Sixteen Years of Teaching with Mathematica: We Have It Right

Jerry Uhl

University of Illinois, Urbana-Champaign

Abstract

We started teaching Mathematica-based mathematics courses in 1989. We made every mistake in the book—mistakes I often see in other attempts at using Mathematica or other math processors at many universities and high schools. But we were fortunate enough to learn from our mistakes and progress to the point at which we have an efficient, effective set of successful courses including precalculus, calculus, vector calculus, differential equations, matrix theory, and probability theory. These courses are in service on campuses and internet distance education at Ohio State and Illinois.

The courses are highly visual, but with a twist articulated by former teacher Scott Mills Gray: “While visualization is an extremely important aspect to a learning system, if the teacher or author is creating all the visualizations then it is of no help to the student. What is more important is that the student have an unbounded set of tools to create their own visualizations.” Our students have this set of tools.

One of our Illinois students put it this way: “As much as Luke Skywalker loved his time in math he had always known something was wrong... His math abilities grew and grew, but he always felt that the methods of teaching were a constraint on his ability to really understand the mathematics being taught. When he had grown old enough he finally met Obiwan Kenobee who told him that he was meant to be a math master and that the slight force he had always felt would eventually become one with him and he would understand all. Obiwan explained to him that all of this would begin with the destruction of the old math empire... In the next year Luke created a calculus program on computer and began slowly defeating the dark side of math that had always haunted him. As time went on he transfered all the mathematics the rest of the world could comprehend on to a computer and defeated the empire of long boring lectures and unnecessary computation. The force prevailed, and true mathematics finally came through.”

For more information, attend the talk and if you can not wait, visit
www-cm.math.uiuc.edu, netmath.math.uiuc.edu, and matheverywhere.com