Teaching a calculus course using "new " materials usually
requires some modification of one's teaching style and some
reorganization of topics. As an aid in this adaptation, we have
included a sample curriculum for a two-semester sequence.
The curriculum is offered as an "existence proof " rather than a
prescription---there are many possible variations that will
result in a successful course based on the materials in
Calculus: An Active Approach with Projects. The sample
curriculum is included as an appendix in the Instructor's
Guide.
The sample curriculum illustrates a change in course
organization---the spiral approach---that we have found to be
particularly effective. Our goal is to present the main ideas of
the course early so that the students will see calculus as a
unified subject. The emphasis at this stage is on concepts and
relationships, not on technical details.
We use the "calculus of graphs " for this purpose. That is,
representing the functions involved almost exclusively in
graphical form, and using the familiar ideas of velocity and
distance as examples, we examine basic ideas from both
differential and integral calculus. Within days, the students
have some basic understanding about rates and slopes, concavity,
and integration (in the context of obtaining a distance graph
when given the corresponding velocity graph).
During the rest of the course, students encounter the same ideas
again and again, each time picking up more of the technical and
computational details.
Most instructors agree that new approaches to calculus call for
new kinds of quiz and examination questions. We have included a
sample of the kinds of quiz and examination questions that we
have used at Ithaca College in conjunction with our courses that
are based on the materials in Calculus: An Active Approach
with Projects. This collection appears as an appendix
in the Instructor's Guide.
Finally, when we have conducted workshops on our active approach
to calculus, a number of questions have arisen about how one can
integrate these materials into a course. We include some of the
most often asked questions and our responses in the next few
sections of this introduction.
Back to exerpts from the Instructor's Guide
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This page maintained by: Diane Driscoll Schwartz, Ithaca College
schwartz@ithaca.edu
Last Modified: January 8, 2000