Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!sharkey!edsews!edsdrd!gss From: gss@edsdrd.eds.com (Gary Schiltz) Newsgroups: comp.ai Subject: Re: Question on Chinese Room Argument Keywords: Understanding, Comprehension, Learning Message-ID: <126@arcturus.edsdrd.eds.com> Date: 3 Mar 89 18:33:58 GMT References: <4298@pt.cs.cmu.edu> <7653@venera.isi.edu> Organization: EDS Research and Development, Auburn Hills, MI 48057 Lines: 63 In article <7653@venera.isi.edu>, smoliar@vaxa.isi.edu (Stephen Smoliar) writes: -> In article <125@arcturus.edsdrd.eds.com> gss@edsdrd.eds.com (Gary Schiltz) -> writes: -> > -> > [anecdote about doing calculus without "understanding" calculus] -> > -> -> This brings me to my second point. At his "gut level" Gary felt, -> introspectively, that he really did not understand calculus. ... -> ... -> ... I, for one, would like Gary to attempt -> to probe further as to just WHY, at that gut level, he felt understanding was -> eluding him. Did it have to do with problems he could not solve? Did his -> eyes glaze over whenever he saw integral signs in the pages of a book? Did -> he just feel that we was struggling more than his fellow students to solve -> problems? Perhaps if we probe these matters deeper, we may yet return to -> my initial point: that Gary's "gut level feeling" may leave something to -> be desired as a criterion for understanding. I'm not sure how far this is probing, but ... I feel I didn't understand calculus because I didn't know what in the "real world" was being represented by the equations I was solving. For example, I didn't know that dY/dX represent the change in Y given an infinitely small change in X. I just knew that "dY/dX" was referred to as the "derivative of Y with respect to X", that Y and X were variables and that the derivative could be generated for an equation by manipulating it in a certain way. I also happened to have picked up a certain amount of knowledge about how to map word problems into equations that could be differentiated and solved. My feeling that I lacked understanding is not the result of lack of competence. I did have a lack of competence, but that's a separate issue. The real issue is my lack of a mental map between a method (differentiation) and something in the real world (determining instantaneous rate of change). -> ... (One last question to Gary: -> Can you identify a moment at which you said, "NOW I understand calculus;" -> and can you recall the circumstances of that moment.) The closest I can remember is that in the "second time around" course, I formulated the equations to describe word problems much more easily. This was the result of two skills I had obtained. First, I could visualize the solution to a word problem in terms of trying to find out about the rate of change of some quantity (velocity, for instance) with respect to something else (time, for instance). To me, this seems to boil down to an ability to analyze a physical system and create an abstract model of it. I believe I had this skill even the first time I took the course. Second, I understood what derivatives stand for in the real world, i.e. rates of change. This is the "understanding" that I lacked in the first course. Without this piece of knowledge, I could not come up with the equations to be used in my abstract model of a problem in order to solve that problem. Another trivial fact (possibly unnecessary): I use calculus so seldom these days that I'm not sure I understand it any better than I did the first time I took it over ten years ago. In any event, I think I understand understanding even less than I understand calculus. Oh well, as Kurt Vonnegut, Jr. might say, "Hi Ho." ----- /\ What cheer, /\ | Gary Schiltz, EDS R&D, 3551 Hamlin Road | / o< cheer,