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.

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...

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?

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.

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).

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.

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 :)

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.

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?....