Random numbersAuthor(s): David MyersSource: The Mathematics Teacher, Vol. 77, No. 2 (February 1984), pp. 84-85Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963891 .

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reader reflections Reactions to articles and points of view on teaching mathematics

Tests on board I enjoyed reading "The 10-Minute

Mathematics Bulletin Board" by Glenn D. Allinger (September 1983) and would like to add to one of his suggestions.

For my freshmen students, I use

the top of a bulletin board to dis

play comics related to mathemat

ics. Underneath is the caption, "No

joke, I got a 100." Below the cap tion I display any perfect quiz or

test papers for that week. The bulletin board serves some

purposes in addition to those listed

by Allinger. The board ?llows the students to look ?t their peers' work, in which they often see sev

eral correct ways to work out the same problem. Some of the quizzes I give are fairly easy, thus giving average and below-average stu

dents a chance to be recognized and

to feel good about their mathemat ics skills. In addition, receiving a

perfect test score challenges

superior students and encourages them to check their work for care

less errors.

Allowing the students to contrib

ute to the classroom bulletin board is a good idea, because students feel

proud when one of their contri butions is displayed.

Barbara Zimmanck Krueger Ursuline Academy Cincinnati, OH 45221

No-borrow subtraction I have always used Bookman's

method for subtraction ("Reader

Reflections," September 1983, pp.

390, 392) and present it to my elementary school teacher prepara tion classes with the following ex

planation:

56 - 29 = (50 + 6) - (20 + 9)

Now, add 10 and then subtract

10. This process gives

(50 + 16) - (30 + 9) = 20 + 7 = 27,

as Bookman's explanation illus

trated. This method is the same as one

presented in 1880 in Ray's New

Higher Arithmetic (p. 28): "If any

figure exceeds the one above it, add

ten to the upper, subtract the lower

from the sum, increase by 1 the

Units of the next order in the sub

trahend, and proceed as before."

Lake Cornett Cooper Morehead State University Morehead, Y 40351

Teacher and textbook After reading the September issue, I felt compelled to add my two

cents worth about John Saxon and

his "ideal algebra book."

Better (ideal) books alone won't

solve our problems. Mathematics education doesn't depend exclu

sively on books but on the teacher

standing at the head of the class, chalk in hand. A good (ideal) teacher can use any book and achieve good r?sulte by converting the book into an "ideal" one during a lesson. Good teachers rewrit? textbooks each time they teach a

topic, tailoring the lesson to the

particular abilities and needs of

their students.

Unfortunately for students cur

rently in school, a shortage of such

mathematics teachers exists. No

textbook can compensate for that.

Julianna Csongor Gwyneed Mercy Academy Philadelphia, PA 19437

Random numbers Since the publication of my letter

"Randomness on a micro" (Septem ber 1983), I have discovered a bet ter way to generate random num

bers on the Apple II+ (thanks to Donald T. Piele, "How to Solve It?With the Computer," in Cre

ative Apple, Creative Computing Press, Morris Plains, N.J., 1982).

Memory locations 78 and 79 are

augmented continuously whenever the Apple is waiting for input from

the keyboard. Therefore, the

number

PEEK(78) + 256 * P?EK(79) is a random integer between 0 and

65535. Th? statement

LET X = RND(- PEEK(78) - 256 *

PEEK(79))

gives th? random-number

"Rich Problems" contest The Mathematics Teacher is sponsoring a problem-writing contest. The

problems entered in the competition should be original and appropri ate for junior high school students. Unique variations to existing prob lems are welcome. Anyone can enter. Each problem should be accom

panied by two extensions of that problem. All problems received will be reproduced and distributed to persons

attending a "Rich Problems" contest session at the NCTM Annual

Meeting in San Francisco, 25-28 April 1984. Participants in the session

will be asked to solve and rate these problems. The most popular ones

will be published in the Mathematics Teacher with credit given to the

authors. All problems will become the property of the NCTM, and

problems in all content areas, including those that require a computer to aid in the solution, will be considered. Problems should be mailed to

the address below.

"Rich Problems" Contest

Mathematics Teacher 1906 Association Drive

Reston, VA 22091

Each problem and its two extensions must be typewritten, single

spaced, on a separate sheet of 8^-by-11-inch paper. The answer and th?

author's name and address should be typed on the back of the sheet.

The deadline is 1 March 1984.

g4_??_ ?Mathematics Teacher

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generator this random seed to start with (the X is entirely a dummy variable). This procedure causes

the computer to give a different se

quence every time it is turned on.

David Myers The Winsor School

Boston, MA 02215

Mathemusical notes Due to publication deadlines, our

article entitled "Sound Foun

dations: A Mathemusical Game Simulation That 'Stanza Part' from

the Rest" was not able to include

several recent developments rela

tive to the course.

1. 95 percent of the group that

completed the program in June

1983 passed the Regents Compe tency Test. Over 90 percent of these

students chose to take a mathemat ics elective this year.

2. We instituted two field trips

during the spring that we plan to

repeat in the course. One trip is a

tour of a recording studio that

highlights the mathematics behind

the recording and business ends of

the studio. A second trip, to a book

ing agency, scrutinizes the mathe

matics in marketing a band. The

students thoroughly enjoyed this

experience. 3. The recent boom in cable TV

music-video channels added a new

"milestone" to our band's travels?the behind-the-scenes

mathematics inherent in producing this new art form.

4. We've been inundated with

inquiries regarding our course and

hope to meet with as many people as we can during our speaking en

gagements at the NCTM confer ences in Houston and San Fran cisco this spring.

Finally, we would like to dedicate our article to the memory of Jules L. Gerver, without whose encour

agement our ideas may never have

reached the mathematics commu

nity. Robert Gerver Richard J. Sgroi North Shore High School Glen Head, NY 11545

Dozenal dealings Anne Petty's letter on "dragon arithmetic" was terrific (September 1983). In this computer age, an un

derstanding of number bases, espe

cially the binary and hexadecimal

systems, is important.

problems of the month

These problems were selected for publication at the "Best Prob lems Contest" session sponsored by the Editorial Panel of the

Mathematics Teacher at the 61st Annual Meeting of the National Council of Teachers of Math ematics in Detroit.

1. Walking up an inoperative escalator takes ninety seconds. The trip takes sixty seconds when the escalator is working. How

long would the trip take if a

person walked up the moving escalator??Lynda Honryak, 4706

Echo Glen Drive, Pittsburgh, PA 15236.

2. Find the ratio of the area of

triangle RVW to the area of trap ezoid STVW.?Roger Enge, Uni

fi

versity of Wisconsin, Eau Claire, WI54701.

3. Grant the Ant crawled two

miles north, then one mile east, then one-half mile south, then

one-fourth mile west, one-eighth mile north, one-sixteenth mile

east, ad infinitum. The point on

which Grant converged (where he was found going around in cir

cles) was how many miles from

his starting point??SP5 Bruce D. Beckett, Company A, USA ARMC #17, Fort Knox, KY 40121.

Answers appear on page 151.

Free information on counting in base twelve is available from the

Dozenal Society of America, De

partment of Mathematics and

Computer Science, Nassau Com

munity College, Garden City, NY 11530.

Gene Zirkel Nassau Community College Garden City, NY 11530

Cover designs

The Editorial Panel of the Mathe matics Teacher welcomes sugges tions for a cover design for the 1985 issues. Please submit color draw

ings or slides by 15 February to the

Managing Editor, NCTM, 1906 As

sociation Drive, Reston, VA 22091.

TODAY'S TWISTER A Daily Math Enrichment Program

180 problems, unusual variety, answers, notes.

4 to a page in quadrants for easy copying. 3-week supply is made in a few minutes.

Students like this instructive program.

See article this issue, "Pre-Algebra Mathematics

for Above-Average Students" for details of con

tent, use, and value.

$8.00 includes postage Paul G. Dickie

26 Lynne Road, Sudbury, MA 01776

February 1984-85

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