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there is another argument used here which is common to people i tend to disagree with, and it goes " i myself did not have such and such, or i did have such and such, and i did fine in college" or life, or whatever.
this is not at all an argument that someone else, or even the speaker himself, might not benefit from having a different experience.
for example some of the posters here has used this sort of argument and i have deduced some of them are from certain colleges and so i have looked at the website of those colleges to discern some information about their math offerings in which the posters "did fine".
some of these colleges list course offerings which are literally teaching grammar school math and junior high math, some for college credit, in the first 10 or 20 or 30 of their courses listings.
But the course offered at harvard in 1960 to the best prepared freshmen, is listed as a 400 or 4000 level course at many of these schools.
well of course a student with AP preparation does fine in courses of the current freshman or even sophomore level of difficulty, but years ago, before the AP revolution destroyed the better algebra and geometry course preparation in high schools, (some) freshmen were prepared for real calculus courses in college, courses that almost do not exist anymore.
one might also ask for the definition of "does fine". If it just means got an A in a shallow course, this is not my definition of fine. more like "suffered deception and consequent delusions of success".
as i have stated here before, the only time i ever got an A+ in a college math course i celebrated for one day and then concluded that I must have been in too easy a course, and transferred into another level of course work. I am much prouder of the sucessive B+ and A- from that harder course sequence than of the A+ in the easier course.
but to respond to another recent plaint again, the low level of preparation of young people is not the fault of the young people themselves, as they are not responsible for setting the standards low. it is their elders who are doing so.
We need to inspire young people, and older people too, to want to understand the world around them, not just in math, but in chemistry, English, history and all other fields. We need to remind people of the joy of thinking deeply, as opposed to treating all learning as a utilitarian pursuit.
we are not asking people to be mathematicians when we ask them to try to understand a mathematical argument the way a mathematician would. to say a car salesman does not "need" to understand algebra, is beside the point. he might enjoy doing so, and might have a more colorful and happy and productive life.
as i recall fermat was a jurist, not a mathematician by trade.
this is not at all an argument that someone else, or even the speaker himself, might not benefit from having a different experience.
for example some of the posters here has used this sort of argument and i have deduced some of them are from certain colleges and so i have looked at the website of those colleges to discern some information about their math offerings in which the posters "did fine".
some of these colleges list course offerings which are literally teaching grammar school math and junior high math, some for college credit, in the first 10 or 20 or 30 of their courses listings.
But the course offered at harvard in 1960 to the best prepared freshmen, is listed as a 400 or 4000 level course at many of these schools.
well of course a student with AP preparation does fine in courses of the current freshman or even sophomore level of difficulty, but years ago, before the AP revolution destroyed the better algebra and geometry course preparation in high schools, (some) freshmen were prepared for real calculus courses in college, courses that almost do not exist anymore.
one might also ask for the definition of "does fine". If it just means got an A in a shallow course, this is not my definition of fine. more like "suffered deception and consequent delusions of success".
as i have stated here before, the only time i ever got an A+ in a college math course i celebrated for one day and then concluded that I must have been in too easy a course, and transferred into another level of course work. I am much prouder of the sucessive B+ and A- from that harder course sequence than of the A+ in the easier course.
but to respond to another recent plaint again, the low level of preparation of young people is not the fault of the young people themselves, as they are not responsible for setting the standards low. it is their elders who are doing so.
We need to inspire young people, and older people too, to want to understand the world around them, not just in math, but in chemistry, English, history and all other fields. We need to remind people of the joy of thinking deeply, as opposed to treating all learning as a utilitarian pursuit.
we are not asking people to be mathematicians when we ask them to try to understand a mathematical argument the way a mathematician would. to say a car salesman does not "need" to understand algebra, is beside the point. he might enjoy doing so, and might have a more colorful and happy and productive life.
as i recall fermat was a jurist, not a mathematician by trade.
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