"I am confused by the illogic of the tortured thought processes you seem to follow.
You are apparently claiming:
a) The construction of plenty of graphs by students to illustrate, for example, various aspects of the 'First Derivative test' does NOT help them to arrive at an effective and usable understanding of those parts of calculus. a) The construction of plenty of graphs by students to illustrate, for example, various aspects of the 'First Derivative test' does NOT help them to arrive at an effective and usable understanding of those parts of calculus."
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).
Whether you guide a first grader through an animated example of the first derivative test, or an 11th grader, they will both get the visual. It is a very easy visual to get. But only if the 11th grader is well prepared in calculus, can they relate the visual to calculus. You cannot relate a visual to something you don't know, even if you get the visual. Showing them an animated example, no matter how nicely done, will not provide that preparation.
And neither you nor Lou have addressed my point that if the idea of technology being an enabler had even a small amount of truth, then why with all the tech available today, and a lot of it finding its way into classrooms, has the mastery of mathematics, even simple mathematics, declined? If more tech and better illustrations are the ticket, and we have those in spades, then why the decline rather than a renaissance? Is it because the whole planet is using tech wrong? I suggest that it is not that at all. The reason for the decline is simple. Lack of preparation. For the sake of inclusion they have abandoned the hardness of math, and with it, essential preparation.
When someone says that they only get it visually, rest assured, they don't get it. Illustration will always be a part of mathematics, but illustration is an analogy, not a replacement. If all you are getting is the analogy, and that is what people really mean when they say they only get things visually, then you are not getting the math.