W. Gary Martin <firstname.lastname@example.org.Hawaii.Edu> writes:
>Ted Alper <alper@Ockham.Stanford.EDU> writes: >>Why is it important to teach that mathematics is a growing body of >>knowledge? I mean, it's certainly true, and it is better to >>be aware of the wide world than not -- but how much attention should be >>paid to this in an 8th grade math class? <etc.> > >This is not just a "fact" to be conveyed to students. It is a mindset, a >way of looking at the study of mathematics. Mathematics is not something >dead people who lived years ago did. Mathematics is a continuing creative >enterprise of developing knowledge done by people who are LIVING. >Mathematicians do this for a living; we share in that enterprise as we make >sense of the mathematics we are studying, no matter what level that may be. >Too often students see mathematics as a body of knowledge to be assimilated >(a product). To me, seeing mathematics as an exciting and worthwhile >activity (a process) is at the very heart of the Standards.
Sure, teaching math is or ought to be about teaching a certain mindset to problems that go far beyond the template problems in the textbook. That is not the same thing as encorporating the study of "all [or even any] of the new mathematics done since world war II" into the K-12 curriculum.
Developing the mindset might be done as well by studying Descarte's "Rules for the Direction of the Mind" (c. 1650) which applies as much to a beginning algebra "word problem" as it does to modern mathematical research. The approach is ancient; the mathematics (at least at the level of high school students) is also pretty old; the world around you, in which you apply the approach and the mathematics, is ever-changing.