
The AMATYC Review A refereed publication of the American Mathematical Association of TwoYear Colleges  Table of Contents From the Editor  Feature Articles  Regular Articles  Book ReviewEdited by Sandra DeLozier Coleman
 Software Review Edited by Brian E. Smith
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Using a Field Experience Component to Improve Mathematics Courses for Prospective TeachersJulie DePree and Linda Martin   Dr. Julie DePree is an assistant professor of mathematics at the University of New Mexico Valencia Campus, where she teaches statistics, college algebra, and classes for prospective teachers. jdepree@unm.edu   Linda Martin is a mathematics instructor at Albuquerque Technical Vocational Institute, where she teaches mathematics for prospective teachers as well as algebra and calculus courses. lmartin@tvi.cc.nm.us  In order to improve the impact of the math courses designed for prospective teachers, an optional field experience component was added to the courses at two New Mexico community colleges. Participating prospective teachers worked in teams throughout the semester designing and teaching math lessons that conformed to the recommendations of the NCTM Standards. Participants reported increased understanding of mathematics and of the Standards, as well as improved beliefs about mathematics, teaching, and their own ability and desire to teach. 
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A Spoonful of Medicine Makes the Mathematics Go Down
Sheldon P. Gordon and Florence S. Gordon   Dr. Sheldon Gordon is a professor of mathematics at SUNY Farmingdale. He is a member of a number of national committees involved in undergraduate mathematics education. He is the principal author of a precalculus text and a coauthor of the texts developed under the Harvard Calculus Consortium. gordonsp@farmingdale.edu   Dr. Florence S. Gordon is a professor of mathematics at New York Institute of Technology. She is a coauthor of a precalculus text, coauthor of Contemporary Statistics: A Computer Approach, and coeditor of the MAA volume, Statistics for the Twenty First Century. fgordon@nyit.edu  A variety of mathematical models, all concerned with the level of a medication in the bloodstream, are developed. These models include applications involving exponential decay functions, surge functions, rational functions, and difference equations. The material introduced can be used at all levels of the curriculum from developmental arithmetic and algebra up through college algebra and precalculus and on to calculus. 
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Why Is the Limit Concept So Difficult for Students?
Sally Jacobs   Sally Jacobs earned her BA degree from RandolphMacon Woman’s College and her BS, MA, and PhD degrees from Arizona State University. She teaches mathematics at Scottsdale Community College in Scottsdale, Arizona. sally.jacobs@sccmail.maricopa.edu  Informed by classroom experience and by the recent research findings reported on student conceptions of limit, the author presents practical suggestions to calculus teachers for addressing college students’ difficulties in understanding limit. Students’ mental models of limit, potential obstacles to their understanding of limit, and the dynamic versus static approach to limit are discussed. Included in this article are instructional strategies and classroom activities designed to help students develop a robust limit conception. The activities were originally developed as supplemental material for a classroom using a traditional calculus textbook. They have been successively refined after several implementations with different groups of community college and university calculus students. 
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The Composition of Functions and Problem SolvingJoscelyn A. Jarrett   Joscelyn Jarrett is an associate professor of mathematics at Gordon College in Barnesville, GA, where he teaches mathematical modeling, precalculus, calculus, and statistics. He received an MS in mathematics from the University of Toronto and a PhD in mathematics education from the University of Iowa. j_jarrett@falcon.gdn.peachnet.edu  The fundamental concepts of a function and the composition of functions are covered in most entrylevel college mathematics classes. So also are problem solving techniques. This article attempts to make a connection between the two. Some problems could be interpreted in terms of a function and its composition. The function could be one of a single variable or several variables. For such problems, a direct (or indirect) solution could then be obtained by simply applying the composition of the function (or its inverse). The examples demonstrate the application of the composition of functions as a problem solving technique. 
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Graphing Technology  Tool of Choice for Teaching Developmental MathematicsEdward D. Laughbaum   Ed is Director of the Ohio Early College Mathematics Placement Testing Program. He is an emeritus professor of mathematics and is actively involved in developmental education. elaughba@math.ohiostate.edu  I read with interest the article "General Education Mathematics: New Approaches for a New Millennium" in the fall issue of The AMATYC Review (Bennett & Briggs, 1999). The authors describe a nonscience, engineering, and mathematics (nonSEM) student population not being served well by the traditional developmental curriculum in mathematics. They argue for a change in the curriculum at the developmental (remedial) level and promote some good ideas. One of special note is the concept of teaching developmental mathematics in the context of realworld problems, situations, or data as further described in Laughbaum, 2001. However, there is one proposal that they make that is open for debate for this population. They suggest the technology needed by this population for their proposed curriculum is a spreadsheet, the web (and a computer with Internet access), and a scientific calculator. Although I have no objection to a spreadsheet since it is available for the TI83 Plus calculator. But the authors must agree that using a computer and the web may restrict students to doing homework during selected times and places. Despite this barrier, my main concern is with Bennett and Briggs’ recommendation of the use of a scientific calculator as the only other piece of technology needed for nonSEM students. This article will provide several examples that form a convincing argument as to why handheld technology (graphing calculators and data collection devices) is the appropriate teaching/learning tool of choice for developmental students. 
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Group Homework: Presentations Reinforce LearningGrisha L. Stewart   Grisha Stewart earned her BA in mathematics and German at the University of Puget Sound and her MA in mathematics at Bryn Mawr College. Between undergraduate and graduate schools, she taught at Northern Marianas College on the island of Saipan. She is now pursuing graduate studies at the University of Washington in Seattle. gstewart@member.ams.org  This article discusses the benefits of a method developed by the author called D^{3} (Do, Discuss, Demonstrate) for teaching mathematics in twoyear college classrooms. The basic premise is to have the students Do homework, then Discuss it in groups, and finally to present their solution on the board to the rest of the class to Demonstrate their knowledge and skill. This article is based on observations of ten courses employing D^{3} at Northern Marianas College between 1997 and 1999. These preliminary results are very encouraging and have prompted the author to do a more scientific study of D^{3} in the near future. 
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Proof Without Words Integral of Sine Squared
Thomas J. Osler   Tom Osler is a professor of mathematics at Rowan University. He received his PhD from the Courant Institute at New York University and is the author of 49 mathematical papers. In addition to teaching university mathematics for the past 41 years, Tom has a passion for long distance running. He has been competing for the past 48 consecutive years. Included in his over 1700 races are wins in three national championships in the late sixties at distances from 25 kilometers to 50 miles. He is the author of two running books. Osler@rowan.edu  The evaluation of the definite integral of sin^{2}x or cos^{2}x usually requires the use of the half angle formulas from trigonometry. However, if the limits are multiples of /2, the integral can be easily visualized and the value calculated without the use of a pencil. 
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An Application of the Factored Difference of Two Nth Powers
Travis Thompson   Travis Thompson is a professor of mathematics and Dean of the College of Sciences at Harding University in Searcy, AR. He received a PhD in mathematics from The University of Arkansas  Fayetteville in the area of topology. thompson@harding.edu  How does your retirement account grow over the years at a fixed interest rate with regular contributions? Compound this question with constant yearly raises to your contributions and you have an ideal realworld problem that is solved by the factored difference of two nth powers. 
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Laplace Transforms and AnnihilatorsMin Zeng   Dr. Min Zeng teaches at Longview Community College. She received her PhD in mathematics from the University of MissouriColumbia. zengm@crc.losrios.edu  The method of Laplace transforms is usually used to solve initial value problems for linear differential equations. In this article, it is used to derive formulas for computing Laplace transforms of many elementary functions through their annihilators. The formulas not only provide ways to find Laplace transforms, but also explain why, for many elementary functions, the denominators in the Laplace transforms F(s) reflect annihilators of f(t). 


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