Robert Lopez
Emeritus Professor of Mathematics
Rose-Hulman Institute of Technology, USA
Maple Fellow - Maplesoft, Canada

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.