On Thu, 23 Feb 1995, Edward S. Miller wrote: > === stuff deleted ===
> Now for my personal spin on algorithms. Humans have spent countless > effort to develop efficient means for accomplishing all sorts of tasks. > In mathematics, we see dozens or thousands of algorithms put to use, > depending on our level of immersion and experience. The long division > algorithm and the multiple digit multiplication algorithm (again, the > one I use based on the distributive law) are the earliest instances I > recall of iterated algorithms with multiple _different_ operations; > division is the first with a nontrivial ending condition.
Could you expand on this a little?
> > Throughout subsequent mathematics we encounter such algorithms of all > types. Sometimes, in "real life," for physical, temporal, or economic > reasons, it is necessary to use algorithms for single or repeated > operations. We do need to teach our students how to apply algorithms. I > happen to prefer long division because if we have to wait for > factoring or Euclid's algorthm or Horner's algorithm or L'Hopital's rule, > we're dead before we start. >
But you are not advocating teaching in the sense of imposing algorithms on students whether or not they make sense, are you? Or, are you saying that there are contexts in schooling (which I happen to believe is a part of "real" life), there are occasions we should?
I will appreciate a little more elaboration.
Tad Watanabe Towson State University Towson, Maryland 21204
PS: I'm sorry that I did not include my "signature" with the earlier post.