Trent University 2001-2002
Mathematics 280
Mathematics for
the Contemporary Classroom
David G. Poole
Lady Eaton College
N127-2
(705) 748-1011 x1358 (office)
e-mail: dpoole@trentu.ca
Mathematics
Beyond the Numbers , by George T. Gilbert & Rhonda L. Hatcher
Wiley, 2000.
Readings
200% of Nothing: An Eye-Opening Tour through the
Twists and Turns of Math Abuse and Innumeracy, by A. K. Dewdney
Wiley, 1995.
Recommended
The I Hate Math! Book, by Marilyn
Burns
Little, Brown & Company, 1975.
This course is an attempt to convey to a general audience an appreciation of
mathematical thinking while introducing some of the many interesting topics in
modern mathematics. It would be impossible to cover the full spectrum of
mathematics, so we will adopt a "smorgasbord" approach, sampling topics from
various fields in mathematics. Mathematics being as much an art as a science,
the emphasis throughout the course will be on developing an appreciation of the
spirit of mathematics and mathematical methods rather than accumulating
computational techniques. At the same time, however, we will focus on some of
the many applications of mathematics and we will discuss the role of mathematics
in society. The course is "activity-oriented": students will work in groups
on problems and projects designed to illustrate and elaborate upon the topics in
the course. In addition, students will be asked, on an ongoing basis, to seek
out examples of the use and misuse of mathematics in society.
This course
has been developed with prospective elementary school teachers as the principal
intended audience. There are many topics in the course that might be adapted
for classroom use.
We will discuss as many of the following topics as time permits. Most of these can be found in Chapters 3 - 8 of the textbook.
- NUMBERS AND NUMBER SYSTEMS
the integers, some elementary
number theory, congruence and modular arithmetic, rational numbers, real
numbers
- GRAPHS AND NETWORKS
graphs and directed graphs, Euler circuits,
Hamiltonian circuits, spanning trees
- SYMMETRY AND PATTERNS
symmetry, patterns, polygons, tilings,
polyhedra, surfaces
- GROWTH AND FORM
similarity and scaling, the growth of
populations, models of growth, renewable resources, measurement
- PROBABILITY: THE MATHEMATICS OF CHANCE
counting principles,
probability, probability models
- STATISTICS: THE SCIENCE OF DATA
sampling, randomness,
distributions and their graphical representations, describing data
The class will meet for three hours weekly, with part of the class in workshop
format and part in lecture format. Videos supplementing the material will be
shown periodically. Class meetings: Thursdays: 7:00--10:00
in BL 107.2
Throughout the course, students will work in groups on 4 assigned problem sets,
with each group submitting its collective solutions. On an individual basis,
students will keep a journal in which they will record a summary of and their
comments on the material discussed in class as well as a weekly example of
"mathematics from the real world" found in the news media. Journals will be
collected twice per term. There will also be a project, in the form of
ascience-fair type exhibit, on a topic chosen by the student but relevant to the
course. There will be a two tests. The breakdown of marks is:
Assignments 50% Tests 20% Project 20% Journal 10%
Sample tests can be found here .
You will need the following for this course: - notebook (for class
notes)
- workbook (for exercises and experimental work)
- journal (for
your personal course record and clippings -- see below)
- coloured pencils or markers
- scissors and scotch tape
- a geometry
set (ruler, compass, protractor)
- a calculator (one with statistical
functions would be nice, but not essential)
- an open mind
Your journal is a space in which you will keep a personal record of the course.
This is separate from your notebook which will contain your notes taken during
class and your workbook where you will work on examples and exercises related to
the material discussed in class and assigned for readings.
Each week, you should record in your journal a short description of what was
discussed that week. Impressions, observations, comments and criticisms about
how each class went or comments about assigned readings would also be
appropriate journal entries. At various times throughout the year you may wish
to revisit some of your earlier comments and possibly add new comments in light
of more recent discussions or information gleaned from the course. At the end
of the year, you will have a record of what we did as well as your comments on
the material.
Your journal will also contain a "clippings file": items collected on a weekly
basis relating to the use and misuse of mathematics in newspapers, magazines, or
seen on television, video, etc. Again, recording your comments about these
items should prove interesting and, as the course progresses, you may find that
your reaction to some of the clippings changes. In the second term, we will
discuss the use and abuse of statistics; your clippings will hopefully provide
us with lots of good raw material!
I will collect your journals at the end of each term. Your journal grade will
be based in part on the amount of effort and care that you put into keeping it.
Trent University's Policy on Plagiarism (printed in the University
Calendar) will be interpreted as follows in MA 280. Students are permitted and
encouraged to work together on the assignments, make use of any books, and ask
anyone willing (especially the instructor and TA) for hints, suggestions, and help.
However, students must write the problem sets up for submission entirely
by themselves and may not copy part or all of their solutions from any other
source (books, notes, or other students' work). Class notes and the
textbook may, however, be referenced as part of a problem solution.
Department of Mathematics Trent
University
This page maintained by David Poole. Last
updated 2001.09.5.