This course is aimed at present and future high school mathematics teachers who already have a formal understanding of calculus, but want a deeper grasp of the central concepts of the subject, so that they can be more effective teachers of calculus in high school.
In this class students will work in a computer based laboratory in groups of three with a variety of hands-on mechanical devices, investigating the kinds of problems calculus was originally developed to answer. One such device consists of a pair of miniature cars that run along parallel tracks controlled by velocity vs. time graphs drawn by the student on the computer screen. Using this device, the students investigate the relative motion of the two cars as they move according to these graphs . In doing this, they will be grappling with many basic questions, such as: Why does the area under a velocity vs. time graph of a car represent the displacement of the car?
Other devices emulate the well-known Related Rate problems found in calculus courses, such as those involving the Falling Ladder, the Man-and-his- Shadow, and the light beam cast on the shore by a rotating light on a lighthouse. Carrying out explorations and investigations with these devices should give the students a more thorough mastery of these problems than they were able to obtain in their study of calculus, as well as a deeper understanding of the concepts beneath them.
This course will be essentially a repeat of the course taught in Winter, 1999, which met with favorable response from students.