Open source calculus with interactive applets
When Alex Himonas agreed to publish his course materials on Notre Dame’s Open CourseWare (OCW) website he had three goals: 1) help students decide which calculus course to take, 2) enrich the learning experience, and 3) reach outside of Notre Dame. MIT started the OCW movement in 2002, but they had not published a business calculus course, so this would be something new.
Steven Broad was enlisted to work on the project; a grad student at the time, Dr. Broad now teaches at Saint Mary’s. He incorporated java applets that allow students to visually interact with concepts on the computer screen. Sites like Thomas Downey’s calculusapplets.com offer hundreds of these mini-programs for free or under a Creative Commons license, and over seventy are now mapped against the content of “Elements of Calculus I.” Interactive visualizations like this are also available in other disciplines, notably in the sciences and engineering.
The illustration at right shows the “Instantaneous Velocity” applet. In a face-to-face course, Dr. Broad has students first imagine the concept in their heads. then gives a visual demonstration. Now for the fun part: he asks, “What if we change this?” Students use the applet to test lots of possibilities and receive instant feedback, and their understanding of the concept grows quickly. Some people explore the course online without benefit of an instructor. A “Try the following” section below the applet leads them through a similar exploration.