The Mathematics Achievement ProjectReview by: Diana C. MargottoThe Mathematics Teacher, Vol. 85, No. 7 (OCTOBER 1992), pp. 587-588Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27967780 .

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Bechnology Reviews Edited by Maurice Burke, Montana State University, Bozeman, MT 59717

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices. Readers interested in reviewing IBM software should write for a set of guidelines and a personal data sheet from the editorial coordinator. Reviewers can expect to review one or two products each year.

Algebra Made Easy. 1991, IBM PC and compatibles, 256K; 44 pp. student handbook, 2 disks, vols. 1 and 2, $39.95. Britannica Software, 345 Fourth St, San Francisco, CA 94107.

This software, titled Algebra Made Easy, generated in me the reaction "Here comes another

simplistic proposed mathemati cal cure-all." Just buy this soft ware, I thought, and life will be perfect. I almost wondered if a

flip side existed that taught "Brain Surgery at Home" in five easy steps.

Thankfully, my fears were ill founded. The software proposes to help students with, not to teach from scratch, material cov ered in most first-year algebra courses. It does just that in a very clean and efficient manner. All the standard first-year alge bra topics are presented from three different perspectives: lessons and demonstration, examples with help, and practice problems. Also, a manual accom

panies the software to allow one to correlate different textbooks with different sections of the software.

In closing, let me simply say that I liked it! I believe this soft ware package could be used nice ly for classroom demonstrations and for remedial work to smooth out any rough spots that some students may encounter. It is easy to use and follow. The top ics are pertinent, and it does what it proposes to do?be help ful!?Joseph D. Cron, Fairfield

High School, Fairfield, CT 06430.

GeoExplorer: A Geometry Draw

ing Tool. 1992, Macintosh sys tem 6.02 or higher and 1 MB RAM, system 7 compatible; 48 pp. user's guide, 79-pp. of instructions + 1 disk, $99.95 (includes license to multicopy). ISBN 0-673-44272-1. Scott Foresman & Co., 1900 E. Lake Ave., Glenview, IL 60025.

GeoExplorer: A Geometry Draw ing Tool is a new entry in the

growing field of geometry exploration software. It is designed for students in grades 9-12, although middle-level stu dents can certainly benefit from its use, also. It offers tools to draw, measure, modify, and transform geometric shapes.

With GeoExplorer students are

encouraged to observe and con

jecture about relationships and to become actively involved in

learning geometry. The program operates in a

standard Macintosh environ ment. A toolbox of functions includes tools to draw such basic geometric objects as points, lines, segments, and angles. Polygons including triangles and

quadrilaterals of all types can

easily be constructed, along with circles and vectors, including vector addition. Additionally, medians, altitudes, perpendicu lars, parallels, and angle bisec tors involving existing objects are available in the toolbox. Con structions are generally accom

plished by interacting with dia

logue boxes on the screen. A nice feature permits these boxes to be

dragged to any location on the screen for easier viewing of existing objects.

Measurements can be made

for any object on the screen and are stored on a window separate from the drawing screen. The measurement window can be

displayed, but I found it a disad vantage that the measurements are not a part of the drawing screen and have to be shown sep arately. A strength of the mea

suring tool, however, is its abili

ty to request measurements of any polygon by figure. Doing so will produce measures of all

angles and sides of the polygon, along with its area and perime ter; this feature is missing from other geometry software.

One of the more exciting fea tures of the GeoExplorer is its

transform menu. In keeping with the University of Chicago School Mathematics Project's emphasis on transformation geometry, the GeoExplorer offers choices of reflections, transla tions, rotations, glide reflections, size change, scale change, affine, and composition. These are easi

ly done and well displayed on the screen with labeling for up to nine transformations of any point.

Two other items in GeoExplor er that I appreciated are the

Glossary/Help menu and Grid option. Located under the apple menu is a Help choice, which offers (a) well-documented and

easily understandable help for any item under the various other menus and (6) a glossary of geo metric terms from acute angle to zero vector. The Grid option allows placement of a grid of dots or lines, with or without coordinates, over the figure being constructed. This capabili ty certainly enhances the study of area concepts and coordinate geometry.

GeoExplorer is not without its weaknesses. Movement around

the various options seems a bit awkward, with many dialogue boxes to navigate through. The cancel button is used often and differently from in most Macin tosh applications. Once a figure is drawn it remains static along with its measures, and repetition of an experiment requires remeasuring objects. A Record feature allows the user to redo constructions quickly, however.

Overall, I like this software. It offers a great deal of potential for exploration at a very reason

able cost. It is nowhere nearly as

powerful as the Geometer's SketchPad, yet it compares very favorably to the Geometric Sup poser. Teachers looking to enter the exciting world of geometric exploration and student discov ery for a small investment will very likely find the GeoExplorer

a good investment.?Robert Daniel, Centaurus High School, Lafayette, CO 80026.

The Mathematics Achievement Project. 1992, Apple II, 48K; includes teacher's guides: Area and Perimeter, Percent, Proba

bility, Ratio and Proportion, and Statistics and Averages, $29.95 ea, $119.95 series. CAE Soft ware, P.O. Box 6227, Washing ton, DC 20015.

The Mathematics Achievement Project Series includes five sepa rate computer programs titled Statistics and Averages, Ratio and Proportion, Percent, Area and Perimeter, and Probability. Each program comes in its own

package with a 5 1/4-inch disk and a teacher's guide. No specific grade level is listed; however, these programs could be used wherever and whenever the pro gram topics are taught.

The objectives of each package are clearly stated both in the programs and in the accompany ing documentation. For example, Ratio and Proportion contains four lessons. Lesson 1 is on the subject of ratio, and its objective is to have the student write ratios comparing numbers. Les

son 2 is on the subject of equal ratios, with the objective being to have the student use cross

products to determine whether two ratios are equal. Lesson 3 is on proportion, with its objective to have students solve propor tions. Lesson 4 involves propor tions, and its objective is solving word problems using propor tions.

The programs are definitely user-friendly to students, assum

ing they have a good background of basic-arithmetic skills, good reading skills, and basic calcula tor skills. The teacher should plan to introduce the packages and their specific instructional features to save time for stu dents who want to proceed through a lesson without inter

ruption. Several classroom ses

sions might be necessary to

explain and demonstrate the use of the control key with certain letters, the use of the imbedded calculator, and the general flow of each program.

Each lesson offers the user two choices, either an instruc tional mode or a lesson mode for

Vol. 85, No. 7 ? October 1992 587

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users ready to proceed without instruction. The next two choices offer either a tutorial for the les son or a problem set for users

ready for exercises without drill and practice. The objective is clearly stated, and a goal is set for completing a certain number of problems correctly without help. A help mode is available when a problem is incorrectly solved or when the user has diffi culty determining how to solve a

problem. It should be noted that each time the help mode is invoked, credit for solving a

problem is not given; however, if the user needs the help of the calculator, credit for solving the problem is given.

Positive reinforcement is given at the bottom of the screen, along with a running total of problems solved and credited toward the limit re

quired for completion of the les son objective. The use of colorful graphics adds to the enjoyment while-learning experiences of the user. The lessons can be used as tests. Suggestions for testing and record keeping are offered in the teacher's guide.

The tutorials in each program furnish excellent teaching, reviewing, or makeup lessons and good drill-and-practice ses sions to prepare the student for the lesson sessions. The tutorials appear to use the same problems for students to solve whereas the lessons use random problems.

Overall, the programs are well written, user-friendly, and rea

sonably priced and fulfill the NCTM's curriculum standards' recommendation for using tech nology in the classroom.?Diana C. Margotto, Green Bay, WI 54311

^publications_ From NCTM 20 percent discount for individ ual NCTM members on NCTM publications. Free catalogs of NCTM publications are avail able by writing to NCTM, Department P.

Applications of Secondary School Mathematics: Read ings from the MATHEMATICS TEACHER (R), Joe Dan Austin, ed. 1991, vi+ 339 pp., $21.50 paper. ISBN 0-87353-336-4. National Council of Teachers of Mathematics, 1906 Association Dr., Reston, VA 22091.

This book is a must for all sec

ondary school mathematics teachers looking for real-world

applications in teaching mathe matics. The seventy-eight arti cles in this publication were selected from the Mathematics Teacher (1974-1989). This collec tion is unique in that editor Joe Dan Austin has grouped several articles into chapters under a

specific course heading (arith metic, geometry, algebra, trigonometry and elementary

analysis, calculus, and probabili ty and statistics). Also included are two indexes, one listing application areas and the other, mathematical topics that help in

finding articles appropriate for one's classes. An additional plus is that "each chapter begins with a short introduction outlining some early historical applica tions of the topic and containing a brief overview of the article in the chapter."

A teacher wishing to use an article for a classroom exercise will need to prepare some addi tional handouts to help the stu dents understand and appreciate the mathematics involved.

As a final suggestion Austin writes, "For additional sugges tions on using applications in

teaching school mathematics, the articles in Applications in School Mathematics (NCTM 1979) are especially recommend ed."?Manny Suarez, Berkeley

Preparatory School, Tampa, FL 33615.

Curriculum and Evaluation Standards for School Mathe

matics: Connecting Mathemat ics (S), Addenda Series, Grades 9-12, GaryW. Froelich. 1991, viii + 69 pp., $9.50 paper. ISBN 0-87353-309-7. National Council of Teachers of Mathematics, 1906 Association Dr., Reston, VA 22091.

When published in 1989, NCTM's Curriculum and Evalu ation Standards for School Mathematics was given an enthusiastic reception by mathe maticians and educators alike. Yet even as that document was still in its developmental stages, its developers realized that acceptance of its recommenda tions by the educational commu

nity was a necessary but not a sufficient condition for the suc cessful implementation of its rec ommendations. Thus the Adden da Project was initiated in 1988 to produce resource materials to

support teachers and supervisors in their individual schools in their drive to a new excellence in mathematics education as chart ed by the Standards document.

The theme of Connecting Mathematics, designed for

grades 9 through 12, is the con nectedness of mathematics. The fabric of mathematics is whole cloth; the branches of mathemat ics, its methodology, and its

applications are not separable pieces or systems somehow stitched together in quiltlike fashion.

Teachers will find much that is useful and exciting in this book. Each of five chapters begins with a particular topic and then fans out to make con nections with applications and other parts of mathematics. The lead-off topics for the chapters are functions, matrices, data analysis, mathematical reason

ing as process for the analysis and solution of problems, and

problems that admit of several different solutions. The five

chapters themselves are connect ed, and the ideas and methods of algebra, geometry, statistics, functions, graphs, coordinates, modeling, deductive proof, and inference are linked throughout.

This volume is "teacher friend ly," well written, and filled with good mathematics. For example, a particularly nice instance of good mathematics is using the technique for determining the

vertex of a parabola to find an

equation for the best line by a

least-squares fit to a data set.

Computer programming and uses of software are natural to the mathematics. Each chapter includes thoughtfully designed activities for the classroom, valu able suggestions for assessment of students' performance, and

"try this" challenges for extra

projects. Connecting Mathemat ics constitutes a model for effec tive education that should be made available to secondary school mathematics teachers striving to realize the vision of the Curriculum and Evaluation Standards for School Mathemat ics.?James N. Boyd, St. Christo

pher's School, Richmond, VA 23226.

Mathematics Assessment: Myths, Models, Good Ques tions, and Practical Sugges tions (R), Jean Kerr Stenmark, ed. 1991, iv + 65 pp., $8.50 paper. ISBN 0-87353-339-9. National Council of Teachers of Mathematics, 1906 Association Dr, Reston, VA 22091.

This book's chapter headings include "Shifting Assessment Practices"; "Performance Assess

ment"; "Observations, Inter

views, Conferences, and Ques

tions"; "Mathematics Portfolios"; "Implementing Models of Assess

ment"; and "Looking toward the Future."

Concise information and numerous illustrative examples are included. Twenty-three bene

fits of assessment alternatives are listed: students think more

deeply about problems, increase self-confidence, and focus on

exploring and communicating ideas; teachers strengthen lis tening skills.

Myths of teaching and testing are discussed. Do students learn

only by imitation and memoriza tion? Does a mathematics prob lem almost always have a single right answer?

A sample five-step assessment

plan is given: (1) state goals, (2) assess your students, (3) build an instructional program based on the NCTM's Curriculum and Evaluation Standards (1989) and a variety of assessments, (4) plan a system to document assessment, and (5) maintain a review.

588 THE MATHEMATICS TEACHER

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