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AMATYC Review Fall 2003
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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


Fall 2003 issue, Vol. 25, No.1

Table of Contents

The National Numeracy Network
Promoting Quantitative Literacy For College Graduates

Susan L. Ganter

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.

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)

Implementing "Best Practices"
in a Developmental Mathematics Summer Bridge Program

Frances Kuwahara Chinn

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.
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)

A Note on Polynomials and Their Derivatives

Ronald Skurnick

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.
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)

The Sphere Game

Alfred P. Lehnen and Gary E. Wesenberg

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.

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.

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)

Factoring Quadratics Part II

Lance E. Hemlow

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.
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.
Kaczkowski, S. (2001). Factoring quadratics. The College Mathematics Journal, 32(3), 203-204. The Mathematical Association of America. (back to top)

Embedding Study Skills into a Developmental Algebra Course

Robert D. Lewis and Katherine H. Clark

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.

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.

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)

The Circle of Curvature: It's a Limit!

John H. Mathews

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.
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
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)

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

Kate McGivney is an assistant professor of mathematics at Shippensburg University. She earned her PhD in mathematics at Lehigh University.

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.

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.

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.
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)

Spreading the Seeds of Inquiry-Based Teaching

Caroline M. Borrow, Jay M. Jahangiri, Mike Mikusa

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.

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.

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.

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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