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April 29, 2014

Louis CK Complains of Baffling Common Core Questions; Matthew Yglesias Helpfully Voxsplains Why Simple Math Is Being Made More Complicated

Louis CK complained on Twitter.

I have to say I don't find the questions he posts particularly baffling, myself, and actually I would expect that kind of question to appear on pre-Common Core/non-Common Core tests as well.

Still, I imagine this is a cumulative thing, having so many unclear concepts thrown at his kid (and at him, as parents are expected to make sense of the textbook), and this is just the problem that compelled him to tweet.

Matthew Yglesias, a reliably thoughtless advocate for Bureaucratic Empowerment, immediately Voxplained it all to Louis CK by sending him a link to another writer on Vox who led her article with this rather self-defeating headline:

The Common Core makes simple math more complicated. Here's why.

She's actually trying to prove that Common Core is Awesome, but the headline sort of hints at the problem at the root of Common Core.

Common Core needlessly complicates the simple. They complicate the simple, supposedly, to impart "number sense" to kids, to get them to understand not just that 9 +3 = 12, but why 9 + 3 =12.

That's a very ambitious goal.

I suppose we should ask this question, however: Given that teachers are currently failing in the less-ambitious goal of simply teaching that 9+3= 12, why do we believe they'll be better at the more-ambitious goal of teaching why 9+3 =12.

You guys see Stand and Deliver, the story (IIRC) of Jamie Escalante, some kind of aerospace engineer (IIRC) who decided to try his hand at teaching math at a poor, underpeforming majority-Hispanic school?

Well, he has a class of higher-level students. He drills them to say "zero times six is zero, zero times seven is zero, zero times eight is zero," and so on, and then, in what the movie industry calls a "Button" (an exit-line designed to end a scene on a dangling, interesting question that either leads organically to the next scene or suggests unfilmed activity going on beyond the filmed scene), he says to the class:

"Good (that you understand that zero times any number is zero).

Now: Why?"

The "Why?" is an interesting question. But note the order in which he introduced it: First he drilled the basics. Then, with his higher-performing students only, he introduced the Why?, not as the foundation of mathematical exploration (the foundation being rote memorization and drilling), but as the apex of it.

The last step, not the first, and not even the fifth.

I have previously written of this, calling it Cargo Cult. Previously uncontacted aboriginal populations would see the great planes flying in the sky, and would see them land and discharge various cargoes, including, say, cans of Coca-Cola.

The aboriginals wanted their own Sky God Chariots, and wrongly believed that Coca-Cola had something to do with aerospace technology; they'd collect empty cans of Coca-Cola and arrange them in red-and-white shrines in the belief that mastery of the Coca-Cola would lead to mastery of the power of flight.

They confuse the end result of a highly technological civilization (standardized cans of mass-produced, globally-sold beverages) with the necessary prerequisites for that civilization.

Similarly, Common Core bureaucrats have noticed that kids who are high-performing in math tend to have a "number sense" that extends beyond rote memorization and the "standard algorithm" for solving problems (the "standard algorithm" is their term for the classic methods of two-digit multiplication and division, the carry-the-one algorithm which will always get the right answer if you're careful with basic arithmetic).

High-performing kids begin to understand that 17+6 can be thought of as 7+6, plus ten.

This is an important thing, as I've mentioned before.

But they're teaching this ass-backwards.

First comes the foundation, then comes the elaboration and sophistication.

Common Core takes the position that you teach all three simultaneously, in hopes that increasing the conceptual difficulty of a problem, and tripling the mental load a kid is required to get an answer for 17+6, will somehow make it "easier" for him.

Douglas Adams wrote:

The History of every major Galactic Civilization tends to pass through three distinct and recognizable phases, those of Survival, Inquiry and Sophistication, otherwise known as the How, Why, and Where phases. For instance, the first phase is characterized by the question "How can we eat?" the second by the question "Why do we eat?" and the third by the question "Where shall we have lunch?"

A kid who hasn't figured out "How can we eat?" is going to starve until he does, and he's not going to profit from the "Why do we eat?" phase until he's got something in his belly.

Anyway, I've written about this before, several times.

They did the same thing with reading, and a generation lost its ability to read:

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.


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

And now they're doing the same thing with Math, figuring, insanely, that the way you get through to kids having trouble with a low-conceptual-difficulty "standard algorithm" is to teach them the high-conceptual-difficulty numerical insight and manipulation of numbers that I personally only became adept at after manipulating my thousandth equation in 8th grade algebra.

Yup, after the thousandth manipulation of an algebra equation, I did learn that I could do this type of thing not just with equations containing an x, with with equations containing nothing but numbers; and to this day I go out of my way to avoid the standard algorithm, always starting with some kind of manipulation of the equation.

Like, just for this article, I tried to think, "How would I really get the answer for 42 - 19?"

How would you do it? If you employ the standard algorithm, you probably got the answer pretty quickly.

What I did was notice 42 was just 21 times two, and I prefer working with smaller numbers, so I subtracted 19 from 21 to get two, then added it to the other 21 to get 23.

Actually, I should point out that when I subtracted 19 from 21 I had no idea what to do with the 2 -- I didn't know if I should add it to 21, or subtract it from 23 --and then I spent about thirty seconds trying to figure this out (is 19 further away from 42 than 21, in which case I should add the 2, or closer to 42 than 19, in which case I should subtract?), so actually my "manipulate the equation for ease and quickness" wound up wasting a lot of time, but still, okay, that's how I really did the problem.

But so what we are now doing is basically teaching kids that convoluted method of getting the answer to 42-19. Yes, it will work (if you remember what the hell to do with the 2).

Yes, a facility at manipulating equations for convenience and speed is a sign of "number sense," and it can be argued that anyone who can't think in this way doesn't have as deep an understanding of math than someone who can.

(Even though, in my case, my convoluted alternate method of getting an answer would up taking almost a minute, instead of the three seconds the standard algorithm would take -- but you know, people who try to avoid hard work do usually wind up doing more work than they would if they just did the hard work they were trying to avoid in the first place.)

But all this elaboration and complication, remember, is being thrown at kids who are barely able to do the basics of math -- all in the hopes that complicating everything and asking them to master Five Different Ways To Get The Answer is somehow going to make them better at math.

And when I say "five different ways to get the answer," do understand, I mean five different algorithms. Five different algorithms, instead of the one.

This is what I mean by "mental load." I don't know about how you think, but I can guess, because I think most humans share a strong preference for a certain way of thinking:

We want the simplest possible rule, the dumbest possible rule, the rule that imposes the least mental load on us first, even if that rule (that algorithm) may not be as fast as other techniques.

And we figure this: Once we have that low-mental-load algorithm in place, we will begin figuring out the shortcuts and adding elaboration to the rules at our own speed, as necessary, and as is convenient.

Most people prefer when rules are simple and complications are emergent, that is, the complications and elaborations emerge from the simple rules.

Most people hate when the rules themselves are complex and onerous. That's why most people, except people who design new operating system interfaces, hate having to learn the New Rules of the operating system interface.

Instead of teaching kids the basic algorithm and letting kids add in these other modular bits of math as needed, we're dropping this Five Different Ways to Confuse and Baffle you from Jump Street.

Two reasons for the most intense of intense skepticism on this New Revolutionary Bureaucratic Solution:

1. Whenever an organization is failing, they propose a New System You Guys!!! for doing things.

This is Standard Bureaucratic Response #1-A -- It's not our people's fault we failed, but rather the fault of the System Itself (note that unions don't care if the "System Itself" gets fired and replaced, only the people) -- and this proposal is issued whether the New System is actually preferable to the old one or, as is frequently the case, not.

An organization needs to explain its failures and needs to propose the hope that if they just change their System, they will finally begin improving their performance.

Usually they continue failing in a different way. Sometimes they even fail worse (as in the case of replacing Phonics with Whole Word).

This New System!!! will be proven to be a failure in 10-15 years, but bureaucratic inertia will keep it in place for 20-30 years; and during that period, the New System!!! will have accomplished precisely what it was intended to accomplish, to wit, solving the problem of the bureaucracy being criticized for failure.

And not, by the way, actually addressing the causes of the failure.

Just getting people off the bureaucracy's backs so they are free to fail without too much aggravation about it.

2. Not only are kids are parents baffled by this poorly-explained multiplicity of algorithms for getting the same result, but I strongly suspect their teachers are as well.

I think if their teachers understood this Dazzling Array of New Tools to Get the Wrong Answer, the kids would understand it better.

I think teachers don't really get this, and one of the most crippling things you can do to a child's mind is put a teacher up in front of him who doesn't understand what the hell it is she's supposed to be teaching him.

He will not be able to get good answers from her -- she doesn't understand it herself -- but she'll be required to pretend as if this all makes sense.

The kid will learn under this regime -- he will learn that education is futile and effort is wasted and thinking hurts your brain, and only leads to more confusion and embarrassment.

The exact opposite of empowerment, which is what learning should be about.

If teachers are not teaching the "Standard Algorithm" well enough at the moment, I am really baffled at concept of giving them alternative ways to fail to teach kids: "Skip-Counting," "Number-Pairs," "Front-Estimation," and all the rest of it.

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posted by Ace at 04:54 PM

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