> Do you think your students, once they complete your course, > maintain their 'understanding'?
To some extent. Some students take more than one of my courses, and in these cases I see how they become more and more `understanding'. But it depends more on themselves - their attitudes etc. than on my competence or efforts. Every student who becomes really competent has been an outstanding person from the very beginning.
> Is your problem the fact they didn't mention that the same idea can be > discussed using geometric progressions? Or is it the fact that they > didn't use geometric progressions instead of the bank example? Does the > mathematics involved lose value when we use 'real-life' situations which > can be solved mathematically? [I think I shared with you that I'm not > personally a fan of the term 'real-life' before.] Is there an occasion > where this type of 'real-life' discussion is more appropriate than more > 'abstract' dicussion?
My problem is that they use fruits of mathematics and reject mathematics. Mathematics has a certain structure: there are assumptions, definitions, deduction, theorems, formulas, examples, problems. All this is rejected in the "standards". Instead there are some cumbersome and unispiring `activities' without any interesting ideas or fruitful results.
> But that is not what you wrote. You said that Prof. Jacobs > is agains relating mathematics as an abstract science.
Because this is what she wrote. She might mean something different, but I am tired of educators who cannot write what they mean.
Andre Toom Department of Mathematics email@example.com University of the Incarnate Word Tel. 210-646-0500 (h) 4301 Broadway 210-829-3170 (o) San Antonio, Texas 78209-6318 Fax 210-829-3153