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The
AMATYC Review
A refereed publication of the American Mathematical
Association
of Two-Year Colleges
Editor: Barbara
S. Rives, Lamar State College
Production Manager: John
C. Peterson
Abstracts
Fall 2003 issue, Vol.
25, No.1
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The
National Numeracy Network
Promoting Quantitative Literacy For College Graduates
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Susan L. Ganter is associate
professor of mathematical sciences at Clemson University.
She has directed several local and national evaluation
studies, including a residency at the National Science
Foundation in which she investigated the national impact
of the calculus reform initiative and helped to develop
the evaluation plan for several programs in the Division
of Undergraduate Education. She is currently Director
of the National Numeracy Network, an organization developed
by the National Council for Education and the Disciplines
at the Woodrow Wilson National Fellowship Foundation
for the purpose of promoting quantitative literacy beyond
mathematics. In addition, her work has included partnerships
with industry that promote outreach to secondary mathematics
students as well as professional development opportunities
for secondary mathematics and science teachers. Dr.
Ganter was formerly the Director of the Program for
the Promotion of Institutional Change at the American
Association for Higher Education and a member of the
Mathematical Sciences faculty at Worcester Polytechnic
Institute.
sganter@clemson.edu |
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In this increasingly technological age, the average
citizen is confronted with a wealth of quantitative
knowledge that can be overwhelming. An important part
of the movement to promote quantitative literacy (QL)
necessary in such a society is the design and formation
of the National Numeracy Network (NNN). NNN is working
to assist sites that are developing QL programs, and
to create and maintain communication links between
these sites and other constituencies. This article
discusses educational goals for QL, as well as the
activities of NNN. (back to top)
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Implementing
"Best Practices"
in a Developmental Mathematics Summer Bridge Program
Frances Kuwahara Chinn
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Frances Kuwahara Chinn is a professor
of mathematics education in the Charter College of Education
at Cal State University, Los Angeles. She received her
PhD from Claremont Graduate School. In addition to teaching
mathematics methods courses for prospective teachers,
she teaches courses in the MA Degree in Education: Option
Mathematics Education. Her special interest lies in
critical mathematics education.
fkuwaha@calstatela.edu
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| The Summer Bridge
Program at CSULA provides a developmental transition
from high school to university life for approximately
300 low-income, first generation freshmen of diverse
ethnicity and cultures. The program is organized into
a learning community composed of students and a skilled
team of faculty, staff, counselors, and assistants,
working together to ensure both the academic and personal
development of all Summer Bridge participants. The mathematics
component begins at the current skills level of the
students and closes the gap between previous schooling
and university-level work by using a constructivist
pedagogical approach to learning. This paper describes
that approach and how it also changes negative attitudes
and behaviors that have been conditioned by the participants'
previous experiences. (back to top) |
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A Note
on Polynomials and Their Derivatives
Ronald Skurnick
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Ronald Skurnick teaches
mathematics at Nassau Community College. His research
interests include graph theory, combinatorics, number
theory, and calculus. He currently serves as a referee
for three mathematics journals.
skurnir@ncc.edu
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| In this article,
we present several formulas that exhibit just how intimately
polynomials are related to their derivatives. We then
apply some of these formulas to derive Maclaurin series
expansions of certain functions for which such expansions
are not readily available. (back to top) |
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The Sphere
Game
Alfred P. Lehnen and Gary E. Wesenberg
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Al Lehnen is a mathematics
instructor at Madison Area Technical College in Madison,
Wisconsin. He received his PhD in physics from the University
of Wisconsin-Madison. He is always looking for interesting
problems that can be solved using elementary methods.
alehnen@matcmadison.edu
Gary Wesenberg is a programmer/analyst in the
Biochemistry Department at the University of Wisconsin-Madison.
He has a PhD in chemistry from this same institution.
He has an extensive background in mathematical modeling
and scientific programming. He proposed and solved
the sphere game while working on a model of protein
folding.
gary@biochem.wisc.edu
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| This work reports
a solution to the following problem: To within a fixed
tolerance, what is the most probable straight line distance
between a fixed point and a second point picked at random
from the surface of a sphere? The surprising results
in three dimensions are values near the diameter. The
paper first reviews Bertrand's Paradox, which concerns
aspects of the same problem in two-dimensions. The probability
distribution of the distance in three dimensions is
then analyzed from several points of view and, in particular,
it is shown that the mode or most probable value of
this distance is the sphere's diameter. (back
to top) |
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Factoring
Quadratics Part II
Lance E. Hemlow
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Lance E. Hemlow is an assistant
professor of mathematics at Raritan Valley Community
College. He received two Masters degrees, one in mathematics
at Western Connecticut State University and one in mathematics
education from Rutgers University. He is currently working
towards his PhD in mathematics education at Rutgers
University. His interests include statistics, calculus,
and applications of mathematics.
lhemlow@raritanval.edu
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| Factoring Quadratics
Part II is an extension of Stephen Kaczkowski's article,
Factoring Quadratics (Kaczkowski, 2001), on factoring
quadratics whose polarity of the constant term is positive
or negative. This article extends that concept to the
polarity of the middle term and the constant term, and
shows how to generate quadratics that factor under all
four cases. It also points out the connection to consecutive
integers and a connection to Kaczkowski's paper. |
| Reference |
| Kaczkowski, S. (2001).
Factoring quadratics. The College Mathematics Journal,
32(3), 203-204. The Mathematical Association of
America. (back to top) |
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Embedding Study Skills into
a Developmental Algebra Course
Robert D. Lewis and Katherine H. Clark
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Rob Lewis received his BS
and MAT degrees in mathematics from Duke University
and his PhD from Oregon State University. He has taught
junior and senior high school level mathematics as well
as the full spectrum of math courses offered at Linn-Benton
Community College. His primary interest is in the process
of how people, from childhood to adult, learn and overcome
barriers to learning mathematics.
lewisr@gw.lbcc.cc.or.us
Katherine H. Clark has taught in developmental
studies at Linn-Benton Community College for over
25 years. After earning degrees in theater and English
literature at University of California at Santa Cruz,
she earned her MA in education of English at Stanford
University. In addition to teaching classes in study
skills and writing, she collaborates with other departments
to increase student success through improving student
study strategies within the classes in which they
use them.
clarkk@gw.lbcc.cc.or.us
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| Many community college
students have difficulty in mathematics due to poor
mathematics learning skills. This paper describes strategies
and results of a project which significantly improved
student success by embedding mathematics-appropriate
study skills into a developmental algebra class, while
maintaining department course requirements and standards
and even increasing course completion rates. (back
to top) |
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The Circle of Curvature:
It's a Limit!
John H. Mathews
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John Mathews earned his doctorate
at Michigan State University. He teaches 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. He is the author of two textbooks.
mathews@fullerton.edu |
| The standard derivation
for the radius of curvature involves the rate of change
of the unit tangent vector along the curve y=f(x).
The derivation in this article starts with the collocation
circle C(x0,h) that passes through
the three points (x0,f(0)),(x0-h,
f(x0-h)), and (x0,+h, f(x0,+h)).
Then the software Mathematica is used to solve the three
nonlinear equations |
(x0-a)2+(f[x0]-b)2=r2
(x0-h-a)2+(f[x0-h]-b)2=r2
(x0+h-a)2+(f[x0+h]-b)2=r2
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| for the center (a,
b) and radius r. When the limit is taken
as , the result is the standard formula for the radius
of curvature, and as a bonus, formulas for a and b are
also derived. (back to top) |
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Equal
Volume = Equal Surface Area?
An Investigation of Hazardous Liquid Containers
Katherine G. McGivney, Jean M. McGivney- Burelle,
Thomas C. DeFranco, and Raymond J. McGivney
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Kate McGivney is an assistant
professor of mathematics at Shippensburg University.
She earned her PhD in mathematics at Lehigh University.
kgmcgi@ship.edu
Jean McGivney-Burelle is an assistant professor of mathematics
education in the Neag School of Education at the University
of Connecticut. She earned her PhD in mathematics education
at the University of Connecticut.
mcgivney@uconnvm.uconn.edu
Thomas C. DeFranco is an associate professor of mathematics
education at the University of Connecticut where he
holds a joint appointment in the mathematics department
and the Neag School of Education. He earned his PhD
in mathematics education at New York University.
defranco@uconnvm.uconn.edu
Ray McGivney is a professor of mathematics at the University
of Hartford. He earned his BA and MA in mathematics
at Clark University and his PhD in mathematics at Lehigh
University. He is currently working on a discrete mathematics
text for a liberal arts audience.
mcgivney@mail.hartford.edu
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| In many cities around
the United States there are holding tanks that contain
a variety of hazardous liquids, including heating fuel,
gasoline, and leachates (rainfall containing nickel,
copper, lead, etc.) that drain through landfills. As
a safety measure another structure, called a secondary
containment system (SCS), is often built around a holding
tank to contain the spread of its contents in the event
of a leak. In this article we discuss how we stumbled
upon a series of unexpected results about the volumes
and surface areas of cylinders and prisms while exploring
ways to determine the heights of SCS's. (back
to top) |
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Spreading
the Seeds of Inquiry-Based Teaching
Caroline M. Borrow, Jay M. Jahangiri, Mike Mikusa
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Dr. Caroline Borrow is a
research associate at Kent State University working
on an NSF-funded project to develop a cognitive-based
assessment system for mathematics in grades K-5. Caroline's
research interests include geometric thinking and reasoning.
cmborrow@earthlink.net
Dr. Jay M. Jahangiri is a mathematics professor
at the Department of Mathematical Sciences at Kent
State University. Jay has twice been nominated for
the prestigious Distinguished Scholar Award at Kent
State University and was awarded the KSU Graduate
Applause for 2001-2002 and 2002-2003.
jay@geauga.kent.edu
Dr. Mike Mikusa is a mathematics education professor
at the Department of Teaching Leadership and Curriculum
Studies at Kent State University. His research interests
include geometric thinking and reasoning and professional
development of secondary mathematics teachers.
mmikusa@kent.edu
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| This article is
based on the experience gained through an experimental
team teaching of college geometry to pre-service and
in-service middle school and high school teachers using
inquiry-based teaching and learning. (back
to top) |
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