN 0-395-34546-4. Also available Resource Problems $1.50 and Solutions to Resource Problems $3. Houghton M iff I in Co., One Beacon St., Boston, MA 02108.

The author states that the purpose of his book is "to help teachers im

prove each student's ability to solve problems." The book is writ ten for elementary and middle school teachers, but secondary school teachers would also find it beneficial.

The book's three sections deal with techniques that seem to be

particularly effective in teaching problem solving, suggest strategies for solving problems, and examine

problem solving in relation to the school mathematics curriculum. A series of related problems is pre sented in the third section. A re source section contains 100 prob lems and solutions related to pre

viously discussed techniques. The reviewer found this book to

be well written and well organized. The clarity of the presentations and explanations of the various

problems will be welcomed by users of this textbook. Teachers will find this book to be a must for their col lection of resources. Cheryl Allen

Hassell, Washington City Schools,

Washington, NC 27889.

Fundamental Concepts of Geometry ( ), Bruce E. Meserve. 1983, ix + 321 pp., $7.50 paper. ISBN

0-486-63415-9. Dover Publica tions, 180 Varick St., New York, NY 10014.

Dover Publications performs a sig nificant service by keeping in print many fine works of mathematical and scientific interest that ought to be available to teachers and stu dents. Fundamental Concepts of Ge

ometry is such a book. First pub lished in 1955, the book evolved from a course, "Fundamental Con

cepts of Mathematics," taught at the University of Illinois. The

merits of the book have been recog nized by those who have read and used it over many years. Thus, this review describes the contents and

makes suggestions for the book's use instead of evaluating it. An evaluation has already been made

by the many mathematicians, teachers, and students who want this work to remain in print.

The purpose of this book is to set Euclidean geometry in the con text of general ideas on geometry today. The author begins with a

survey of the required background in logic. Thereafter, he develops synthetic and analytic projective geometry as formal axiomatic sys tems. He then adopts the view that

geometry is the study of the proper ties of objects under a group of transformations. He defines an

affine geometry and shows Eucli dean geometry to be a special case of an affine geometry. As a special case, Euclidean geometry is the ge ometry of rigid motions.

A splendid chapter on the his torical development of geometry follows. This historical survey is, in turn, followed by a study of the

non-Euclidean, hyperbolic, and el

liptic geometries, which are then

compared with Euclidean geome try. The concluding chapter deals with topology as the most general of geometries.

This book deserves a place in the mathematics library of any sec

ondary school or college. It should be available to geometry teachers wherever the topic is taught with

any degree of sophistication. How

ever, even very able secondary school students will experience dif

ficulty in using the book directly. A thoroughgoing knowledge of Eu clidean geometry is necessary, along with some understanding of

groups, transformations, and matrices.

The geometry teacher will find Fundamental Concepts of Geometry a fertile source of projects and spe cial topics. The introductory sec tions on finite geometries even contain material for a computer programming project. James N.

Boyd, St. Christopher's School, Richmond, VA 23226.

Geometry: A High School Course (Ts, Tt), Serge Lang and Gene

Murrow. 1983. xxiii + 470 pp., $24 paper. ISBN 0-387-90727-0. Springer-Verlag, 175 Fifth Ave.. New York, NY 10010.

This textbook takes an eclectic ap proach to the high school geometry course. The authors one a re search mathematician and the other a high school teacher try to match the teaching approach to the topics being discussed. Thus, they abandon the "one point of view" approach to teaching geome try.

Certain traditional topics have been omitted, for example, common

tangents to a circle and the power of a point. The reason given by the authors for these omissions is that these topics are of "little signifi cance." Topics of "fundamental

importance" are included that are not usually found in high school

geometry textbooks. These topics include change of area under a di

lation, proofs of the standard for mulas for volume, vectors, dot

product with its connection to per

pendicularity, and transforma tions. The proofs are written in

paragraph form, and the flow of

logic is very natural. (Some of the

proofs are presented by other text

books.) The Pythagorean theorem is proved with area concepts in stead of the more traditional simi lar triangles.

This textbook warrants the at tention of high school geometry teachers. My first impression was that the text was too difficult, but a further look made me change my mind. The text can be read by most

high school students, and the prob lems are stimulating. The students

get the enjoyment of developing some of the geometric theorems. The price of the text, $24 in paper back, is a bit steep for most schools. Ronald E. Keutzer, Mar mion Military Academy, Aurora, IL 60504.

Introductory Geometry (Tt), Mary Kay Hudspeth. 1983, 563 pp., $18.9*5 paper. ISBN 0-201

March 1984- 243

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