MathAMATYC Educator
A refereed publication of the American Mathematical Association of TwoYear Colleges Editor: Pete Wildman, Spokane Falls CC Production Manager: Jim Roznowski, Delta C Volume 1, Number 1, September 2009 Issue Earlier and Later Issues AMATYC Members can view entire articles of this issue by clicking on the button below
 
This Issue's Features MathAMATYC Educator’s Departments Walking Beyond Crossroads Use This Now Teaching Math With Technology Fun Math Stuff 

  International Inequalities: Algebraic Investigations into Health and Economic Development Susan Staats and Douglas Robertson University of Minnesota  Abstract The Millennium Project is an international effort to improve the health, economic status, and environmental resources of the world’s most vulnerable people. Using data associated with the Millennium Project, students use algebra to explore international development issues including poverty reduction and the relationship between health and economy. The applications support the AMATYC and NCTM connections standards that recommend helping students to apply mathematics across disciplinary boundaries. TOP
  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. TOP
  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? TOP
  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. TOP
  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. TOP
  Affecting Students’ Ways of Knowing Mathematics Jackie Coomes Eastern Washington University Amy RothMcDuffie 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, problemsolving, and reasoning, and see mathematics as a useful tool in solving realworld 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. TOP
  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: TOP
  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. TOP
  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 = (x3). 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. TOP
  Jing: A Tool for Math on the InternetMaria H. Andersen Muskegon CC  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. TOP
  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. TOP

