These activities were funded by the Associated Colleges of the South (ACS) Calculus Pilot and a Mellon Teaching with Technology Fellowship.
Predicting
Functions is a pre-technology leveler that reviews
basic ideas.
Derivative
Evidence uses numerical and graphical evidence to show how the average
rate of change function approximates the derivative. Three functions
are used. For each, it is easy to relate properties of derivatives
to those of the function (increasing, concave up, etc.). It can be
used as a demonstration or to fuel exercises for students.
A lab on Newton's Method only requires that students can calculate derivatives and use a graphing calculator. Specific instructions are given for the TI-85. The lab adapts material from several sources, found in an annotated bibliography . No previous knowledge of or instruction in the method is required.
A lab on Velocity&Distance is designed in modules. Students can generate data on time and velocity using a CBR (Calculator Based Ranger) program. If desired, the instructor may give the data to all students. Another module is a preliminary exerice in calculating distances from velocity-time data. Students are then asked to use knowledge of definite integrals to write expressions for various quantities (net distance, total distance, average velocity, etc.) Students essentially perform a Riemann Sum approximation of integrals, even before they know Riemann Sums. Finally, the calculator can be used for numerical integration. Throughout, students are asked for graphical interpretation of answers. The lab was presented at the International Conference on Technology in Collegiate Mathematics in Nov. 98; access the Power Point presentation.