Interactive Calculus at a Distance

Article excerpt

In 1988, Dr. Horacio Porta and I, along with professor Bill Davis of Ohio State University, wrote Calculus & Mathematica (C&M), a three-semester, interactive calculus course that combines textbooks with Mathematica-based instructional software. Developed by our colleague Dr. Stephen Wolfram, Mathematica is a sophisticated, highly graphical math program and programming language. We designed C&M to exploit Mathematica's unique capabilities and today, C&M is used on campuses across America and abroad.

* The C&M Course, in Brief

The course is directed squarely at students who envision a career in calculation, measurement and modeling. Of all the new calculus courses, C&M leans on technology the most, exploiting students' natural interest in technology to slip in the math. It is based on entirely interactive text in which each example is, literally, as many examples as a student wants.

The courseware consists of four types of Mathematica files (called notebooks): Basics, which present fundamental ideas; Tutorials, samples of the basics; Give It a Try, actual student work; and Literacy Sheets, questions that the student answers away from the computer. Four textbooks accompany the software. The courseware always puts the mathematics in the context of measurement, and puts the programming in the context of mathematics. We put new ideas into students' heads by having them interact with Mathematica graphics, and by having them explain what the graphics mean. Thus, students get a vivid image of things.

We wrote C&M in informal American English, a vernacular that students will read and, most importantly, imitate in their own writing. The heart of the course is the Give It a Try section, in which students use Mathematica's calculation, graphical and word-processing capabilities to work and write assigned problems and projects. The, goal of C&M is to help students make a smooth transition from the classroom into engineering, science and mathematics. In a nutshell, C&M gives them:

* Work that is relevant to the real world;

* Professional tools;

* New ideas, communicated visually and experimentally;

* A chance to organize their thoughts by explaining themselves in writing; and

* The opportunity to learn the math, programming and writing in context.

Calculus&Mathematica gets instructors out of the way and ends the one-size-fits-all calculus course, giving students freedom to think for themselves. The real-world issues and models that appear in C&M's first semester include: Japanese economy cars versus big American cars; data analysis of the Challenger disaster; living off an inheritance; oil slicks; drinking and driving; war games, including a model of the Battle of Iwo Jima; and grading on the curve.

* From These Roots...

When we first wrote these lessons and offered the course, an alarming number of students began dropping the class. We soon realized, however, that they hadn't dropped it, they simply weren't coming to the lectures. At that point, we saw that the students understood the course better than we did. We changed it, and today students are in the classroom just one day a week--for a class discussion, not a lecture.

Then in 1990, Porta and I gave a presentation on C&M to the Illinois Council of Teachers of Mathematics. A few high school teachers lingered afterwards, and one said, "If we take you seriously, then I have a question. Do your students even have to be on your campus?" After some thought, we decided that they didn't, although they'd miss the discussion section. We've since realized our approach is really distance learning (defined only as two-way video). Technology shrinks distance and that's the key. This, too, is distance learning--by computer.

The year following our presentation, that same high school teacher, Shirley Treadway, organized some of her colleagues into a Distance Education Program. …