why should we even bother to teach Algebra
It like asking gucci, "now that we have spell-checkers, why bother with English class?" Spelling is a small and trivial portion of English class. Just so the manipulation of equations in algebra エルメス スカーフ.
Unfortunately, drill work has swollen up until it consumes nearly the entire algebra curriculum エルメス. It as if students in English class learned the definitions, spelling, and parts of speech of 20,000 vocabulary words, but never learned of Shakespeare, Hemingway, or Orwell, much less wrote their own work バーバリー コート.
In algebra class, students who use computers to do the grunt work could focus more on applying algebra to real situations, and thereby understanding what it does. When I supported myself as a private tutor, parents repeated told me, "my son is really good at math. He just having a little trouble with word problems." Most people honestly think that if you can solve a quadratic equation, you understand algebra, but there just this little extra thing called "word problems" that is one last detail you have to take care of.
For example paul smith, in algebra class students could start developing the intuition that I use as a physics student every day. x^2), exponential growth ポールスミス バッグ, and superexponential growth. These concepts come back in calculus バーバリー 時計, but understanding and applying them first in algebra class is a good start.
I also use algebra to answer questions by referring to the way things scale - volumes proportional to length cubed, areas proportional to length squared, and therefore surface area-to-volume ratio inversely to length. That has important consequences in things like biology (why do large cells have so much internal structure while bacteria are just bags of jelly?) and thermodynamics (why is flour explosive, but not bread?). That the sort of intuition and application you could learn in algebra class, but you don because you too busy doing the work that computers ought to do for you.
Students who don have to do endless drill work could also do problem solving of the sort currently reserved for math competitions. They could learn new and related concepts such as group theory. Math is incredibly rich ヴィトン, as you can learn by picking up a serious survey book like the Princeton Companion or a recreational book like those of Martin Gardner シャネル バッグ.
It a sin that such a tiny portion of math is taught in math class, and that the portion we focus on is dull and rote. The way we do math class now is symptomatic of teachers being overworked, underpaid, and undereducated, of the homogenization impressed by state-mandated standards and tests, and of the now-ingrained cultural attitude towards math.
If we were truly freed from the "do problems 17 to 53 odd" paradigm of math class, students would spend more time engaging in ideas, learn more, find that class more enjoyable, and begin to view it as a genuine lifelong intellectual outlet the way literature is エルメス バーキン.
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