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Wed Jul 23, 2014, 01:57 PM

Why Do Americans Stink at Math?

The Common Core should finally improve math education. The problem is that no one has taught the teachers how to teach it.

The Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them.

It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.

The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. One 1965 Peanuts cartoon depicts the young blond-haired Sally struggling to understand her new-math assignment: “Sets . . . one to one matching . . . equivalent sets . . . sets of one . . . sets of two . . . renaming two. . . .” After persisting for three valiant frames, she throws back her head and bursts into tears: “All I want to know is, how much is two and two?”

Today the frustrating descent from good intentions to tears is playing out once again, as states across the country carry out the latest wave of math reforms: the Common Core. A new set of academic standards developed to replace states’ individually designed learning goals, the Common Core math standards are like earlier math reforms, only further refined and more ambitious. Whereas previous movements found teachers haphazardly, through organizations like Takahashi’s beloved N.C.T.M. math-teacher group, the Common Core has a broader reach. A group of governors and education chiefs from 48 states initiated the writing of the standards, for both math and language arts, in 2009. The same year, the Obama administration encouraged the idea, making the adoption of rigorous “common standards” a criterion for receiving a portion of the more than $4 billion in Race to the Top grants. Forty-three states have adopted the standards.

The opportunity to change the way math is taught, as N.C.T.M. declared in its endorsement of the Common Core standards, is “unprecedented.” And yet, once again, the reforms have arrived without any good system for helping teachers learn to teach them. Responding to a recent survey by Education Week, teachers said they had typically spent fewer than four days in Common Core training, and that included training for the language-arts standards as well as the math. . .

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.


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Response to elleng (Original post)

Wed Jul 23, 2014, 02:17 PM

1. when we go metric we can get rid of useless things like multiplying/dividing fractions lol nt

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Response to elleng (Original post)

Wed Jul 23, 2014, 04:28 PM

2. They do and they don't.

I've found that relating things to pizza and money works wonders.

"Would you rather have a pizza split up 4 ways or split up 3 ways, if you're hungry?"

The kid who blithely writes 1/2 as 2 immediately spots the problem. There's no way dividing a pizza two ways gets you 2 pizzas. And I teach juniors. Science, not math.

And yet as soon as it's related to something else, they're suddenly math stupid. They can't generalize. They don't even remember their math facts: Education is for the purpose of passing a test and getting a low-ranked letter on your report card. Everything else the Internet or a calculator can tell you.

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Response to Igel (Reply #2)

Wed Jul 23, 2014, 04:31 PM

3. Exactly. That's how my daughters' early math teacher taught,

Hands On, Food and Money! Begin by sorting and classifying Halloween candies!!!

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Response to Igel (Reply #2)

Tue Jul 29, 2014, 02:54 AM

5. Here is a lecture "On teaching mathematics" that you might find interesting...

It is a challenging lecture, but it makes several good and intriguing points:

On teaching mathematics
by V.I. Arnold

Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense.

In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun).

Since scholastic mathematics that is cut off from physics is fit neither for teaching nor for application in any other science, the result was the universal hate towards mathematicians - both on the part of the poor schoolchildren (some of whom in the meantime became ministers) and of the users.



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Response to elleng (Original post)

Wed Jul 23, 2014, 11:34 PM

4. My experience as an elementary grade teacher....we DID that.

Lordy, all of us used pizzas, pies, cakes, we had flannel board cut-outs for the kids to use...I could go on and on.

What the teachers did in middle school and high school was more concrete, and mostly rote.

We in the primary grades taught 128 as 100 + 20 + 8, had them add subtract hundreds tens ones. We used sticks of ten blocks, then placed them on hundreds blocks, etc. etc.

I could go on and on.

Some responsibility must lie later on.

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