Education Technology

Seeing Is Believing

Published on 07/30/2007

Activity Overview

This activity is intended for the AP Calculus classroom. Students are presented with a function on the Graph Tab of Activity Center. The same function is sent to the student calculators as a GDB file. Students investigate the graph of the derivative by returning a set of (x, dy/dx) data points. As students return data points for the derivative, they are plotted on the Activity Center screen and a graphical picture of the derivative evolves.

Before the Activity

Students at this stage are expected to have an appreciation for the value of the derivative at a point on a function being equal to the slope of the tangent line. Derivative data can be developed by having the students manually estimate the slope of tangent lines using the Manual-Fit regression analysis option under the STAT | CALC menu; or by simply using the dy/dx option under the CALC menu. The Manual-Fit approach has the benefit that students grow to better appreciate the value of the derivative as the slope of the tangent line. To speed up the activity and to ensure that the entire domain interval is adequately covered, individual students should be assigned a particular interval to investigate.

During the Activity

Have students load the GDB file corresponding to the function displayed on the Activity Center screen. Students may not be familiar with storing and recalling GDB files. From the Home screen on their calculators, have students select DRAW | STO | RecallGDB. The RecallGDB command will transfer to the Home screen. Type the appropriate GDB number and press ENTER. Students can press GRAPH to make sure they have loaded the function corresponding to the Activity Center display. Monitor student understanding and progress using Screen Capture.

After the Activity

Students should be encouraged to enter into discussions comparing the function and derivative graphs, and among other things the implications of function extrema, zero and undefined slopes, points of inflection, and critical points on the function.