Making General Mathematics And Precalculus Courses Of Service
To Mathematics Sarah L. Mabrouk, Framingham State
University,

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? Abstract: College Mathematics
at UWStout 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
lectureanddiscussion methods: inclass 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 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
socalled 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 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
firstyear 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 Abstract: As an
instructor at a large community college, I am discovering ways to introduce
to my lowerdivision 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 openended 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 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 handson 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

MAA Mathfest 2001
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This page was last modified on Friday, January 08, 2010.