1THEME 3 / PRESENTATION Theories that Inform the Use of CAS in the Teaching and Learning of

It is almost twenty years since I first had the opportunity to experiment with the use of a symbolic manipulation program in mathematics instruction. The software I first used was a symbolic manipulation program and not a computer algebra system (it processed symbolic expressions and did not generate graphs or tables or curves of best fit). The program was muMath, the computer was an Apple II Plus (48K) with a CPM card, and the course was an introductory calculus course. Students used muMath along with separate computer programs I had written for graphing, curve fitting, and production of tables of function values. Each class, I rolled carts into the classroom with two such configurations for demonstration; the nearly forty students shared out-of-class access to four Apple II Plus computers that were stored in a metal closet in a mathematics professor’s office. I described what I was doing in a somewhat primitive way. I was having the students use the computer as a tool for learning mathematics. I hypothesized that the computer could be used as a tool to direct student attention to the formulation and interpretation aspects of mathematics while outsourcing the computational aspects to the computer.1 I was focusing their attention on what I calle