An excerpt from my thinking:
…How does undergrad math build upon high school math? What do they expect from college first-years? Rational arithmetic definitely. I heard about a multi-variable calculus course that was no calculator allowed, so definitely fractions. Why, when the calculator can do them all for you?…
Off spun the tangent.
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Particularly if you’re not actively engaged in the discussion, it’s easy to think school math is all about one question, “can they do it or not?” It’s a relic of antiquated mindsets about math education, but multiplying, converting, adding, and reducing fractions have played an enormous role in curriculum and the general understanding of what math should be for young people. Now, these skills are tested for at every turn, in an attempt to answer the above question, “can they do it, or can’t they?”
No Child Left Behind says, “well, they had better.”
Actually, everyone can do this stuff, and it doesn’t take long to learn! We spend years in school teaching techniques and tricks, when much simpler algorithms exist. (Pick up calculator, type in expression, and hit enter, to name one.) We get a “head start” by teaching 3rd graders to convert and add 1/2+1/3, but as Salviati says in A Mathematician’s Lament, “It’s just not a question very many eight-year-olds are asking.”
Elementary and middle school student should have engaging experiences with fractions and rational arithmetic, but I’m happy to bolster their ability with calculators. Something amazing about a societal megastructure like ours is how unnecessary (let alone impossible) it is for everyone to know how to do every part of everything. Someone had to program the calculator, but the work is done. Now let’s spend less time training children to perform tasks so soulless a computer can do them incredibly better.
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Mathematical expertise, the kind that creates apple products and energy efficiency doesn’t come from standard material. It comes from the individual relationship a student has with her subject. It comes from internal wonderings, wanderings, and discoveries that lead you on your path of investigation.
If an interested someone takes an interest in really figuring out what’s really going on with fractions, the discussion could last as little as a week. When you truly care to know, and someone talks you through it, sometimes it’s that easy, especially if you leave math class feeling capable and clever.
Give students gratifying mathematical experiences as they grow up, and when fractions come up in a project, program, or piece of avant garde music they care about, they will have a chance to get right down to it.
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We’ve tricked students (and the public at large) into thinking math is about things you can or can’t do, with fractions only a part of that. Along the way, the human tradition of creative discovery and exploration that is mathematics is dying. Let students be the kind of mathematicians they want to be, because some of them (students and mathematicians alike) don’t care much for fractions.
YES, you can use calculator! Would you like to know why?