NEW projectsAuthor(s): J. Phillip Bennett, Margie Hobbs, Johnny W. Lott, Anthony Piccolino, MargarieteMontague Wheeler, Nancy C. Whitman, White and CodySource: The Mathematics Teacher, Vol. 74, No. 8, Microcomputers (November 1981), pp. 664-666Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27962657 .

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zles work with the vocabulary of mathematics, they can be useful in the classroom. Students enjoy puzzles of this type. The set makes the puzzles easily available

and immediately reproducible, which makes them

much more useful. The masters cover a wide range of

topics from integers and radicals to proofs and identi

ties, so several teachers at different levels can use the

set. The algebra masters have both algebra 1 and al

gebra 2 topics. As with other similar materials, the teacher must

key the material to the textbook. Some of the puzzles

might be of more use than others but these puzzles can be useful if used properly. They are most appro

priate for the secondary school.?Roslynn Seidenstein.

NEW projects

Edited by J. Phillip Bennett, Mid-America Nazarene College, Olathe, KS 66061

Margie Hobbs, State Technical Institute at Memphis, Memphis, TN 38134

Johnny W. Lott, University of Montana, Missoula, MT 59812

Anthony Piccolino, Dobbs Ferry Union Free School District, Dobbs Ferry, NY 10522

Margariete Montague Wheeler, Northern Illinois University, DeKalb, IL 60115

Nancy C. Whitman, University of Hawaii, Honolulu, HI 96822

Microcomputers for Junior High

The Columbus, Kansas, school system has found

microcomputers to be a successful curriculum support device for 250 seventh- and eighth-grade students

each year. Since 1979, computer-assisted instruction

with 16K, level II, Radio Shack TRS-80 computers has been used to facilitate student learning in mathe

matics and to provide qualified students with pro

gramming opportunities. Six approaches are used?

five prepared teaching programs and one BASIC pro

gramming program. The first approach uses drill and practice programs.

Using a stimulus-response mode, additional computa tional drill work is provided for students at many abil

ity levels. One example is a program on measuring length that displays the facsimile of a ruler and asks a

student either to name the length of a segment drawn

above the ruler or to draw a segment above the ruler

with a given length. The second approach uses tutorial programs to

teach students a mathematical concept in a step-by

step manner rather than require a one-step answer.

For example, a program for teaching the addition of

fractions asks the student to first, supply the common

denominator; second, change the fractions to equiva lent ones with a common denominator; third, add the

fractions and so on through the process. The com

puter will not proceed from one step to the succeeding step until each question is answered correctly. This

program appears particularly useful for slower stu

dents and for students who are absent when the mate

rial is originally presented.

Using competitive mathematical games that rein

force various mathematical concepts is another pro

gram alternative. Some of the programs adjust the

level of problem difficulty for each player independ

ently so that two students of unequal ability can com

pete against one another. These programs frequently make extensive use of the computer's graphics capa bilities. For example, in tug-of-war if a student an

swers the question correctly, the student's player pulls the opponent's player closer to the stream of water be

tween them. Play alternates until one of the players is

pulled into the water. The rules of the game are kept

simple so that the mathematical concept to be learned

is emphasized. The fourth approach uses simulation programs.

Programs that simulate management or career oppor tunities allow students to apply their mathematical

and general reasoning skills to a "real life" situation.

Students can manage a company, run for president, or

make congressional political decisions. These chal

lenging games are cross-referenced with the curricula

of other subject areas.

The fifth approach uses a program with a variety of

applications. Students discover how varying the inter

est rates, down payments, and pay-back time affects

monthly loan payments and how varying the coeffi

cients of a quadratic equation enhances the shape and

orientation of the graph of the curve. Such programs facilitate a more comprehensive study of these con

cepts because the computational time is reduced.

Programming allows students to design, run, and

document BASIC programs. Initial efforts are re

stricted to ten to twenty commands. With the com

mands, students generate simple programs such as

those dealing with area and volume. As student abili

ties increase, tables of multiples or factors are gener

664 Mathematics Teacher

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ated or solutions to word problems found in the text are computed.

Since each microcomputer represents an investment

of $800-$ 1000, the school is concerned that the effec

tiveness of each computer is optimized. As a result, as

sessing which students would best be served by use of

the computer on a particular day is done on an indi

vidual basis rather than on a rigid schedule or a rota

tion scheme. Thus, in addition to the time spent on

the computer during class, students are encouraged to

use the machines after school, before school, or during lunch periods.

The most difficult part of implementing the use of

computers in the classroom was acquiring good edu

cational software. A few of the programs were ac

quired from commercial software sources, but most of

the programs were written by the program director

and members of the faculty.

Although the six alternatives are not the only ways in which computers can be used in the classroom, the

Columbus schools have found these to be appropriate for the junior high school environment. For addi

tional information concerning the purchase or the use

of programs, contact Ralph G. White, Computer Pro

gram Director, Central Junior High School, 850 South

Highschool, Columbus, KS 66725.? White/Bennett

A High School Computer Programming Course

Comstock High School in Comstock, Michigan, has

developed a one-semester computer programming course and began an advanced course this past Sep tember. The course was developed to enhance the

learning of mathematics and to present students with

another career option. It emphasizes individualization

and the use of personal-interest projects. Flowchart

ing, documenting, tracing, debugging, and program

ming techniques through double-subscripted variables

are taught. At the beginning of the semester each student is

given an explanation of programming forms used,

programming techniques to be learned, BASIC lan

guage requirements for the six programs and the per sonal-interest project, and due dates. The course is in

dividualized with each student choosing and

designing programs based on his or her ability and in

terest.

For greater comprehension, the student designs and

constructs a flowchart, writes the program on a coding form, and then runs the program. Each program must

be well documented and the output clearly labeled.

Tracing forms are also completed for two of the pro

grams to aid in the debugging process. A debugging

analysis form has been developed that defines de

bugging techniques. The student checks the debugg

ing techniques used, lists each run date, and identifies

errors and the debugging response. Comstock time-shares through the Kalamazoo Val

ley School District using a DEC 11/34 minicomputer. There are four computer terminals in the school and

one microcomputer. Twenty to fifty students are in volved each semester with former students being used as programming consultants to help other students.

Supplementary books and periodicals are available in the classroom.

Students choose personal-interest programming projects during the second part of the semester in the areas of mathematics, science, business, music, farm

ing, nutrition, athletics, and so on, or they may write

utility programs for school staff members. These pro

grams are usually exhibited at local and regional sci ence fairs.

A variety of instructional techniques and activities are used to maintain student interest. Audiovisuals, lectures, textbook assignments, chapter tests, and the

programming assignments are the basis for assigning grades. Field trips to computer centers and program

ming contests with other schools highlight some of the semester's activities.

Plans have been made to integrate this program

ming instruction into the college preparatory mathe matics courses: algebra 1, geometry, algebra 2-trigo nometry, and precalculus. Two levels of some of these

college preparatory courses exist, so the present pro

gramming course is needed for students in the lower level courses.

Readers desiring additional information should write to Carol Cody, Mathematics Department Chair

person, Comstock High School, P.O. Box 369, Com

stock, MI 49041.?Cody/Bennett.

Computer Literacy

A study of Computer Impact on Society and Com

puter Literacy Courses and Materials was a project of

the Education Board of the Association for Comput

ing Machinery funded by the National Science Foun

dation. Project objectives were to review and catalog materials, courses, and programs related to computer and society courses, to provide methods of dissemina tion of such information; to identify minimum knowl

edge requirements for computer literacy; to develop behavorial objectives for various types of computer and society courses; and to develop decision mecha

nisms for such courses. During the first phase of this

project, an ACM committee developed a comprehen sive annotated bibliography of over two thousand ti

tles. This bibliography is managed by an information

storage and retrieval system developed at the Engi

neering Computing Laboratory at the University of

Wisconsin. Entries in the bibliography include the

identification of activity, area, function, level, and

type. This bibliography is now available on micro

fiche.

To develop ideas concerning the content, level, ob

jectives, and minimum requirements of courses in

computer impact on society and computer literacy the

ACM committee conducted panel sessions at confer

ences and discussions with various professionals from

education, government, and industry. The computer

literacy course is directed primarily to noncomputer

November 1981 665

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science majors for the purpose of providing sufficient

information and knowledge necessary for them to

function as informed citizens. Whereas, the course on

computer impact on society is directed at computer science or information systems majors or individuals

in computer-related occupations.

During the second phase of the project, the bibliog

raphy and the information storage and retrieval sys tem were expanded, workshops were conducted for

individuals other than computer professionals, and

position statements in the area of computer impact were developed and disseminated. Final products of

this project were guidelines for courses in computer

literacy and computer impact on society, suggestions for a taxonomy of the field, position papers on major issues relative to societal impact of computers, an up

dated bibliography, and a mechanism for the continu

ance of the bibliography. A final report of the study was made in the summer of 1980 and is reported in

the fall 1981 issue of the SIG/CAS Newsletter avail

able from the Association for Computing Machinery, 1133 Avenue of the Americas, New York, NY 10036.

For further information on the project, contact Rich

ard Austing, Department of Computer Science, Uni

versity of Maryland, College Park, MD 20742.?Pic

colino.

For page numbers of other projects relating to com

puters see the December index under the heading,

"Computers and Calculators."

NEW publications Code: Tj

= Textbook, junior high L = Library Ts = Textbook, senior high

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

Computing Texts

For page numbers of additional reviews of comput

ing textbooks, see the December index under the

heading "Computers and Calculators."

The Computer in the School: Tutor, Tool, Tutee

( ), Robert Taylor, ed. 1980, viii + 274 pp., $14.95

paper. Teachers College Press, 1234 Amsterdam

Ave., New York, NY 10027.

This book is absolutely required reading for those

parents, teachers, administrators, and others ponder

ing the role of computers in education at the second

ary or college level. Robert Taylor, who is director of

the Teachers College Program in Computing and

Education at Columbia University, has done a superb

job in assembling a collection of nineteen papers about the application of computing to education by five pioneering and noted authors in the field: Alfred

Bork, Thomas Dwyer, Arthur Luehrmann, Seymour

Pap?rt, and Patrick Suppes.

Taylor suggests a tutor/tool/tutee framework for

understanding the application of computing in educa

tion. In the tutor mode, the student is tutored by the

computer as in computer-assisted instruction. To

function in the tool mode, the computer performs sta

tistical analyses or word processing, for example. In

this modern day, the use of the computer as tutor and

tool can improve and enrich classroom learning with

out requiring student or teacher to have much techni

cal knowledge of the computer. To use the computer as tutee is to tutor or program the computer in the lan

guage it understands. This use of the computer can

shift the focus of education in the classroom from end

product to process, from acquiring facts to manipulat

ing and understanding them.

Anyone wondering either what role computers can

play in education or why their incorporation into the

curriculum should receive the highest priority should

certainly read this book from cover to cover. It is not

difficult to read and does not require prior computer

expertise.?Dale R. Comstock, Central Washington

University, Ellensburg, WA 98926.

Educational Software Directory: APPLE II Edition (L), Sterling Swift Publishing Co. 1981, vii + 103 pp., $9.95 paper. ISBN 0-88408-141-9. Sterling Swift Publishing Co., P.O. Box 188, Manchaca, TX

78652.

Brief descriptions of educational software for the

Apple II with the publisher's name and address, the

price, and the system requirements for its use.?Rich

ard H. King, Essex Junction Educational Center, Essex

Junction, VT 05452.

666 Mathematics Teacher

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