Classical Values :: Divining and dividing the pi in the sky

December 15, 2004

Divining and dividing the pi in the sky

If God is the source of law and government, and if law and government are the source of education, then logically, that means God is the source of the educational system which, um, teaches children how to, um, calculate and stuff.

Right?

With that in mind, I want to turn to an item accompanying this article on American education:

A Sample Question
A scoop holds 1/5 kilogram of flour. How many scoops of flour are needed to fill a bag with 6 kilograms of flour?

According to the Inquirer, only 52% of eighth grade students were able to answer that question. This means that 48% apparently don't know that six times five is thirty. The percentages are so tantalizingly close to the election results that I'm tempted to ask which group votes for which party.

But I won't!

Instead, I'll return to the task at hand in today's Inquirer, which (apparently) is to determine why eighth graders do not know that:

5 x 6 = 30

On this central point, there doesn't seem to be much disagreement.

Huh? What point? Am I talking about whether five times six is thirty, or the fact that so few eighth graders can make such a determination? I don't mean to be facetious, but yesterday I heard a conversation in which an engineer agreed that engineers were not political because there's no way you can politicize Pi. I don't have the symbol for Pi handy right now, but most of us, um, know that it's 3.14 and then some. Certainly, that wouldn't strike any reasonable person as political.

Would it?

Well, maybe I should back up a bit, and return to today's Inquirer. Here's someone who ought to know:

Cathy Seeley, president of the National Council of Teachers of Mathematics, said that the call for change boils down to this: "From K to 12... we must embed computation in a strong foundation of problem-solving... . You anchor arithmetic by shifting from teaching kids math procedures and then giving them word problems to getting them involved in a much broader range of problem-solving techniques" from the beginning.

What does that mean? Learning about Pi, perhaps? I don't know, but the article talks about real life situations and making math "meaningful...." ("Meaningful?" Isn't that doubletalk for simply defining a definition?) In any event, there's a difference of opinion:

Bruce Normandia, chairman of the department of curriculum and instruction at Monmouth University and a cochair of the task force, said he agrees with many of Seeley's and Schmidt's observations. "In many K-8 programs, there still remains a great deal of emphasis on obtaining procedural knowledge and less on conceptual knowledge," he said. "When we develop more of a conceptual approach, we'll see more children turning to math."

Some education experts, however, say that a one-sided emphasis on teaching problem-solving and math concepts is holding back U.S. students. Tom Loveless, of the Brookings Institution's Brown Center on Education Policy, says that, instead, mastering basic math procedures should be the foundation.

"The successful countries have in common... a relentless emphasis on arithmetic, especially in the early grades," he said. "In learning about arithmetic, students learn how numbers work; it's the phonics of math. There are some things you do have to memorize. Drill and practice have their place."

How are we to conceptualize Pi? Telling children that there's a ratio really isn't helpful if they don't know the number, or how to obtain it. And what makes these educators so certain that conceptualizing meaningful theories will cause children to learn that 5 x 6 =30? Why would they?

I have to ask, in all seriousness: why would "showing" a child that there's a "meaningful" ratio between the diameter and the circumference of a circle make him want to learn it?

Whatever the process is, apparently, the kids have to repeat the same stuff year after year without learning it. So says William Schmidt, of the International Policy Center for Curriculum Studies at Michigan State University:

In many middle schools, he said, students "are still relegated to studying the same basic math they studied for the previous five years, except at a higher level."

Well, I'm glad they're studying the "same stuff" at a higher level! We wouldn't want them studying at lower levels, would we?

Pi is not political?

I say it is political. (At least, the gulf between those who know it and those who don't certainly is.) There's only one way the problem of students studying basic math at ever-higher levels can occur -- and that's by politicization of education. Somehow, somewhere, there has been an official determination (and implementation of that determination) that there can be no such thing as failure. It is axiomatic that when failure is prevented, success is also prevented. I realize that a strong argument can be made that children should be promoted in school regardless of failure to learn things like 5 x 6 = 30, but such an argument always boils down to simple politics.

At the heart of the argument in favor of promoting the ignorant to a higher grade is the assumption that ignorance is OK: that it does not matter whether or not a child knows 5 x 6 = 30. At the heart of the other side is the assertion that it does matter. This is a policy argument. By definition it is political, and it is called "social promotion," defined by one critic as follows:

the misguided belief that school children should be kept with their age group regardless of their academic performance lest it adversely affect their self-esteem and their attitude toward school.

Which means that according to the people who are making the rules, things like pi are highly political.

If you still doubt me, I suggest asking the advocates of the "socially promoted." Just don't ask the socially promoted themselves, because they can't be expected to know about things like Pi.

Maybe ignorance is strength after all, but is it really fair to blame God?

MORE: Via Joanne Jacobs, I found this New York Times piece, which highlights the politicized nature of "social promotion" -- even at the third grade level.

The debate in New York City over promotion standards in the public schools has played out across the nation and has long been the subject of intense discussion among education experts.

Over the last two decades, dozens of studies have led many educators to conclude that policies forcing students to repeat a grade are costly and counterproductive, resulting in no gains in student achievement and sharp increases in dropout rates. Such policies, like one in New York City in the 1980's, are often quietly abandoned after just a few years.

"The problem is not social promotion," said Jay P. Heubert, a professor at Teachers College at Columbia University and co-author of a major National Research Council report on the issue. "The problem is low achievement, and just about anything we can do for low-achieving kids will be better if we simply leave retention out of the equation."

But if illiteracy and ignorance are rewarded by promotion, isn't it obvious why schools turn out functional illiterates?

Add to that this Christian Science Monitor piece (also via Joanne Jacobs):

The rise in retention and dropout rates has revived and retooled a controversy over whether schools retain students for the right reasons, and whether the shame and frustration of retention is prompting more teenagers to quit school.

Is it heresy to ask whether chronic low-acheivers even belong in regular schools?

posted by Eric on 12.15.04 at 09:43 AM

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Two great posts on mathematics education: one at Classical Values, and another at Baldilocks. I can tell you from experience that these issues ring true. [Read More] Tracked on December 15, 2004 08:05 PM

Comments

Well... I think you're beating at something of a straw man here. I think the problem is deeper than social promotion, and I think it *is* important to teach kids how to conceptualize things. (An answer to your question about "why" is given below.)

I would bet most of those kids know that 5 x 6 = 30. (Although you're right, if they don't, don't promote them!) It's the word problem that they don't get. (And maybe fractions, too.) I have seen this a lot while tutoring kids: the kid will know that 5 x 60 = 300, and (if the kid drives) she will know perfectly well that if she drives for 5 hours at 60 mph she will have gone 300 miles, but ask her to "conceptualize" it ("A vehicle is traveling at a rate of 60 klicks per minute. After five minutes, how many klicks has it gone?") and she will throw up her hands in despair, or try to plug it into a formula her teacher has given her. What she will not do is deduce immediately that she needs to multiply 5 x 60.

It's a hard question, though. On one hand I absolutely think that drill, drill, drill is required, especially in the early years when one is learning multiplication tables. But after that you have to show them *why* they might want to know that 6 x 5 = 30 (See, you can use it to figure out things!) if you want them to retain it.

Case in point of why meaningful relationships help: for many years I was taught in science class about the electron, the neutron, and the proton. Every year I would dutifully learn which had positive vs negative vs no charge, which was inside the nucleus, and which were heavier. And then I would promptly forget it, because a) I knew it would just be taught again the next year b) as far as I could see there was no point, it was just busy work. I suppose all my friends felt the same. And then, finally, in high school, I took chemistry, which was a total epiphany: Oh!! THIS is why you care about electrons!

And i was a *good* science student, who ended up loving science and went on to become a scientist/engineer.

ca · December 15, 2004 01:23 PM

There's ANOTHER way that pi is political, in the sense that you mean "3.14..." I'm referring, of course, to the nafarious and evil base ten numeral system, which is adopted by people purely through the use of brainwashing techniques. I have been a base twelve partisan for some time, and I swear I will not rest until pi is 3.18480949...

rumpy doppelganger · December 15, 2004 02:12 PM

McLuhan tells us Number is sense of touch extended, so working through word problems ought to engage the imaginary sense of touch. I'd re-write the word problem:

We need to fill a 6 kilo bag from a barrel of flour. The scoop we're using is labeled 1/5 kg. How many times will we scoop flour from the barrel before we fill the bag?

Stephen Hoy · December 15, 2004 02:18 PM

Thanks for your thoughtful comment. The reason I focused on 5 x 6 = 30 is because it's the MOST complicated part of the problem. If eighth grade students cannot grasp that it takes FIVE 1/5 kilogram scoops to make a kilogram, then once again, they don't belong in the eighth grade. And if they don't understand the "wording" of this simple problem, they also don't belong in the eighth grade.

Obviously, conceptualization is relevant, even "meaningful" -- but I suspect that these teachers are simply using reassuring language to hide the fact that either they aren't teaching or the kids aren't learning.

But whoever is at fault, simple common sense suggests that students who are unable to compute not be promoted.

Eric Scheie · December 15, 2004 02:24 PM

This could be the fault of "instruction vs education". Surely they all know that 6*5=30, but how are you supposed to connect that fact to a problem about scoops and bags?

It's a short step from that one to the one about a man and a half digging a hole and a half in a day and a half; how long would it take 6 men to dig 2 holes?

I cringe when I see things like Seely's quote. I just finished Diane Ravitch's "Left Behind", a history of the fits and starts of education in this country since the late 1800s. It's a discouraging story about false trails, of things proposed simply because they were "new", an almost complete abandonment of things that worked (like phonics), of educators whose main idea was producing useful, compliant citizens, not people who knew how to think and solve problems (life problems, not just math ones).

Mike · December 15, 2004 06:11 PM

I wish the republicans could work out some education reform for us...reform that ensures that teachers are qualified to teach and students will not be left on the wayside (which is necessary, despite your oh so qualified assessment)...oh what could they call it?

And it would work too. Definitely. Yep.

Anonymous · December 15, 2004 08:57 PM

Oh, man. Based on my experience, if you left behind everyone who couldn't do a simple word problem involving fractions easily, that would have been the majority of my ("academically gifted") eighth-grade class, and probably a significant portion of the 12th-grade physics students.

This isn't strictly relevant (it has more to do with abstract thinking than word problems), but when I was a TA for algebra II at the TIP nerd camp (you had to take the SAT, get the cutoff math score, etc.), it was AMAZING to me how many of these academically gifted eighth-grade kids, the top of their classes at home, would say with a straight face that 1/a + 1/b = 1/(a+b). We fixed that, but still...!

Both more drills and more conceptualization and more "Is that answer really reasonable?", that's what I say :)

ca · December 16, 2004 03:54 PM

Also, that word problem is worded in such a way that ONE could be argued as a justifyable answer. That is, if you are filling up a bag, you wouldn't use 30 different scoops once each, you'd use one 30 times. As a former math teacher, you have to be really careful in how these sort of problems are worded, or you end up with "trick" answers that don't have anything to do with the math skills being tested.

spodbox · December 16, 2004 04:09 PM

I was real dumb and lazy in math. I always got D's and F's. ha! ha! Occasionally, I got C's, but only in arithmetic, never in algebra or anything abstruse like that. In 1st grade, I turned in an arithmetic workbook with nothing in it. I said I wrote it in invisible ink. ha! ha! In 6th grade, our teachers divided us up into the smart kids like my brother (who always got A's and was doing trigonometry on his own for fun ), the average kids, and the dumb kids like me. We dumb and bad kids had a lot of fun goofing off. ha! ha!

I was far more interested in myth than in math.

One thing I did learn from my brother is that pi = 3.14159265 (plus an infinite number of other digits....)

Hmmm.... The smart vs. the dumb -- math vs. myth -- the left hemisphere vs. the right hemisphere -- Wanda vs. Dawn?....

Steven Malcolm Anderson (Cato theElder) the Lesbian-worshipping man's-man-admiring myth-based egoist · December 16, 2004 05:52 PM