### Electronic Proceedings of the Thirteenth Annual Conference on
Technology in Collegiate Mathematics

*POSTER: 13-P3*
### Exploring Optimization in Calculus-Student Projects in Finding Absolute
Extrema on a Closed Interval Domain

Barbara L. Power

Penn State Erie, The Behrend College

School of Science

Station Road

Erie, PA 16563-0203

Phone: (814) 898-6349

Fax: (814) 898-6213

E-mail: blp4@psu.edu

#### ABSTRACT

Many calculus problems involve finding the greatest or smallest value (or values)
that a function assumes over an appropriate domain. These greatest or smallest
value points are called global or absolute extrema. In this Calculus I optimization
project, Finding Absolute Extrema on a Closed Interval Domain, students work in
groups outside of class to investigate absolute extrema.
The calculus reform movement of the early 90's has revitalized the teaching of calculus.
The reform projects that have evolved over the years vary widely, in curriculum and
in technology. However, several themes emerge in most projects:

- Calculus should be learned as an interplay of algebraic, numerical, and graphical data.
- Students must be actively involved in discovery, experimentation,
and open-ended problem solving. Cooperative learning is more active than individual learning.
- Appropriate technology can facilitate the transformation from manipulating
symbols to understanding the concepts of calculus.
- Technical writing is an important component of active learning.
As students explain their mathematical work to others, they deepen their
understanding of that work.

The Calculus I optimization project presented at this ICTCM conference was
designed to meet the four criteria, which are stated above. As the student groups
investigate the problems algebraically, and/or numerically, and/or graphically,
they are learning an important application of the derivative.

The graphing calculator was chosen as the technology vehicle for this attempt
to improve the students' understanding of calculus. Penn State Erie requires a
graphing calculator for all calculus students (TI-83 recommended). This enables
the students to experience hands-on learning without the need for additional
computer facilities for the calculus program.

I have incorporated group projects in calculus since 1993. It has been my experience
that the amount of time that the students invest in learning calculus algebraically,
numerically, and graphically (using cooperative learning, technology, and technical
writing) is well worth the effort.