The AMATYC Review
A refereed publication of the American
Mathematical Association of Two-Year Colleges
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| From the Editor |
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Articles
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Regular Articles
- Notes From the Mathematical Underground by Alain
Schremmer
- Book Review Edited
by Sandra DeLozier Coleman
- Software Review Edited
by Brian E. Smith
- The Problems Section Edited
by Stephen Plett and Robert Stong
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Advertisers Index
AMATYC Institutional Members
AMATYC Reviewers
AMATYC Executive Board and Committees
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College Algebra Reform Through Interdisciplinary Applications
William P. Fox, Jane E. Gower, George E. Schnibben, Jr.,
Elizabeth Gasque, and Richard D. West
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William Fox is professor and chair at Francis Marion University.
He received his PhD at Clemson University. His interests include
mathematical modeling and real world applications. wfox@fmarion.edu
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Jane Gower is an instructor in the mathematics department
at Francis Marion University. She has an MS in mathematics education
from North Carolina State University. Her interests include using
Geometer's Sketchpad in trigonometry. jgower@fmarion.edu
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George Schnibben is a professor in the mathematics department
at Francis Marion University. He received his PhD in mathematics
from Clemson University. His interests include mathematics history.
gschnibben@fmarion.edu
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Elizabeth Gasque is an assistant professor in the mathematics
department at Francis Marion University. She received her PhD
in mathematics education from the University of South Carolina.
Her interests include T3 and preparing mathematics
teachers for tomorrow. egasque@fmarion.edu
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Richard West is an assistant professor in the mathematics
department at Francis Marion University. He received his PhD
in mathematics education from New York University. His interests
include interdisciplinary applications in mathematics. rwest@fmarion.edu
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FMU has been teaching college algebra since the school’s
establishment in the early 1970s. We tried an experiment using
applications and projects to motivate college algebra students.
Our students had many positive comments about the experience.
In this article, we give a few illustrative examples of the applications/projects
used in our courses, and we share some student comments about
the courses. Based on the overall positive experience, two new
freshmen algebra courses were added using modeling and problem
solving as their framework.
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College Algebra With Applications: Mathematics for Biology
Catherine M. Miller and Tamara B. Veenstra
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Catherine M. Miller is professor of mathematics education
at the University of Northern Iowa. She received her PhD from
the University of Arizona. In addition to teaching classes for
mathematics and mathematics education majors, she is interested
in teacher cognition and pedagogical content knowledge. millerc@math.uni.edu
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Tamara B. Veenstra is professor of mathematics at the University
of Redlands in California. She received her PhD from Dartmouth
College. Her research interests include many topics in number
theory, especially student projects and educational issues related
to teaching mathematics. tamara_veenstra@redlands.edu
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Abstract not available
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The Effect of an Integrated Learning System on Two-Year College
Students
Angela T. Barlow
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Angela T. Barlow is assistant professor of mathematics at
the State University of West Georgia. She received her PhD in
mathematics education from Auburn University. In addition to teaching
mathematics content courses for preservice K-8 teachers, she is
interested in the role technology plays in the mathematics classroom.
abarlow@westga.edu
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The purpose of this study was to investigate the effectiveness
of an integrated learning system in terms of algebra achievement,
mathematical attitude, and mathematical anxiety. During Spring
Semester 1999, students enrolled in elementary algebra at a
community college participated in the study. The non-computer
group received teacher-led instruction, while the computer group
received instruction via Learning Logic, an integrated learning
system designed to teach algebra.
At the beginning and at the end of the semester, students responded
to the Descriptive Tests of Mathematics Skills (Elementary Algebra
subtest), Aiken’s Mathematics Attitude Scale, and the Phobus,
a mathematics anxiety scale. T tests analyzed the responses
to each instrument. On the algebra pretest, the analysis found
no significant difference between the computer group and the
non-computer group. Low power was a concern for this analysis.
On the post-test, however, the computer group scored significantly
lower than the non-computer group. In terms of attitude for
the computer group, a t test revealed no significant
difference for a medium or large effect between pre-course attitude
and post-course attitude. Similarly, for the computer group
pre-course anxiety was not significantly different from post-course
anxiety for a medium or large effect. Gender comparisons were
made for the computer group in terms of achievement, attitude,
and anxiety. While analyses revealed no significant differences,
low power limited the interpretations of these analyses. Results
suggested that Learning Logic, as implemented in this study,
was not as effective as teacher-led instruction for teaching
elementary algebra in this community college with regard to
achievement.
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Adapting a Workshop Calculus Model to College Algebra: Instructional
Challenges
Teri J. Murphy and Kathy Wahl
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Teri J. Murphy is associate professor in the Department of
Mathematics at the University of Oklahoma. tjmurphy@math.ou.edu
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Kathy Wahl is a teaching associate at the
University of Illinois at Urbana-Champaign. wahl@math.uiuc.edu
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Abstract not available
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A Commonsense Approach to the Precalculus Presentation of
Complex Numbers
Edwin F. Moats
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Edwin F. Moats received his MS degree in mathematics from
Western Washington University in Bellingham,WA, his MA in philosophy
from Colorado State University, and his JD in law from Case Western
Reserve University. He has been a community college mathematics,
logic, and law instructor. His principal mathematical area of
interest is analysis. edmoats@yahoo.com
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Complex numbers are typically introduced to students in precalculus
courses as a device necessary for finding roots of quadratic functions
with negative discriminants. This approach is misleading to students,
both historically and mathematically. In these presentations,
students learn to competently perform algebraic manipulations
to find roots of quadratics over the complex field, but they never
learn what a complex number is.
Rarely is it mentioned that complex numbers are
not quantities in the ordinary sense; that you cannot go to the
grocery store and buy 3 + 2i dozen eggs. The student is inevitably
left with the impression that complex numbers are "imaginary"
in the sense of some amalgamation of magic and fiction, justly
characterized by Leibnitz as "that amphibian between existence
and nonexistence."1
My pedagogy of complex numbers is based upon
on my conviction that students have a right to know the truth
about the complex numbers: that they constitute the E2 vector
space with the peculiar complex multiplication defined thereupon.
The implementation of this pedagogy calls for deferring the presentation
of complex numbers until students have a sufficient foundation.
This means presenting complex numbers immediately after presenting
E2 vectors, and presenting E2 vectors immediately after right
triangle trigonometry.
1 Needham, T. (1997). Visual
complex analysis. Oxford: Clarenden Press, p. 1.
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The Method of Gnomons and a New Scheme for Approximating
Square Roots
Steven J. Kifowit
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Steve Kifowit is associate professor of mathematics and chair
of the Mathematics Department at Prairie State College. skifowit@prairiestate.edu
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Abstract not available
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Entry-Level College Mathematics: Algebra
or Modeling
Dan Kalman
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Dan Kalman is associate professor of mathematics
and statistics at American University. His interests include matrix
theory, curriculum development, and instructional technology,
particularly the Mathwright software. Kalman has won three writing
awards from the MAA and is the author of a book on mathematical
modeling. kalman@american.edu
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In the past several years there has been increasing discussion
of elementary mathematical modeling as an entry-level college
course. In several institutions, modeling is now offered as an
alternative to the more traditional college algebra course, and
students can choose to complete a modeling course in fulfillment
of a general education requirement. Of course, not everyone agrees
with this approach. How can math teachers make an informed choice
between college algebra and modeling? This paper argues that no
such choice is necessary, for many of the instructional goals
of the college algebra course can be addressed in a modeling course.
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The Cube Root Fallacy: Does
(1 + z)3 = z3 Imply That
1 = 0?
John Mathews
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John Mathews earned his doctorate at Michigan State University.
He is currently teaching at California State University, Fullerton,
where he is active in the areas of complex analysis and numerical
analysis. Ongoing projects embrace the pedagogical use of computers
to enhance the teaching of mathematics at the university level,
and he is the author of two textbooks. mathews@fullerton.edu
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Abstract not available
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Optimizing Functions of One Variable without
Calculus
William B. Gearhart and Harris S. Shultz
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William B. Gearhart received his BS degree in engineering
physics and his PhD in applied mathematics from Cornell University.
He is currently professor of mathematics at California State University,
Fullerton. His research interests include approximation theory,
numerical analysis, optimization theory, and mathematical modeling.
wgearhart@fullerton.edu
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Harris S. Shultz, professor of mathematics
at California State University, Fullerton, received his BA degree
in mathematics from Cornell University and his PhD in mathematics
from Purdue University. He has directed numerous institutes for
secondary mathematics teachers and has been a frequent contributor
to The AMATYC Review. hshultz@fullerton.edu
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Abstract not available
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