Henry Baker wrote:
In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic.
Actually I disagree about teaching GCD and LCM. These are the concepts where kids are genuinely introduced to thinking about the integers from the multiplicative point of view -- GCD and LCM are the thing that actually gets them to think about prime factorization. Most kids will never be taught any "number theory", but I think even rudimentary math education should make you think about why 15 and 16 and 17 are not all pretty much the same. --Michael -- Forewarned is worth an octopus in the bush.