MathAMATYC Educator

A refereed publication of the American Mathematical Association of Two-Year Colleges

Editor: Pete Wildman, Spokane Falls CC
Production Manager: Jim Roznowski, Delta C

Volume 1, Number 1, September 2009 Issue
Earlier and Later Issues

International Inequalities: Algebraic Investigations into Health and Economic Development
Susan Staats and Douglas Robertson
University of Minnesota

Technology resources: Mathematics accessibility for all not accommodation for some
Irene M. Duranczyk
University of Minnesota

Abstract
When faculty and learning assistance staff create teaching documents and web pages envisioning the widest range of users they can save time while achieving access for all. There are tools and techniques available to make mathematics visual, orally, and dynamically more accessible through multimodal presentation forms. Resources from Design Science, the National Aeronautics and Space Administration, Microsoft, and Adobe can be used alone or in combination to create dynamic mathematics pages and resources. This article presents a few examples of why faculty and learning assistance professional would make these changes and how the enhanced delivery of mathematics benefits all students.

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Developing Students’ Relational Understanding: Innovations and Insights
Sheryl Stump
Ball State University

I recently had the opportunity to teach a developmental mathematics class at a community college, something a little different from what I usually do as a mathematics teacher educator at a university. I welcomed the chance to examine the curriculum and try some new approaches. In particular, I wanted to explore the development of some fundamental ideas and look for ways to promote students’ mathematical understanding. I entered the experience in a spirit of inquiry, seeking insights in relation to questions such as the following: What kinds of tasks can engage community college students in developing their mathematical understanding? What are the challenges to the students? What are the challenges to the instructor?

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Mathematics for the Laboratory Sciences
Sheldon P. Gordon
Farmingdale State College of New York

Abstract
Each year, well over a million students take college algebra and related courses. Very few of these students take the courses to prepare for calculus, but rather because they are required by other disciplines or to fulfill Gen Ed requirements. The present article discusses what the current mathematical needs are in most of those disciplines, particularly the laboratory sciences that are responsible for sending us the majority of those students. The lab sciences, as well as others in the social sciences, need an emphasis on conceptual understanding and graphical reasoning, the ability to work with data and knowledge about statistics, and problem solving via mathematical modeling instead of the development of algebraic skills. The discussion in the article is accompanied by a variety of illustrative examples that highlight the kinds of mathematics that is used in the various fields, especially in the biological sciences. The article also discusses ways in which statistical reasoning and methods can be integrated into college algebra and precalculus courses in natural ways that support the usual topics in those courses.

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Smooth, Differentiable, and Tangent Line Approximations
David Yopp
Montana State University

Abstract
This paper takes a careful look at the terms smooth, differentiable and tangent line approximation and the terms’ usage in several beginning calculus texts.

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Affecting Students’ Ways of Knowing Mathematics
Jackie Coomes
Eastern Washington University
Amy Roth-McDuffie
Washington State University

Crossroads in Mathematics (AMATYC, 1995) and Beyond Crossroads (AMATYC, 2006) provide a vision for teaching and learning of mathematics in which students actively participate in exploring, problem-solving, and reasoning, and see mathematics as a useful tool in solving real-world problems. These standards also suggest pedagogies such as collaborative learning, use of technology, and teaching for conceptual understanding. However, many instructors have found that their students are not accustomed to engaging in learning and doing mathematics in this way and are at a loss as to how to help them develop. Students’ ways of engaging with mathematics are affected by their ways of knowing; their beliefs about whether mathematical knowledge is certain and how they acquire knowledge influences learning. In this article we use examples from two precalculus classes to look at how students’ ways of knowing may be affected by classroom environment.

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Using Predictions to Introduce Limits and Continuity
Courtney Nagle
Penn State Erie/The Behrend College

The concepts of limit and continuity are fundamental to the understanding of calculus.
Tall and Vinner (1981) found that students could often work through examples that required them to calculate limits of functions, but were not capable of demonstrating a conceptual understanding for the definition. Interestingly, Tall and Vinner also reported that even among those students who did demonstrate a conceptual understanding, few applied this understanding when asked to calculate limits, relying solely on calculation techniques. Sadly, I noticed this same phenomenon in my own Calculus classes. On the first exam of the semester, the majority of my students demonstrated an ability to calculate limits using direct substitution, the Replacement Theorem, and the Squeeze Theorem. However, they had much less success on the following problem:

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Using Excel in the Calculus Classroom
Azar Khosravani
Science and Mathematics Department
Columbia College Chicago

The use of technology in the classroom has revolutionized the teaching of Calculus over the last two decades. When used appropriately, technology enhances instruction, allowing instructors to efficiently illustrate important concepts. To date, most of the attention concerning instructional technology has been focused on graphing calculators. However, we have found that Excel can also be a valuable tool in Calculus instruction. It is particularly well suited for recursive calculations, and is widely available, both in campus computer labs and on students’ home computers.

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An Enhanced Approach To Solving Equations With Radicals
Leonid Khazanov
Borough of Manhattan CC

Doris, a student in my Intermediate Algebra class, came to see me during my office hour and asked for help with a homework problem. The equation she had difficulty solving was = (x-3). Doris was one of my best students, so I was surprised that she had difficulty with this pretty standard problem. As it turned out, Doris made a mistake in copying the problem from the book. As a result, this equation had ”messy” solutions rather than the nice integer solutions intended by the authors. The solutions to the modified problem were, involving radicals. Checking them in the original equation, as suggested by the textbook and the instructor, proved difficult even for Doris.

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Before you dismiss this as a column that will only help online instructors, let me assure you that Jing is a tool that all of us can use, whether we teach online or not. As long as you use a computer, Jing can change the way you communicate. Let me first illustrate with a fairly typical example.

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The Mathematical Hall Of Fame
Don Bigwood
Bismarck State College

If you are a little nasty
And football is your game
You could be headed for Canton
And the Football Hall of Fame

If your fast ball reaches a hundred
You don’t need a cap and gown
And if you can win 300 games
You’ll end up in Cooperstown.

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