Why American Kids Aren't Learning Math
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(Beautifully written by Professor Ralph A. Raimi)
Parents across the country, now with the support of scientists and mathematicians ... have also been finding their voices.
The real contest in ... hundreds of school districts across the country - is between mathematics and non-mathematics, between academic content and childish time-wasting, between what children can learn and what the present curriculum is pretending to have them "develop." A good mathematics program takes advantage of the mathematical discoveries of thousands of years of civilized effort, while [some would have] them counting with sticks, starting history all over again.
The systems of decimal and fraction notation are marvels of compressed information, intellectual advances that Euclid did not have available. Arithmetic is not trivial mathematics, and it certainly will not be "discovered" by school children. It must be taught, and practiced.
Arithmetic is not "a list of formulas to memorize"; its algorithms, such as "long division" and "invert and multiply," are not made obsolete by hand calculators. They are not merely "ways to get answers"; their understanding is basic to the understanding (not the "memorization") of more advanced mathematics such as is used in the daily work of electricians and machinists - among many, many others, including of course college mathematics and the scientific professions.