>On Fri, 24 Feb 1995, Dr. Susan Addington wrote: > >> ... >> I am teaching a course in topology for math majors. >> ... >> [Historical note: Point-set topology has been taught by discovery >> methods for many decades--the Moore method, or Texas topology. >> However, this isn't feasible for a 10-week course in which >> many new concepts must be introduced and understood.] >> > A certain mystique has developed around what Moore did but in its >simplest form, he expected students to solve significant problems. The >idea that "covering" some laundry list of topics is more important than >this is not a new one whether the time available is 10 weeks or 10 months. >(A variation of Murphy's Law: In mathematics courses, the topics will >expand to well beyond what can be covered in the allotted time.) It >makes no more sense today than it did in the past to trip lightly over >many topics while doing nothing in depth. The Standards can be read in >so many ways that there is a valid question as to whether they stand for >anything at all; but if they do, then clearly understanding is stressed >and "covering the material" spurned. > >Jack Roach <jroach@NeoSoft.com>
Jack, I don't think that covering the material is spurned in the standards. What is spurned is covering the true understanding with a bunch of meaningless.....well...for lack of a better word ...nonsense. I think Dr Addington hit on a key and that is allowing students to take a problem and really discuss it and see what things they can learn from it and get a the underlying concepts. Lastly, I want to know what is the big thing with covering the material? To whom is that important? Do you think the student cares whether they cover the material if they don't have a clue as to what is going on? I would have to think not.
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