I guess we have reached the point of fundamental disagreement. I do not make such a generalization that disucssion of "advanced" topic is a disguise for teacher's inability to teach.... I don't know how you can get to such a conclusion after reading so many of very thoughtful responses in this list.
I have no disagreement that problem solving is important, and there are many interesting and worthwhile problems within arithmetic. And, I have no objection to including those interesting problems in place of many meaningless skills [when I say "meaningless," this is in reference to a particular child at a particular juncture of his/her mathematical learning - not a general condemnation of those skills].
I wonder what the real problems of your college students are. You seem to think it is the kind of teaching that include discussion of fractals and other interesting "advanced" mathematics ideas because teachers cannot teach the basic arithmetic. Is it really the case? Have you asked, systematically, your students what their k-12 mathematics teaching/learning was like?
Tad Watanabe Towson State University Towson, Maryland
On Mon, 8 May 1995, Andrei TOOM wrote: > I am sure that in many cases discussion of fractals or something > `advanced' like that in middle schools actually is a disguise > for the teacher's inability to teach students to solve > elementary, but substantial problems.
> snip snip snip
> I do not agree with you, and this is important. > Arithmetics IS mathematics, or, more exactly, can be. > There are very good arithmetical problems and every human being > in this century MUST go through an experience of SOLVING > (rather than just DISCUSSING) them. > Too many of my (college) students have not had enough of > this experience and this seems to be the main root of > their further difficulties. > Andrei > > > >