Teaching Communication Skills
Those of us who have been teaching for some years will
probably agree that students often lack sufficient communication skills.
Teaching such skills tends to be an incidental part of imparting mathematical
knowledge. This is especially true of beginning courses where emphasis
has traditionally been on learning basic concepts and techniques. However,
over the last few years we have seen developments in our department, and
in the University as a whole, that place learning communication skills
on a more even footing with gaining command of the course material itself.
This is a desirable change, since there is a real need for good communication
skills in the workplace as well as in graduate study. In this note we
would like to outline some related developments.
To begin with, we are happy to say that our department has
been somewhat ahead of the curve. Thus when the University's new writing
requirement of at least one writing intensive course in each student's
major took effect in the Fall 1999, we had just the right kind of course
for this purpose. It was Math 2283, "Sequences, Series and Foundations,"
developed by Professor Wayne Richter about ten years ago as a transitional
course between lower level courses emphasizing basic manipulative skills
and more advanced courses with more attention to proofs. In this course
students have been expected to make a serious effort to write simple proofs
in a setting familiar to them from the first two years of calculus. In
Fall 1999 this course was upgraded to Math 3283W where students are expected
to carefully write proofs of theorems and expositions of the subject matter.
In order to get the maximum benefit from their assignments, students in
writing intensive courses must typically rewrite their papers at least
once after getting the instructor's feedback. Most math majors are now
satisfying their writing requirement by taking this upgraded course. We
also continue to offer the original course, Math 2283, for students who
satisfy their writing requirements in other ways. Another way to satisfy
the writing requirement is by writing a Senior Project paper (Math 4997W.
All CLA math majors are required to do a Senior Project). A faculty member
guides the student in the writing of the paper which must be at least
ten pages long. It is also required that the project demonstrate acquisition
of new mathematical material. Extra one-on-one student-faculty contact
is an added benefit of the senior projects.
Here are the titles of the Senior Projects carried out to
date, together with the names of the faculty advisors. Professor Paul
Garrett supervised three such projects: "The content of sports statistics,"
"The Enigma Cipher," and "The NP-completeness of well-posedness
of positions in the game of Minesweeper." Professors Bert Fristedt
and Max Jodeit have supervised one project each: "WallisÕs attempt
to prove the parallel postulate," and "The definition and properties
of the complex exponential function." In the articles "Thoughts
on Writing Skills" and "Senior
Project Goals," Professors Garrett and Fristedt share their thoughts
about teaching writing skills and about the goals of the projects.
We would also like to mention some other approaches involving
interactive learning that our faculty are using to improve student communication
skills in our IT Calculus and Mathematics for Elementary School Teachers
courses. In IT Calculus the in-class time is divided into two hours of
large lecture, one hour of recitation and two hours of lab/workshop each
week, compared to three hours of large lecture and two hours of recitation
in the traditional format. Both faculty and TA's participate in the lab/workshop
sessions but not in the recitation sessions, thus there is an additional
one hour of faculty-student contact per week in the new format. In the
lab/workshops students develop verbal technical communication skills by
interacting with each other as well as with TA's and faculty, while at
the same time "learning by doing." Use of graphing calculators,
Matlab and Mathematica during the second year allows treatment of more
interesting applied problems than can be done in the traditional course.
And, from the very inception of this format, students have been required
to write more: already in the January 1998 issue of this newsletter it
was noted that in the fourth-quarter course in fall 1997 students wrote
up four lab reports.
In the elementary school teachers' course there is no formal
division into lectures and recitations (or labs). Rather, the professor
briefly explains a concept, assigns a suitable problem illustrating it,
and then students break up into groups of four to work on the problem.
After a few minutes, typically not more than ten, a student presents the
work done by her/his group at the blackboard. Another problem is then
assigned, or a new concept explained, and so on. The expectation is that
any student in a group should be able to do the blackboard presentation.
Therefore, even those students who contribute somewhat less to solving
the assigned problems have to communicate, both within the group and at
the blackboard. The examinations are more traditional, requiring individual
Professor and Director of Undergraduate Studies
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