On Tue, 02 May 2017 16:44:02 -0600, Robert Hansen <email@example.com> wrote:
> First, that is not what I said, I said that guiding the students through > graphing on a computer does not prepare them for understanding the first > derivative test (or any mathematical concept).
Who said that it did? That's a straw man, Bob. No one claimed to claimed that "guiding students through graphing" produces anything other than graphs. The guidance my students had was in what kind of graphs to examine---not how to draw those graphs. How to get the computer to produce graphs was part of the preparation. One could do this without a computer with a similar effect, but it would take weeks or months instead of an hour or two.
Nor has anyone suggested that preparation isn't necessary. Those are more words you're putting in other people's mouths---another straw man.
And to head off your next objection, I'll point out that they didn't prove that the First Derivative Test works. We did that later. But that's how mathematics works: First we figure out what we think is true, and then we see if we can prove it---making some adjustments to definitions, hypotheses, and conclusions as necessary. The latter part wasn't needed here, as hypotheses and definitions were already in place because those who did the guiding knew where it was all going.
Why don't we see more of this? Could be because certain troglodytes (I won't mention any names) block progress, thinking that only what they went through can be successful.