Effectively Melding Computer Algebra Systems into the Calculus Curriculum

Patrice Geary Tiffany
Manhattan College
Manhattan College Parkway
Riverdale, NY 10471
patrice.tiffany@manhattan.edu

CAS in the Calculus curriculum can motivate and clarify.  It can visualize and
spark discussion.  It can enable students to inquire “what if” and go on then
to investigate and postulate.  It can be wonderful if used in a pedagogically
sound way.  It can be detrimental to learning if we allow it to be a typing
exercise lab with lines of code.

I have developed pedagogical materials that foster the inclusion of technology
in the curriculum of Calculus I and II.  I do concentrate mainly on the
computer algebra system, Maple.  This material can be easily adapted to
different CAS software.  The idea is not to rely on one specific software
package but to educate our students, especially our engineers, in the 21st
century electronic culture.  The manual that I am developing is not a cookbook
of Maple handouts with code.  That approach to the use of technology in the
classroom is how the original labs were written when CAS was first introduced.
None of this material is a stand alone “lab” that can just be distributed, but
rather a guided activity within a mathematics lesson using a CAS.

There are three ways that I have found computer algebra systems to be effective
tools in the teaching of mathematics.  Though I do not like to categorize,
because the following categories can and should overlap, I have developed three
different types of lab materials.

1.      Labs that can be worked on by the student individually
2.	Labs that can be worked on by groups
3.	Interactive teaching labs
4.	Turn it on, turn it off activity

I have not developed these labs as major projects.  They are developed to be a
part of a 50 minute class.  Some are completely contained within the class
period and some may be completed out of class.  All begin in the classroom.
Some use CAS to visualize mathematics, some use the power of CAS to see quickly
and easily “what if I change this,” some use data from the web and some
reaffirm what they have learned in class.

My talk will present how I use CAS in my Calculus I and II classes.