Temple University mathematics professors Dan Reich and Gerardo Mendoza are providing free access to their COW. That is, to their "Calculus on the Web" Internet site, an interactive teaching tool for college and high school students in introductory calculus classes.
With 123 different program modules and thousands of available problems, the site is being used by Temple students as a way to submit their homework assignments and study for exams. Though some students were initially resistant to working on-line, after the second or third week of the semester "they apparently love it," according to Reich. In fact, when a student was injured in an automobile accident last semester and forced to withdraw from classes, he was able to keep up with his calculus work by using the COW from his hospital bed.
Reich and Mendoza have found that the COW works best when it is used to explain the fundamentals of concepts and functions. "The COW takes the skill development load off of class time and puts it where it belongs--at home," Reich explains. Each student who has trouble with a specific type of problem can get intensive help with that concept outside of class, freeing classroom time for professors to develop theory and investigate more complex subjects with their students.
Both professors are great believers in the teaching potential of the Internet, but argue that its power "does not lie in static pages . . . there must be an intelligence on the other side." All the calculus problems on their site are accompanied by graphics and explanatory material. Some are entirely pictorial thought experiments in which the student "plays" with equations, and some ask the user to pose a problem of their own.
"The most important thing is that the students get immediate feedback so they know exactly where they went wrong," explains Reich. Such feedback is, of course, unavailable from standard calculus textbooks, which merely list the answers to select questions. "Multiple choice is cheap and easy and beneath the COW's notice."
Since introducing the program, Reich and Mendoza have noted a significant increase in student enthusiasm and retention, and are eager to see the end-of-semester results. Other college professors and high school teachers have also responded very favorably to the COW, and the Temple professors have been advising them on how to integrate the program into their own lesson plans.
The COW's code is written using the PERL string-processing language and the MAPLE mathematics analysis package. The incorporation of these large and complicated components, as well as the sheer number of modules accessible by the program, makes the web the only reasonable venue for the COW. Neither professor sees immediate commercial development in the COW's future--they just hope that it will be widely used by teachers and students "in any university, in any high school class."
The Alliance for Minority Projects, The National Science Foundation, and Temple University share that hope and have provided substantial financial support for the project. With funding through the year 2000, Reich and Mendoza plan to expand their battery of modules to include pre-calculus, as well as more advanced calculus classes.
Students, teachers, or anyone who craves a calculus flashback can visit the COW at www.math.temple.edu/~cow.