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April 10, 2014

Common Core Continues Teaching Kids the Most Important Lesson of All:
Life is a Fog of Confusion and Every Choice is Wrong

Yup.

Kids shouldn't have to wait until they're 30 to make this realization, like I did, last year. (Ahem.) They should be taught the Lessons of Kaboom while they're still young enough to give up without exerting too much futile effort.

The pic (at the link) shows a Common Core question. What they want kids to do is this:

Rather than just memorizing that 13 - 7 = 6, they instead want them only to memorize the minus tables up to ten.

Then they want them to realize that 13 = 10+3, so the problem of 13-7 can be thought of as (10 + 3) - 7. 10 minus seven is three. So, three plus three. The answer is six, of course.

Here's the problem with this, and I've said this before, so I won't belabor it: The method that they are offering to avoid rote memorization or the mechanical method of subtraction involving two digit numbers is actually more conceptually difficult than the memorization or mechanical "carry-over-the-one" method.

It is true that there is a mathematical insight in realizing that 13 is just 10+3, and that various mathematical laws (the Associative property, maybe? I forget) permit one to subtract 7 from 10 and then add 3.

But this is a higher-level, higher-conceptual-insight view of the problem.*

Confronted with kids who aren't proficient with the low-level, low-conceptual-insight view of the problem, they decide... we'll teach them the high-conceptual-insight method of doing it.

If kids "aren't getting math," it seems to me the wrong way to go is to go higher concept on them.

In addition, parents don't understand this. Parents were taught the old method of doing this problem. And parents are, let's face it, the primary teachers of children. (The actual in-class teacher is really just the pacesetter for any kid who's learning -- because that kid is really learning at home, from his parents. It's the parents who sit with him over homework and serve as in-house personal tutors, after all. A kid who is learning primarily from his teacher probably isn't learning very much at all, alas. Ultimately, you either learn from your parents or you learn on your own.)

The mistake here seems to be the exact same mistake that these Professional Education Theorists made with respect to reading. They realized that high reading ability kids weren't using Phonics to sound out words, but instead were reading new words via the "whole word" method-- they were just looking at the word and saying it.

So educators said, "Hey, let's stop teaching this stodgy Phonics stuff, and start teaching Whole Word reading, like the proficient readers employ!!!"

Well, one problem with that: The proficient readers had begun as Phonics readers, but then, having become adept at reading, then began Whole Word reading only when they were reading at a near-young-adult level.

By attempting to treat the lower-level readers like the more accomplished readers, the educators stopped teaching the lower-level readers the skill that the accomplished readers had used to become accomplished readers in the first place. And that skill was Phonics.

Similarly, it seems these people have realized that kids who have internalized the times tables and arithmetic tables have, after a few years of fluency with them, noticed certain patterns and rules they could employ -- tricks, shortcuts. Stuff like breaking 13 into 10 and 3 (and invoking the Associative Property, even if they don't know what that is) to make computation simpler.

And once again they are trying to teach lower-performing kids the tricks that higher-performing kids are using, but skipping over the basic stuff that higher-performing kids had to internalize themselves to become higher-performing kids.

This just seems wrong to me, and faddish, like Whole Word learning was -- the Cult of the New, you know. If it's New, it must be Better.

Right?

Well, if Whole Word reading was indeed Better, why can't Johnny read?

* Frankly, these tricks usually occur to someone when they understand the subject well enough that they no longer need tricks at all. At least not to get the answer; but understanding the math, they begin looking for faster (or at least different) methods of getting the answer.

I really do not get the idea being sold here that the way to make a kid who's struggling with math understand math better is to teach him the insights that come from a deeper understanding of the material.

He doesn't have the basics down yet. Why are you getting tricky with the second and third order deductions?

Understanding that 13 - 7 is the same as 10 + 3 - 7 is a very useful insight. And all higher mathematics -- and note that modifier, "higher" -- relies greatly on such manipulations-of-the-numbers-for-computational-convenience.

Right? Algebra is (almost) nothing but manipulating figures for computational convenience. When you factor out (x -2) from x(squared) -4 so you can divide both sides by (x-2), that's manipulating the expression to make it easier for you to work on.

But note this manipulation of expressions for computational convenience is chiefly introduced at... the algebra level, 8th grade at the earliest. (Oh, sure, the ideas of the Communicative and Associative properties are introduced before that, but that's like a day or two in the lesson plan.)

It's a tricky business. Memorization and mechanical operation ("carry over the one...") are boring, of course, these methods will get you the right answer.

And they're conceptually dead-simple. Why is 13-7 equal to six? Because 1, it just is, but 2, if you don't believe me, count out 13 jelly beans, then take away seven of them, and count up what you have left. You have six jelly beans left.

Dead simple from a conceptual standpoint.

People mistake memorization as some kind of high-level mental task. It's not. It's hard, it's tedious, it takes time. But it's conceptually easy. Just like walking 5 miles is conceptually easy. I don't want to walk 5 miles, but I know exactly how to do it. As a conceptual matter, it's as easy as putting one foot in front of the other. It'll take hours and hours, but it will be done with little mental exertion.

Executing a proper flop on a high-jump is much more conceptually difficult, although, once you know how, it will only take a second.

I am very skeptical that the way to cure a problem in learning conceptually-simple things is to teach some revolutionary new method of conceptually-difficult things.


That's why they were taught as the primary pedagogy in math for like... 2000 years.

Until now, I guess. Now our kids, who are struggling, are all geniuses who are going to be routinely manipulating expressions for computational convenience just like the first-track eighth grade algebra kids.


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posted by Ace at 05:47 PM

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