For other information, send us e-mail:
calculus@ithaca.edu
Supported by grants from the National Science Foundation and
Ithaca College, we have developed instructional materials for a
projects-based curriculum in first-year calculus. Our course
emphasizes graphical and numerical approaches throughout; a
modeling thread begins early and continues throughout the first
year. We use large problems, often open-ended, to drive the
curriculum: students work on projects outside of class in groups
of about three, spending two to three weeks on each project.
In addition, students often work on activities in the classroom,
sometimes individually and sometimes in groups.
The broad goals in our curriculum are to:
We use a spiral approach in teaching the course, referring to a number
of recurring ideas to which we return throughout th course. These
"threads" emphasize the unity of calculus and are a source of continual
review of the important concepts. Some of these are:
For a more complete descussion, see threads.
Involving students actively is central to our approach. In one of the
first classes of the semester the students form groups and the groups work
on a problem. The class activities are designed to accustom the students to
active participation in the course and to introduce some of the material and
methods we have identified as important. The activities also help the students
learn how to create and interpret graphs and allow us to introduce most of the
fundamental ideas of calculus early in the course.
We want our students to be able to solve meaningful problems. Many of the
problems we assign are much longer than textbook problems, and the solutions
often involve many different parts of calculus. Traditional methods have been
reasonably successful at teaching techniques, but students often need considerable
help in developing problem-solving skills. We employ the following techniques
to increase our students' problem-solving skills:
Our curriculum is technology independent; use of technology by various
instructors has ranged from nothing more than a simple scientific calculator
to limited use of a computer algebra system. We have used our approach
successfully with a variety of different textbooks: Purcell and Varberg,
Strang, Finney and Thomas, and most recently, Hughes-Hallett, Gleason, et al.
For more information about our approach, see exerpts from the Instructor's
Guide to our book.
Many of our activities and some of our projects are contained in our book,
Calculus: An Active Approach with Projects, published by John Wiley
& Sons, Inc. An Instructor's Guide includes a sample curriculum,
notes on the activities and projects, and more information about our course
and our approach. See exerpts from the Instructor's Guide and the table of contents of our book.
This page maintained by: D. Schwartz, Ithaca College
schwartz@ithaca.edu
Last Modified: January 8, 2000