Students
enrolled in the Clipper Calculus used the same textbook
as the on-campus version of the course and had the same
required structure of readings, homework, quizzes, and exams.
This entailed the following:
Assigned
homework problems from the text, some using a computer-algebra
program to do a portion of the computations and graphing.
The majority of these problems, however, stressed on-paper
computations and techniques, and by-hand graphing was be
required. A mixture of drill exercises and more subtle problems
were assigned to develop both skills mastery and critical
analysis.
Exercises
on each topic were provided on-line both to offer immediate
reinforcement of the key concepts and to gauge each student's
difficulties as they developed, allowing intervention by
the instructor before the student became lost.
Two
major exams were taken at specific points in a student's
progress through the material. These were proctored, written,
essay-type exams. These exams were the same as the on-campus
mid-term exams, although the timing of their administration
was determined by the student's pace through the material
(subject to deadlines), rather than the rigid pace of the
on-campus course.
When
the student completed the course (or reached a predetermined
deadline), a comprehensive final exam was be administered
in the same manner as the major exams. Again, this exam
was of the same nature and scope as for the on-campus course.
The
course presentation was divided into discrete topics, as
with the on-campus course. Students were instructed to first
do the assigned reading, then to go through the on-line
presentation accompanying that topic. This presentation
was a written lecture component highlighting the important
points of the topic and audio/video (or audio alone) commentary
on those points by the instructor meant to be played at
specific times while the student is going through the lecture
material, along with examples that can be presented in various
formats.
Drill
and practice examples of the mathematical techniques were
presented as a step-through textual presentation, with animated
graphics as warranted, along with either textual or audio
(or video) commentary as needed. Examples could also encourage
students at key points to develop their ability to apply
the proper technique.
Students
could view these materials as often as necessary for them
to understand the topic, which presented an advantage over
in-class lectures. Feedback and interaction, between the
student and the instructor individually, among the students
with or without the instructor's participation, and in a
group discussion, were provided. Individual interaction
between a student and the instructor was provided primarily
via exchanges of e-mail. Experience has shown that, although
students occasionally had difficulty expressing mathematical
topics through e-mail, forcing them to write their questions,
thus completely expressing themselves, is beneficial. E-mail
responses often accomplished the objective of steering a
student towards the right path better than an office visit.
Group
discussions among students were achieved through use of
a discussion group and/or a chat room, where students can
post questions or observations and follow up on questions
posed by other students. There was a considerable learning
and exchange of information in these discussions
The
instructor participated in this discussion forum but did
not dominate it. The instructor also kept the discussion
on-topic and corrected any misleading information that might
be propagated. Both e-mail and discussion exchanges were
not limited to text. Formatted mathematics, graphics, and
even video clips were attached where needed during the exchange.
Group discussions took place in a chat room, with specific
hours of operation. Visual as well as textual interaction
were used.
Additional
material that students could explore as their interests
lead them were provided. Links to historical information,
more advanced topics, and more general mathematical discussions
were included in the material. A general mathematical discussion
was provided in a question-and-answer format led by the
instructor, where questions from students were (selectively)
discussed in a general mathematical setting, leading students
to explore mathematics beyond the scope of the course material.
The aim of this feature was to replicate the general questions
that occasionally arise, either during office hours or in
a lecture, that provide opportunities to discuss topics
that were not directly related to the course, but which
came out of connections students make between course material
and other subjects that interest them. The model for this
format is Frank Morgan's "Math Chat", available on-line
at the Mathematical Association
of America site. Similar forums are provided by Swarthmore's
"Ask Dr.
Math".