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Topic: regarding infinity
Replies: 4   Last Post: Apr 20, 1995 10:30 PM

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W Gary Martin

Posts: 80
Registered: 12/6/04
Re: regarding infinity
Posted: Apr 19, 1995 12:57 PM
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Uhhh.... Having done some research with adults and with 15 year-olds on
concepts of infinity, I hope folks are recognizing that these are very
non-trivial ideas. For example, about two different lengths of segments
having the same number of points. Hey -- 98% or more of the educated, adult
population could tell you -- a longer segment has more points! It's
obvious! In fact, many important understandings of infinity are quite young
historically.

What tends to happen in schools is that students are "told" all about
infinity, leading to school-knowledge that has little impact on their
underlying knowledge structures. Their intuitions in this area are very
compelling and very resistant to change! I could write an article on this.
In fact, I have. :) But just to say, PLEASE be careful in pushing students
into premature "generalizations" about infinity that are not their own!
It's better for them to be confused than to come to believe something for
the wrong reasons, which leads to brittle, unusable knowledge.

Rev. Gary, on his soapbox again


============================================================
W. Gary Martin 1776 University Ave.
University of Hawaii Honolulu, HI 96822
Curriculum R & D Group (808)956-9956; FAX (808)956-4984







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