> > For me it was the most difficult since I came to USA. > Most of my present students are very poor in arithmetics. > Suppose you are escorting a blind person along a street. > You have to notice a lot of things you did not care before: > every footstep, every stone, every crack in the pavement > needs special attention. Same with my students: I have to > explain every simple arithmetical and algebraical action. > Same about simple facts, such as the formula for perimeter > and area of a rectangle, what is a percentage, velocity equals > distance divided by time, there are 60 minutes in an hour... > To make a long story short, it took 3 years of me to learn to > accomplish (2) when teaching `college algebra' to students I have. >
Do you think your students, once they complete your course, maintain their 'understanding'?
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> Look at the pages 132-133 of `Curriculum and Evaluation Standards'. > There is a story about a bank deposit. Why did the authors choose > a bank for such a prominent place in the book? Because nobody can > say `why should I care about it...' - everybody cares about his > bank account. But the authors did not even care to mention that > there is such a thing as a geometrical progression in general, > with its definition and properties which can be deduced from it! > These are really acorns without the oak! The NCTM "standards" > are based on the assumption that humans are pigs under the oak. >
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?
> > > Pay attention that Prof. Jacobs is against relating to > > > mathematics as an abstract science! This does not concerns her! > > > > I think she was expressing the thinking of (some of) students. > > Exactly!!! That is my point. That is her image of students. > My (and Vygotsky's) image is different. >
But that is not what you wrote. You said that Prof. Jacobs is agains relating mathematics as an abstract science.
Tad Watanabe Towson State University Towson, Maryland