ERIC ED373817: The AMATYC Review, Volume 15, Numbers 1-2, Fall 1993-Spring 1994.

189 Pages·1994·4.6 MB·English

by  ERIC

DOCUMENT RESUME
JC 940 466
ED 373 817
AUTHOR Browne, Joseph, Ed.
The AMATYC Review, Volume 15, Numbers 1-2, Fall
TITLE
1993-Spring 1994.
American Mathematical Association of Two-Year
INSTITUTION
Colleges.
ISSN-0740-8404
REPORT NO
PUB DATE
94
NOTE
189p.
.t
AMATYC Treasurer, State Technical Insti
AVAILABLE FROM
Memphis, 5983 Macon Cove, Memphis, TN 38134 (2 issues
free with $25 annual library subscription fee).
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AMATYC Review; v15 n1-2 Fall-Spr 1993-1994
JOURNAL CIT
MF01/PC08 Plus Postage.
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*College Mathematics; Community Colleges; Computer
DESCRIPTORS
Simulation; Functions (Mathematics); Linear
Programming; *Mathematical Applications;
*Mathematical Concepts; Mathematical Formulas;
*Mathematics Instruction; Mathematics Teachers;
Technical Mathematics; Two Year Colleges
ABSTRACT
Designed as a-avenue of communication for mathematics
educators concerned with the views, ideas, and experiences of
two-year college students and teachers, this journal contains
articles on mathematics exposition and education, and regular
features presenting book and software reviews and math problems.
Volume 15 includes the following articles: "Two Mollweide Equations
Detect Triangles," by David E. Dobbs; "Using Recursic.n To Solve a
Probability Problem," by Thomas W. Shilgalis and James T. Parr;
"Calculus to Algebra Connections in Partial Fraction Decomposition,"
by Joseph Wiener and Will Watkins; "Guidelines for the Academic
Preparation of Mathematics Faculty at Two-Year Colleges: A Report of
the Qualification Subcommittee of AMATYC"; "Fractals and College
Algebra," by Kay Gura and Rowan Lindley; "Using Computer Technology
Quantitative
as an Aid in Teaching the Introductory Course in
Methods," by Joseph F. Aieta, John C. Saber, and Steven J. Turner;
"Summing Power Series b: Constructing Appropriate Initial Value
Problems," by Russell J. Hendel and John D. Vargas; "Simpson's
Paradox and Major League Baseball's Hall of Fame," by Steven M. Day;
"The Ubiquitous Reed-Solomon Codes," by Barry A. Cipra; "Predicting
Grades in Basic Algebra," by Elsie Newman; "Why Do We Transform
Data?" by David L. Farnsworth; and "Student's Perceptions of Myths
about Mathematics," by Victor U. Odafe.
(KP)
***********************************************************************
*
Reproductions supplied by EDRS are the best that can be made
from the original document.
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THE A ATYC REVIE
Published by the
AMERICAN MATHEMATICAL ASSOCIATION OF TWO-YEAR COLLEGES
VOLUME 15, NUMBER 1
Fall 1993
U S. DEPARTMENT OF EDUCATION
Odic, of Educational RIfircn and unproutment
"PERMISSION TO REPRODUCE THI:
EDUCATIONAL RESOURCES INFORMATION
MATERIAL HAS BEEN GRANTED Bt
CENTER (ERIC)
J. Browne
7.Th.s COcurnent NIS been reproduced as
,ece.ved from ine persOn Or organliat.on
ong,nanng .1
M.n0, cnanges nave been made to improve
reproduction aualtly
Points &view or Opinions stated mINSCOCu
ment Co nOt neCeSSantv represent othoal
TO THE EDUCATIONAL RESOURCE
OE RI position or 00t Cy
INFORMATION CENTER (ERIC).-
A glimpse rf the Mandelbrot Set
ALSO IN THIS ISSUE
C3
Guidelines or Faculty Preparation
Final Report
Web Puzzles
2
- "Dalmation Damation"
BEST COPY AVAILABLE
DEVELOPMENTAL MATHEMATICS 1994
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The Official Journal of the
American Mathematical
Association of
Two-Year Colleges
PURPOSE: AMATYC remains committed to its original purposes:
To provide a national forum for the exchange of ideas
To further develop and improve the mathematics education of students of two-year colleges
To coordinate activities of affiliated organizations on a national level
To promote the professional development and welfare of its members
The AMATYC Review provides an avenue of communication for all mathematics
educators concerned with the views, ideas and experiences pertinent to two -year college
teachers and students.
SUBMISSION OF MANUSCRIPTS: Manuscripts must be typed, doubled-spaced,
on
one side of 8-1/2" x 11" paper. They should not have been published before, nor should
they be under consideration for publication elsewhere. Photographs should be black and
white glossy prints. To provide for anonymous reviews, the author's name and affiliation
should appear on a separate title page. The title should also appear on the first
page of the
exposition. Authors are advised to consult the Publication Manual of the American
Psychological Association. A guideline for authors is available from the editor. Five copies
of each manuscript should be submitted to Joseph Browne, Onondaga Comm. College,
Syracuse, NY 13215.
PHOTOCOPYING AND REPRINTS: General permission is granted to educators to
photocopy material from The AMATYC Review for noncommercial instructional
or
scholarly use. Permission must be sought from the authors in order to charge for
photocopies, to quote material in advertising, or to reprint articles in other educational
publications. Once permission is obtained, credit should be given to the
source of the
material by citing a complete reference.
ADVERTISING: For information concerning advertising rates and schedules, contact the
advertising manager, Larry Gilligan, at the address given below.
STAFF
Editor:
Joseph Browne, Onondaga Community College, Syracuse, NY 13215, [phone]
Production:
Jane Covillion, Onondaga Community College, Syracuse, NY 13215, [phone]
Advertising:
Larry Gilligan, OM1 College of Applied Science, Cincinnati, OH 45206 [phone]
EDITORIAL PANEL
Mike Davidson
Cabrillo College
Aptos, CA
James Fryxell
College of Lake County
Grayslake, OH
Brian Hickey
East Central College
Union, MO
Charlotte Newsom
Tidewater Community College
Virginia Beach, VA
Dennis Reissig
Suffolk County Community College
Sclden, NY
Nelson G. Rich
Nazareth College
Rochester, NY
Mary Robinson
U. of New Mexico, Valencia Campus
Los Lunos, NM
Larry Runyon
Shoreline Community College
Seattle, WA
Carla Thompson
Tulsa Junior College
Tulsa, OK
Jacqueline Thornherry
DcKalh College
Clarkston, GA
August Zarconc
College of DuPage
Glen Ellyn, IL
PUBLICATION: The AMATYC Review is published twice a year in the Fall and Spring.
ISSN 0740-8404
4
Volume 15, Number 1
Fall 1993
The AMATYC Review
TABLE OF CONTENTS
p. 4
EDITOR'S COMMENTS
p. 4
LETTER TO THE EDITOR
P. 5
ABOUT THE COVER
p. 6
THE AMATYC REVIEW GUIDELINES FOR AUTHORS
VIEWPOINT
P. 8
Time, Indeed, for a Change in Developmental Mathematics
by Jack W. Rotman
MATHEMATICAL EXPOSITION
p. 13
Two Mollweide Equations Detect Triangles
by David E. Dobbs
p. 20
Using Recursion to Solve a Probability Problem
by Thomas W. Shilgalis and James T. Parr
p. 28
Calculus to Algebra Connections in Partial Fraction Decomposition
by Joseph Wiener and Will Watkins
SHORT COMMUNICATIONS
p. 32
Web Puzzle
by Don St. Jean
p. 36
The Prime Division Method of Finding the Greatest Common Factor
by Terence Brenner and Michael Shapira
p. 38
Dalmat ion Darnation
by Kathy Sparling
MATHEMATICS EDUCATION
Guidelines for the Academic Preparation of Mathematics Faculty
p. 40
at Two-Year Colleges
A Report of the Qualifications Subcommittee of AMATYC
p. 51
Fractals and College Algebra
by Kay Gura and Rowan Lindley
Using Computer Technology as an Aid in Teaching the Introductory Course
p. 57
in Quantitative Methods
by Joseph F. Aieta, John C. Saber, and Steven J. Turner
REGULAR FEATURES
p. 64
The Chalkboard
Edited by Judy Cain and Joseph Browne
p. 67
Software Reviews
Edited by Shao Mah
p. 71
Book Reviews
Edited by John J. Edgell, Jr.
p. 74
The Problem Section.
Edited by Michael W. Eckcr
p. 82
Mathematics: An International View
Edited by Igor Malyshev and Joanne Rossi Becker
5
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College Algebra with Graphing
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Geometry, Second Edition
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Editor's Comments
Thanks to several of you for writing or calling with your comments on the last
issue (my first one). The encouraging remarks are appreciated, and the suggestions
are being considered.
Lucky Larry Correction
Several readers pointed out that in "Lucky Larry #3" Larry made one too many
(or is it one too few) errors. The last line should read "- 2 < x." Enid M. Nagel
added a few thoughts on how we should be teaching "Lucky Larry" and others.
See her letter below.
Call for Papers
In this issue you will find an article by Gura and Lindley on the inclusion of
fractals and chaos in a college algebra course. I would welcome a few more
articles on including these topics in courses aimed at the first two years. Another
area of considerable interest recently is collaborative learning. One aspect that
seems to need more treatment is methods of collaborative assessment, with
safeguards to prevent a loafer from passing when all the work is done by
groupmates.
Letter to the Editor
To help Lucky Larry out of the dilemma of manipulating algebraic symbols
willy filly, I suggest that this problem [Lucky Larry #3, Spring, 1993] be solved
using a graphing calculator or a computer graphing program. If Larry graphs
3, the result is a
f(x)
2x
5 ry
hyperbola [see graph]. Larry can
then easily see the values of x for
4
which this function is greater than
3
zero, since the graph will be
2 1-
above the x-axis. Instead of
repeatedly trying
instill
to
algebraic manipulations into our
2
3
students, let's help them look at
problems differently using the
-a /
technology that is available to us.
-3 .1
-4 TI
Enid M. Nagel
Cincinnati OH
'7
4
About the Cover
A close up view of a boundary region of the Mandelbrot set reveals many
examples of the concept of "self-similarity" as well as a near copy of the
Mandelbrot set itself. The set may be defined as follows: Let co be a complex
number and define a sequence by c = c _12 + cn_ t.
If the sequence is bounded,
co is in the Mandelbrot set. As might be expected, all points in a nearly round set
near the origin. are in the set. The boundary, however, is not a simple convex
curve, but rather a fuzzy area with nearby points exhibiting vastly different
behavior (which is referred to as chaos).
For most choices of c the arithmetic quickly becomes messy and is given to a
computer. Indeed, such sets were not significantly investigated before the
computer was available. This, in turn, leads to some interesting discussion on how
a computer with approximate arithmetic can determine convergence or divergence
of the sequence. Altering the criterion used can sometimes have profound effect
on what points are included.
More spectacular pictures are generated when points for which the sequence
diverges are colored differently according to how fast it diverges. A typical routine
counts how many terms are needed to get more than two units from the origin. The
cover picture was originally in 16 colors, with the black region (lower left) being
the Mandelbrot set. The three-dimensional appearance is an illusion since we have
merely selected a color for each point according to its behavior in the sequence.
There are now several software packages on the market for exploring chaos,
the Mandelbrot set, and fractals (entities with fractional dimension). A fast
computer, math co-processor, and high-resolution graphics display are highly
desirable. The cover was produced by "Chaos: the Software" (Autodesk, Inc.)
which was issued to accompany James Gleick's excellent introductory book,
Chaos: Making a New Science.
Lucky Larry #6
(Lucky Larry is the infamous student who, in spite of making numerous errors,
manages to get right answers. Send your samples of his work to the editor for
inclusion in future issues.)
(Lucky Larry vs Pythagoras) The object was to find the missing side. Lucky
Larry proceded as follows:
x2 = 13 + 12
= 25
13
x = 5
Submitted by Sharlene Cadwallader
Mt. San Antonio College
12
Walnut CA 91789
5
8
TYC Review
The A
Guidelines for Authors
The AMATYC Review is a semi-annual publication of the American Mathematical
Its purpose is to provide an avenue of
Association of Two-Year Colleges.
communication for all mathematics educators concerned with the views, ideas,
and experiences pertinent to two-year college teachers and students.
Subject Matter: The AMATYC Executive Board has identified the following
priority areas:
a. Developmental mathematics
b. Technical mathematics
c. Mathematics content of the two-year college curriculum
d. Educational theory and practice
e. Academic computing
f. Research in mathematics education in the two-year college
g. Equal opportunity in mathematics
h. Problems, issues, and trends in two-year college mathematics
Perspective: No article should simply be a rewrite of a topic readily available
from other sources. Preferably, articles should present traditional concepts
with a new perspective, give extensions to such materials, or reach out just
beyond our current teaching content for enrichment. Articles devoted more
to methodology than to exposition may be either research-oriented or
descriptive case studies. Authors are encouraged to offer personal opinions
and suggestions. Letters to the editor may be used as a format to comment
controversial topics, or
on previously published articles, to offer opinions on
to offer short expository notes.
Computers and Calculators: Technology-oriented articles may be grouped into
two, not necessarily distinct, categories: technology used as a teaching aid
and technology used as a mathematical tool. In either case, the major intent
of an article should be to help teachers and students to learn about
mathematics, not about the machine or software. References to technology
should be as generic as possible (e.g. "using a computer algebra system we
find..." rather than "using Derive's [specific command] on an IBM PS/2-55
yields [specific output]"). Program listings, specific commands, and
sequences of button pushes are usually inappropriate, though short segments
(mathematical
may be included when they are essential to understanding the
or pe -agogical) point being made.
Regular Features: Authors are invited to submit reviews of books and computer
software with which they are thoroughly familiar. The materials should be
of exceptional interest (outstanding/poor) to our audience. The Problem
Section depends on reader involvement, and the other features incorporate
Please communicate directly with the
reader input on a regular basis.
columnists. (There is no need of five copies of anything submitted for the
columns; one will do.)
9
6
Review Criteria: The AMATYC Review is
a refereed publication. Each
appropriate submission is reviewed by three mathematics
educators: two
members of the review panel and a member of the Editorial Board.
The
Editorial Board member will analyze all reviews and
make a
recommendation to the Editor on the acceptance
or rejection of an article.
The Editor makes final decisions on the publication of articles.
The following review criteria are used:
a. relevance to two-year college mathematics content or pedagogy
b. significance of topics
c. originality
d. accuracy of content
e. explicit, clear, logical, and concise writing style
f. appropriate length and format
In general, The AMATYC Review is seeking lively articles
dealing with
topics that will enrich the reader's mathematical background
or help the
reader improve his or her classroom teaching.
Manuscript Style:
Articles may vary in length from less than
one page up to
about 15 pages (typed, double spaced, with wide margins).
Brief, "to the
point," articles are encouraged.
Illustrations should preferably (but not
necessarily) be camera ready and be placed on separate
pages from the text.
Graphics produced on dot matrix printers usually reproduce
poorly and
should be avoided.
The AMATYC Review uses the Publication Manual of the
American
Psychological Association (Washington DC)
as its style reference. In particular,
note that the author-date method is used for citations within the text,
e.g.
Smith and Jones (1987) demonstrated that....
The reference list at the end of the article should include only the
sources
that were used in the preparation of the article.
References should be
arranged in alphabetical order by the surname of the first author,
e.g.
Smith, John R., & Jones, David (1987).
Sets with missing elements.
The AMATYC Review, 7(2), 104-113.
Wallace, Donald P. (1992). Digital arithmetic: counting
on your fingers
(2nd ed.). Centerville: Farber and Sons.
To provide for anonymous reviews, the author's
name and affiliation should
appear (only) on a separate title page. The title should also appear on the
first page of the exposition.
Submission: Send five copies of articles for possible publication
to: The
AMATYC Review, Joseph Browne, Editor, Onondaga Community
College,
Syracuse, NY, 13215.
The method of "postull:ting" what
we want has many advantages;
they are the same as the i.eivantages of theft
over honest toil.
Bertrand Russell
10
7