Much of the discussion on graphing calculators that has appeared here lately has wandered away from the subject of graphing. One of the teachers in my district shared the following story of a student in his class that illustrates the benefit we all hope would come from graphing experience. The story is second hand so I may have some details wrong, but the point accurately reflects the student's work.
His student had just completed the AP Exam (1994) and commented to him regarding one of the problems, "Of course the graph was a parabola that turned down, so I proceeded to ..." (Recall that the 1994 exam did not permit use of graphing calculators.) The teacher interrupted with "How did you recognize it as a parabola having the properties you describe so quickly?"
The student answer was that he had graphed so many parabolas in classwork both that year and the previous year that recognition was immediate and that the details were obvious from his considerable experience. (End of story.)
My point is that even though I took an analytic geometry class 35 years ago and taught courses which included analytic geometry for many years, I have far less experience with graphs that I created than most students who use graphing calculators today have in a few days in their classrooms.
It's starting to happen. Students are beginning to be able to recognize functions from algebraic, graphic, tabular, and yes, even verbal forms, and make tranisitions from one format to the other. The progress of students is amazing.
Steve Cottrell Mathematics Supervisor K-12 Davis School District 45 East State Street Farmington, UT 84025