"Resequencing of skills – stressing concepts
first and delaying skill development by relying on a CAS – is an idea
approximately 20 years old. This talk will revisit this pedagogical
technique, using examples implemented in Maple, a CAS that doesn’t have
to be taught.
Intuition and the “big picture” are addressed by using the computational
and visualization power of the CAS. The concept is experienced, its
connection to other parts of the curriculum explored, the correctness of
solutions verified, all within the computational framework of the CAS.
Then the steps of applicable algorithms are implemented in the CAS.
Here, it is essential that the software tool be easy to use, flexible,
and “in sync” with the flow of the mathematical calculations. After a
bit of practice with this approach, students can be set to acquire those
manipulative skills necessary for the overall curriculum.
This approach to the pedagogical implementation of a CAS in the
classroom will be illustrated with several examples. From these
experiences, participants can determine the viability and soundness of
the approach. And they can observe the added clarity that derives from
the syntax-free environment of Maple’s point-and-click paradigm.
This point-and-click paradigm is sufficiently transparent that an
instructor can simply use it as appropriate in a lesson, and students
who observe its use will be able to imitate and extend the calculational
approach without specific instruction on the use of the software tool.
The GUI devices built into the software are natural enough that they
require little or no explanation. This simplicity in the use of the
tool means implementing the steps of a calculation in the software will
not seem like more work for the student, and the instructor will not be
inclined to neglect an appropriate amount of drill-and-practice that
leads to the mastery of skills necessary for success in mathematics.