Calculus: An Active Approach with ProjectsCalculus: An Active Approach with ProjectsCalculus: An Active Approach with Projects is a
collection of materials for first-year calculus developed and
tested at Ithaca College. It is not a complete textbook, but a
complementary volume that can be used in conjunction with any
textbook.
The authors are convinced that students who are actively
involoved in class are more likely to succeed than those who are
passive. We also view calculus as a unified subject rather than
a linearly ordered sequence of topics and believe that this view
should be conveyed to students from the outset of their studies.
The materials in Calculus: An Active Approach with
Projects were designed with these beliefs in mind.
There are two main sections in the Instructor's Guide.
The first section contains activities that can be done in class
or as homework. The second section contains large projects for
the students to work on (usually in groups) outside the
classroom.
The class activities are designed to accustom students to active
participation in the course and to introduce some of the material
and methods we have identified as important. Through the
activities, students participate in the development of many of
the central ideas of calculus. The key is active participation.
This kind of student involvement fosters understanding and
retention of course material. By doing activities, students also
learn modeling and how to use the top-down approach to solve
problems---both are useful for successful completion of projects.
Activities also help students learn how to draw and interpret
graphs---a key element in learning ways to represent functions
that are not necessarily given as formulas. Finally, the first
set of activities provides an overview of most of first-semester
calculus. Doing a number of these activities early in the course
helps students see the unity of the subject.
Each activity requires between five and fifty minutes to
complete---our estimate for each activity in the book is given in
the {\it Instructor's Guide}. Activities that you schedule to
be done in class can, at your option, be done by individual
students, or by pairs or groups of students working together.
Many are suitable for use as homework assignments. In our
courses we like to have an activity in as many classes as
possible.
See also Questions about Using Activities
Projects serve to reinforce material already presented, motivate
concepts, or introduce topics that might not otherwise be
covered. Most projects involve more than one mathematical
concept, and many have open-ended components. We have students
work on the projects in teams of three or four, submitting a
single report, although many of the projects have parts that are
completed by individual students. Most of the projects require
about two weeks to complete. In a typical semester course, we
have our students do three or four projects.
A significant benefit of this project-oriented approach is that
students learn to solve non-trivial, multi-step problems. Working
on the (shorter) activities in a guided classroom environment
helps them succeed on projects.
See also Questions about Using Projects.
Efforts to revise the way calculus is taught have focused on a
number of different issues. As stated above, the materials
presented in Calculus: An Active Approach with Projects
are designed to empower the student to take an active role in her
or his own learning. We emphasize the role of calculus as a tool
for understanding the world and hence focus on modeling as a
central theme. We also emphasize the notion of function and are
careful to show that functions can be represented in many
different ways: as graphs, as tables of values, as algebraic
expressions, as descriptions (written or verbal), as physical
relationships, and as theoretical models.
Back to exerpts form the Instructor's Guide
Back to the Ithaca College Calculus Project Home Page
This page maintained by: D. Schwartz, Ithaca College
schwartz@ithaca.edu
Last Modified: January 8, 2000