Improving math education: a conjecture
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4 4 + 2
4 + 3
Of course, they could figure out that 9/16 is 0.5625, that 35/64 is 0.546875, and that the former is thus bigger than the latter, but they wouldn't immediately convert 9/16 to 36/64 and see it was bigger.
When I expressed my surprise, we discovered that they never studied fractions in school. We decided the only likely reason US students studied fractions in elementary school was to be able to deal with inches, gallons, and the like. From vague recollection, I must have spent the better part of a couple of years in elementary school arithmetic studying fractions plus memorizing how many feet in a mile, pints in a gallon, and teaspoons in a cup (not to mention conversion factors from those units to metric). By comparison, my European colleagues had to learn a set of metric prefixes, the names of basic units of measurement, and the universal conversion factor of 10 (just to show there's a Wikipedia page on almost anything!).
As it's often written that students in other countries are often, on average, well ahead of US students in math skills and that such a gap makes us less competitive in world markets, what if we switched to the metric system (or, more precisely, the International System of Units)? Would that make a year or two long hole in math education that could be filled in with more advanced topics? Would that help us in the USA catch up?
I don't know. I recognize that it's a challenging problem, and there is no silver bullet, not even in my idea. I would be curious to know if anyone has evaluated this approach.