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The examples given seem to be a bit of a strawman argument. Sure, asking a single, focused question tests less for understanding than the multi-part Common Cor
by douche 11y ago
The examples given seem to be a bit of a strawman argument. Sure, asking a single, focused question tests less for understanding than the multi-part Common Core examples. But at least from what I remember, you'd be drilled on all the different permutations of these kinds of word problems anyway, so the net effect is the same.
Also, I really don't see how their reasoning follows on their first example. 3 shirts, $4/per shirt = $12. 7 shirt, 6 buttons/per shirt = 42. All that multiplication is, on the integers, anyway, is repeated addition. The only real difference I can see is that you can do the first example on your fingers and toes, whereas you'd have to scratch some tally-marks in the dirt or on paper to do the second if you don't know multiplication tables.
What I wonder about with these Common Core curricula, is whether students will ever get enough practice working through mathematics operations to really be comfortable with it. When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, etc. Maybe five or ten minutes, every day; they were probably graded enough to make us do them, but not enough to really matter. Most of the Common Core style math worksheets I've seen require far too much rewriting the algorithm from mathematical notation into grade-school English to ever allow that kind of repetition.
- DanBC 11y ago> When I was taught math (and it really wasn't that long ago), we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, A child can do sheet after sheet of calculations and co-incidentally get the right answer, without having any understanding of what they're doing. They can manipulate these symbols because they've memorised a routine. But because they lack understanding they stumble when they move onto something more advanced - they need to forget what they thought they knew, re-learn it properly, and learn the new thing. I agree that the first example is a confusing example to use, and that there doesn't seem to be much difference.
- nmrm2 11y agoYou'd be absolutely astounded at the number of vector calculus students at highly regarded universities who: * identify a rote procedure to apply when a problem of a particular form is seen * execute the rote procedure * come up with "<equation here> / 0" * ... and then turn the thing in anyways.
- jerf 11y agoTo me, this is the real problem. I see little reason to believe that Common Core fixes it. But then, I have a bit of an unusual perspective on the problem. My position isn't that the old curriculum is good and this new one is bad. They're all pretty darned bad. Common Core has some neat bits in it, but it's still polishing a turd; Lockhart's Lament still applies to it in full force.
- nmrm2 11y agoCommon Core is an improvement. But things won't get much better until teaching pays a competitive salary.
- tempestn 11y agoThat, or very slowly as iterative improvements to education eventually produce better-educated teachers.
- nmrm2 11y agoI am one of little faith. At the high school level, there's really only so much that can be done without the instructor understanding the end-game. It's just fundamentally difficult for an algebra teacher to effectively teach algebra is they haven't really groked any group or ring theory or linear algegra. And it's really hard for a Calc I instructor to teach effectively without having really mastered some elementary analysis. Especially the second one. I'm not sure what a calc I teacher is supposed to say if a student has any foundational questions, which any bright student probably will.
- debacle 11y ago> we were never allowed to use calculators, and we did sheet after sheet after sheet of additions, subtractions, multiplications, divisions, polynomial expansions, equation simplifications, etc. Both occur. I was very averse to the calculator use in the classroom, but from what I have seen that part of the curriculum is more about learning how to use a calculator than doing math with the assistance of a calculator. Memorization of arithmetic is still very important and focused on.