We provide "crutches" for the lack of algebra, when knowing it would save paper and money. Tax booklets have 40+ pages of tables with each income level in $50 increments printed with the corresponding tax. If the average American could do the simple piecewise function calculation:
T(x) = 0.15x for x<= 40,000 (or whatever the cutoff income is for the 15% rate)
or = 6000 + 0.28(x - 40000) for x > 40,000 (assuming 28% tax on excess earnings
it would take only an inch of paper on one page, not 40+ pages.
Lack of knowledge of compound interest is a great contributor to the mortgage crisis. A friend from China (an English major) told me "Most of us have our apartments (the equivalent of houses) fully paid off because we know the effects of the formula A = Pe^rt." We can blame our legislators and bankers, but each person is responsible for managing his/her own finances and making informed/prudent choices is something that people in many other countries seem do better than we do. In the county where I live, over 1/3 of homes owned in 2006 have foreclosed, and over 50% of the remaining currently owned homes are "underwater" (with less equity than debt). I can't help thinking that while a knowledge of algebra might not be "necessary", it could potentially save a lot of grief.
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Originally Posted by JVN
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As a jr. college math instructor, I have to admit that I'm not crazy about the appeal to math as an art, with self-discovery as a necessity.
In robotics, not many students can invent the (mecanum) wheel, but many more are capable of copying and using the designs of others. Strict copying (similar to memorization and application of formulas) allows students to practice until understanding kicks in, and allows them to reach much higher levels (and generate more enthusiasm) than self-discovery would in the same timeframe. Shortly after the Vex platform was released, I watched students spend months building robots less functional than the Squarebot. That's where self-discovery without copying gets you (especially if you have solid but not stellar talents), and I would never want to return to that.
Exceptionally talented people seem to pick up the concepts and use them for their own purpose, no matter how badly a subject is taught. They're also the ones who see patterns and beauty in discovery. However, I have a child who struggles with math, and for her, "drill and kill" math has been very effective. Like washing dishes, she may find it boring, but with hard work, she can do it,and there's pleasure in doing something well, even if you didn't discover it yourself.
Motivating students to do the boring work helps, and connecting math to previously discovered concrete examples (rather than to what they can imagine/discover) seems to work well with my lower level students. For example, whenever students ask "Why do we have to know about singularities?", the
Tacoma-Narrows Bridge, coupled with a discussion of resonance caused by undefined frequencies gets their attention. I don't expect them to discover the formulas on their own. And I don't see being on a time-table to teach a broad-based curriculum as necessarily bad.