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Making General Mathematics And Precalculus Courses Of Service To Mathematics

Sarah L. Mabrouk, Framingham State University,
Session Organizer and Moderator

Saturday, August 4, 3:15 pm - 5:15 pm



General mathematics and precalculus courses, service courses to colleges/universities, can serve mathematics departments by inspiring students and by providing the skills and the mathematical sophistication necessary to enable students to pursue mathematics as a major.  Exposure to thought provoking puzzles and proofs, especially proofs without words, and the use of projects, applications to other disciplines, especially those involving real data, and innovative assignments, including those involving creative writing, can help students to view mathematics as real, creative, and enjoyable. This session invites papers describing efforts to use general mathematics and precalculus courses to attract students to study mathematics. Participants are encouraged to discuss course changes made to improve student attitudes and to attract students to study mathematics as well as assignments/projects, demonstrations, and activities used to stimulate interest in mathematics. Of particular interest are professor/student reactions, the ease/difficulty with which changes are made, and the overall effect of course changes.


3:15 p.m.


College Mathematics What Can You Do with This Course?
Maria Fung, University of Wisconsin-Stout

Abstract:  College Mathematics at UW-Stout is a general course taken by many students and feared by the majority of them as very difficult. This talk will discuss how the following pedagogical techniques have been used as an alternative to traditional lecture-and-discussion methods: in-class activities, semester projects, writing assignments, and group work both inside and outside of class. Samples of activities and assignments will be presented, together with the results of a small comparative attitude survey that shows that using these methods of instruction seems to relieve mathematical anxiety and to boost interest in the subject to a larger extent than traditional routes.


3:35 p.m.


Meeting The Quantitative Reasoning Of A General Education Program And Having Fun Doing It
Philip S Blau, Shawnee State University

Abstract:  At my institution there is a one mathematics course to meet the quantitative reasoning component of the general education program. Of the many courses that meet this requirement a precalculus course and a so-called core course are the ones with the fewest prerequisite and/or the lowest score on a placement exam. The precalculus course, while it uses graphing calculators, is a fairly traditional (as opposed to reform) course, covering functions and their graphs. I will talk about some of the writing short writing assignments and projects I have assigned in this course an effort to give the students a broader experience and to better meet the objectives of the general education program. I will also discuss student feedback about these assignments. I will also discuss the content of this core course, seen as a terminal mathematics course for nonmajors and its role in the general education program.


3:55 p.m.


Numbers and Codes:  Revealing The Secrets Of Mathematics
Cathy Gorini, Maharishi University of Management

Abstract: Secret codes fascinate everyone. This paper describes a general education course that introduces students in a gentle way to the charms of mathematics, the nature of mathematical research, and the ubiquity of the applications of mathematics. As part of M.U.M.'s first-year program, this course introduces students to mathematics as a discipline of human knowledge and shows how mathematics is related to their own lives.


4:15 p.m.


Using Parity As A Source For Student Proofs Throughout A Precalculus Course
Andrew Nestler, Santa Monica College

Abstract: As an instructor at a large community college, I am discovering ways to introduce to my lower-division students the fun of exploratory mathematics, while building mathematical maturity and sophistication in motivated students.  I will discuss how I use the notion of parity of functions throughout my precalculus course to generate student proofs.  The definitions of "even function" and "odd function" are short algebraic statements that are simple to memorize.  They lend themselves to a large number of open-ended questions and short proofs, which require students to make conjectures and create counterexamples.  Parity, together with graphical symmetry, is an excellent device to reinforce the interplay between algebraic conditions and geometric consequences.  Often the results proved using parity are meaningful and useful.  The notion of parity can be addressed while studying many precalculus topics such as trigonometric, polynomial, rational and inverse functions, and algebraic combinations and compositions of functions.  Also, I will discuss specific course changes I have made, student reactions, problems I have encountered, and suggestions for implementation.


4:35 p.m.


Workshop Precalculus:  Functions, Data and Models
Nancy Baxter Hastings, Dickinson College
Allan Rossman, Cal Poly - San Luis Obispo

Abstract: The Workshop Mathematics Project is developing instructional materials for an integrated precalculus course in functions, data analysis and modeling. Since many students who take precalculus do not continue their study of mathematics, Workshop Precalculus seeks not only to prepare students for calculus, but also to help students develop the skills and understanding necessary to use mathematics in the real world. To help achieve these goals, data analysis and probabilistic concepts are integrated throughout the materials and real world applications serve as the essential vehicle for motivating mathematical and statistical ideas. The materials are appropriate for both mathematics and liberal studies majors and for use in the quantitative reasoning component of a university’s general education program, since they focus on topics essential to the study of calculus, while emphasizing fundamental concepts, mathematical modeling and problem solving.  In this presentation, we will describe some hands-on activities and group projects that exemplify the materials, demonstrate how technology is used to help students understand fundamental ideas, and provide references to assessment tools that can be used to analyze student attitudes and learning gains.


4:55 p.m.


Applications, Skill Building, And A Human Cannonball In A General Mathematics Course
Sarah L. Mabrouk, Framingham State University

Abstract: At Framingham State College, General Mathematics is a no credit course designed to teach students the basic algebra and problem solving skills that they need to take the mathematics courses required to complete the College’s quantitative general education requirement and for their major.  Students take this course based on their performance on a required placement exam.  Those taking the course lack algebraic skills and problem solving skills.  In the course, students learn how to manipulate and to apply variables, variable expressions, and equations:  they analyze and simplify polynomial, rational, and exponential expressions as well as relearning how to solve linear, quadratic, and quadratic-type equations.  They analyze standard word problems as well as applications that would be helpful for their majors, interests, jobs, and life.  These applications culminate in a human cannonball problem that enables students to learn a little physics, apply what they have learned, and have a little fun at the same time.  This presentation will include some of the applications used in the course as well as explanation of how these applications help students to learn mathematics, to improve their attitude toward mathematics and to change their views of their mathematical ability.


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This page was created and is maintained by S. L. Mabrouk, Framingham State University.
This page was last modified on Friday, January 08, 2010.