Why is it one or the other? Because with the mass education system teachers do not have time to devote to each student a full varied curriculum.
While a calculator can do double or triple digit dividing (polynomial division = many numbers division) they cannot point out when you accidentally hit an extra 3 in there. (though I admit all that texting practice the kids get these days certainly helps with the calculator use...)
Calculators are also generally not at the grocery store when deciding between size A and size B. Your brain on the other hand is conveniently attached at all times.
But then knowing more details about any one of the million careers out there is not quite as helpful as you might think. There are after all TONS of options out there, specializing is over done IMO.
I figure a kid aught to be a jack of all trades, till one clicks. Then one should be a jack of most trades and learn as much as possible about the favorite. Unfortunately in America with the forced education system we have we do not allow for varied time of choosing a trade.
My son asked me the other day when the last time I used algebra was...I asked around, haven't yet found anyone who used it since highschool classes (or teaching) but I still teach it. More for the logic than the actual future need. If he decides on engineering or something he will need it, if not, no big.
Finances on the other hand we talk about when we discuss turning lights off, not wasting water, buying brand A vs Brand B (and the math for which size is cheaper by the oz) paying bills, not eating out whenever we want, and so on.
(there is also of course plenty of other 'home ec' stuff, history, music, art, language, writing, reading, science, ect)
So I don't see why it needs to be one or the other, for a homeschooler, for public education ah well can't help really. You do have limited time and need to keep millions happy....I
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