Gary Martin writes: >Steve: The question that I have with the Basics idea is... When does >tomorrow come? When do the specifics finally appear? In other words, >students learn whole numbers so they can do fractions, fractions so they >can do algebra, algebra so they can do precalculus, precalculus so they >can do calculus, ad infinitum. I have heard calculus teachers say, don't >worry about understanding, they'll get that in real analysis. Just >wondering... Gary Martin, Univ. of Hawaii
Yes....we do, indeed, need to learn fractions in order to do algebra etc.....but while learning fractions (for later algebraic use) there is nothing wrong in solving problems that rely only upon the use of fractions TODAY. The way I see it.....1)we show a kid how to add two fractions with unlike denominators....then 2)we let him try a couple himself....then 3)we ask him something like..."one third the atmosphere of Mars is hydrogen and one fourth the atmosphere is carbon dioxide...what fractional part does this represent?". Then 4) the kid goes onto algebra knowing fractions and can now solve fractional equations with little difficulty when the topic arises....but in the mean time he also can solve Mars problems today.