> Lou Talman, as quoted by Robert Hansen in his post dt. > 2-May-2017: > "I've watched students in a Calc I course use > technology to discover, for > themselves, the First Derivative Test. They wouldn't > have done so if they > hadn't been guided to produce a lot of > graphs---something that there would > not have been time for if not for their computers. > That technology wasn't > "pedagogically inert" at all. It provided exactly the > tool they needed in > order to construct and examine a lot of examples > within a short amount of > time. Those folks will never forget the First > Deriative Test; they think > they invented it." > > Robert Hansen's response: > > No doubt, plotting a graph with a computer beats > plotting one by hand any day, unless, like in the > case of arithmetic, the point isn't just the > arithmetic, but the insight gained by learning > arithmetic. We didn't seem to have an issue with the > instructor drawing the graph of a function on the > board, adding some key tangents, and seeing the > application of derivatives to curve tracing and > critical points. Something that took a lot less time > than setting up a lesson plan with computers. > > But by calculus, we already had quite a bit of graph > sense, didn't we. In those days, when we wanted a > graph, and it wasn't in a book, we had to draw it. > And I drew quite a few graphs, traced quite a few > curves, and even identified quite a few critical > points. Before calculus. > > Back to the issue of inertness. Student group A > learns the first derivative test via direct > instruction, with the instructor illustrating the > point on the board, talking to it, and discussing it > with the class. Student group B learns the first > derivative test through a guided discovery exercise > using computers and graphing. > > Either, group B could have just as easily learned the > topic via direct instruction, as did group A, or, > group B was not as prepared as group A, correct? And, > unless we are talking a month of graphing exercises > with much variety, I am saying that group B is no > more prepared after the guided discovery than they > were before it. In fact, it is group A doing the > discovery, on top of all their preparation. Not group > B. But there probably are some students in group B > who are prepared and will discover, and some students > in group A who are not prepared and will not > discover. > > Illustration can be useful, but taken too far, it is > like a poison. It replaces insight with something > artificial, like the way carbon monoxide binds with > hemoglobin, taking up the spot where oxygen was > supposed to bond. > > I have not seen any situation where technology, > beyond practical issues, like lighting, replacing the > mimeograph, providing word processing, etc, have a > positive effect on preparation. Either it is used in > a manner that you don't even notice (the good way), > or too much, with results that are artificial. > > Bob > GSC:
I see HUGE (YUUUUGE??) confusions in Bobert Hansen's response, much of which could quite easily be removed by the construction of a couple of 'systems models'. The underlying issue is that these models would need to be constructed by 'the confused person' him-/herself, else the confusion is not likely to be removed.
It's like this: The learner does need to open his/her mind and exercise it him-/herself, else learning will not occur, confusions will not be removed. This is as true in learning arithmetic, or calculus, or systems modeling.
I observe that Lou Talman has made what is probably the best response to such confusion:
QUOTE This is even more tortured than your usual logic. UNQUOTE
Suggestion: A couple of quite simple systems models (specifically, Interpretive Structural Models) could help very significantly in removing much of the 'tortured logic'.