Title: The Symbolic Math Guide in Calculus

Author: Doug Child* (child@rollins.edu)

Affiliation: Texas Instruments, Dallas, USA

Abstract: Texas Instruments recently released the Symbolic Math Guide (SMG), a concept application for TI-89 and TI-92 Plus calculators. It consists of a set of core technologies that may form the basis of several future applications. Even in its initial form SMG can help students learn to write correct textbook like solutions to common precalculus and calculus problems. This presentation will consider function notation, logarithmic and exponential equations, difference quotients, and derivatives. Can SMG help students learn to think about these problems in a way that not only helps them learn to write careful textbook like solutions for them, but which also helps them develop skills that extend to other areas of calculus and other mathematics? SMG is a white box computer algebra system that is controlled by students. Students select an appropriate part of a mathematical object and SMG suggests several transformations that might help achieve the goal of the problem. Once a transformation is selected, the student has time to think about (even write down) the result. So, a student has three points of learning for each step in a solution: which part of the object, which transformation, and what is the result. Steps can easily be undone and others tried as students learn to think about the structure of mathematical objects while they develop successful strategies for developing correct solutions. Finally, what does an instructor need to do to integrate the use of SMG into a calculus classroom?.