From the anti-intellectualism department, arguably:

An emeritus psych professor, Peter Gray, has made the argument in *Psychology Today* that we should not teach math in elementary school (K-6). (Hat tip, BrillKids Forum.) Well, I flatter Prof. Gray in calling it an “argument.” Maybe he has an argument elsewhere, but there isn’t much of one in this mini-essay.

In what I will call his first premise, he reports on research from 1929 in which a group of kids were not taught math until the sixth grade, and instead, were taught “recitation,” meaning “to talk about topics that interested them–experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion.” Then, at the beginning of the sixth grade, they were tested. While they didn’t do nearly as well as their math-trained peers on most of the problems, they did better on simple word problems that could be solved with simple, intuitive math thinking. And, according to Gray (for what it’s worth), the math-deprived kids were doing as well on all of the problems by the end of the sixth grade. The (intermediate) conclusion suggested is that early math education was unnecessary and actually made the kids less able to do word problems.

Then in his second premise, Gray says, in effect, that most elementary school teachers are very poor at math themselves. No great surprise there.

Those, as far as I can make out, are the essay’s two reasons for concluding: “At the present time it seems clear that we are doing more damage than good by teaching math in elementary schools. Therefore, I’m with Benezet [who did the 1929 research]. We should stop teaching it.”

There are two basic problems with this: the first is with Gray’s analysis of the study, and this forms his main premise. The second is that the conclusion does not even come close to following logically from the premises.

As to the study, what are the problems with Gray’s analysis? Let me count them:

1. The conclusion’s proposal is radical. Radical proposals demand rock-solid proof. So, even if the study *perfectly* supported the conclusion, it would be, after all, just one study, and that is not strong proof, regardless of the study. It is surprising that a distinguished scholar would make such a dramatic proposal on such a slender basis.

2. An important part of Gray’s analysis is that by practicing “recitation,” the experimental students were learning how to do the sort of reasoning done in word problems. This is plausible. But it doesn’t follow from that that kids exposed to traditional math education were *hampered* in their ability to do word problems. After all, there was not a third group–as perhaps there should have been–which received *both *math and “recitation” training. My guess is that such a group would have outperformed the others.

3. Another part of Gray’s analysis is that most sixth graders are unmotivated to study math. This is surely true, in general. But he seems to assume that the math-untrained sixth graders were enthusiastic about math at the end of their year of math, and–maybe more to the point–remained enthusiastic through the rest of their schooling. Gray’s assumption appears to be that unpleasant experiences in the early grades turn students off to math, and if we waited, they would not be so turned off. He could be right, but the study doesn’t give any basis for thinking so. If there had been a follow-up study, in the ninth or twelfth grade, that indicated love and motivation for math, then his point would have some support. But it might turn out to be the subject itself, regardless of how it is taught, that turns off students.

4. Why the seventh grade? Why not wait until the twelfth grade? Why not start a little earlier, like in the fourth grade?

I could go on, but that’s enough.

Now to the other problem. Let’s suppose that Gray’s analysis is correct, and that, for the kids in the study, the math education they would have received in their classes would not have been beneficial. But does it follow from that–and the fact that most elementary school teachers aren’t good even at basic math–that we should not teach math before seventh grade?

Uh, no. Here are just a few reasons this doesn’t follow:

1. If we’re going to get all clever with studies, let’s compare recitation-only not just to the math education they would have received in their school, but according to the most effective curriculum as measured by test scores. (And don’t forget to compare it to that curriculum *plus* recitation, too.)

2. It’s easy to agree that kids will not receive a high-quality math education in most classrooms in most public schools in the U.S.–no thanks to all the half-baked failures of the education professors and educational psychologists, who are so often not interested in what has actually been proven to maximize student knowledge. But this for me (as for a BrillKids commenter) illustrates why my boys, like two million students (and growing), are being or will be homeschooled. Until you can establish that doing math below the seventh grade is pointless even for homeschoolers, your recommendations are going to sound awfully foolish to a lot of the homeschoolers out there. (Of course, some of them agree with Gray. The more radical Unschoolers don’t want to start their kids learning anything like math or reading until the kid is all in favor of learning them. But then, Gray looks like a radical unschooler himself–see the link to his CV below.)

3. The effect might have been real enough for the experimental group, but Gray’s advice regards the whole country or world (as far as I can tell). But why think it wouldn’t be a complete, unmitigated disaster if we started teaching math in the seventh grade *en masse?*

I suggested with my snarky opening line that Gray’s position is anti-intellectual. Of course, if he were *right,* and avoiding math for seven years (K-6) on average were to help kids to learn math better later, then of course that wouldn’t be anti-intellectual. That would be pro-intellectual. But I stand by the label. Gray doesn’t supply even remotely enough in the way of argument and experimental evidence to seriously suggest that we should stop teaching math in elementary school. For a distinguished scholar, who no doubt has the ear of many education decision-makers and whose recommendations are, therefore, of some practical import, he seems to be surprisingly willing to be play fast and loose with the educational futures of children. This is the sort of half-baked, sloppy thinking and scholarship that got us disasters like the new math and whole language teaching of reading. I’m just guessing, but it seems very possible that, more than by the evidence he presents, Gray has a general animus against abstract thinking. This is all the rage in discussions of education methods these days; learning should be maximally hands-on, “experiential,” project-driven, etc. That whole trend is anti-intellectual. A glance at Gray’s (very distinguished) CV more or less confirms my suspicions: he’s a Sudbury Valley (radical unschooling) and “free play” advocate.

Larry,

Have you read “Why Minimally Guided Instruction Does Not Work.” You can find a link to it here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.169.8810&rep=rep1&type=pdf. It is an analysis of multiple studies that have been done on hands on learning. According to this analysis:

“Although unguided or minimally guided instructional approaches are very popular and intuitively appealing,

the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance.”

As for teaching math early, a while back I read that prior to the 1950’s, students learned only very basic math at school. Advanced math was reserved for a very privileged few. I would think most children would pick up some basic math knowledge from day-to-day living, even if they weren’t taught any at school. Those 6th graders most likely had some basic math knowledge already. Considering that schools didn’t teach a whole lot of math back then, there may not have been a huge difference in the level of math knowledge of both groups in the study.

Our modern economy requires students to learn so much more math. Could we realistically have students learning Calculus in high school, if they didn’t start any math education until 7th grade? Sure, this may work for some unschoolers because they have far more time to teach per day than the average math teacher has.

Students in many other countries have excellent math skills, even though they start math instruction at 4 or 5. I think this would prove that the problem our students have is not one of bad timing in math teaching, just bad math teaching. Most math curricula in the US are a joke. Before making such radical proposals, it would make far more sense to look at countries that are succeeding in math and model our math curricula on theirs.

Very interesting quotation, that!

And I agree with you regarding modeling successful math education programs from other countries. (I’m using Singapore Math with H…)

I read an article a while back suggesting that formal math education should start at age 10 or 11 – the article is here, and backs its arguments with a wide variety of sources dating back to antiquity.

On the other hand, my 4-year-old daughter is learning to add and subtract, and my 21-month-old daughter can count to 10 already.

Thanks very much for that link. I’m definitely going to have a look.

I hope it’s clear that I haven’t ruled out Gray’s advice. I just think it is very implausible and poorly supported.

You can find a response to the Bluedorn article here: http://hubpages.com/hub/Should-Elementary-Schools-Stop-Teaching-Math.

The response is largely (but not entirely) attacking a straw-man version of Bluedorn’s argument. The anonymous response deliberately misses some of the points which Bluedorn doesn’t develop well, or only implies, and in some cases exaggerates to the point of nonsensicality or misrepresents what Bluedorn is actually saying.

There are arguments to be made against Bluedorn – my personal experience with math is one: I learned addition via workbooks by first grade, and could multiply (and had memorized the multiplication table) by the end of third grade. Long division and fractions were introduced, and mastered by me, in fourth grade, leaving the next three years of math, which did nothing new, an utter waste of time. I escaped into a high-school algebra class in eighth grade (age 13), and from there did quite well until well into college.

Of course, my own example is not much more valid for the general case than the hubpages example of the retarded 40-year-old that the author overheard, for the same reason: we’re both statistical outliers. But the top 25% of my (middle-class white public) elementary school classes had similar experiences to mine, though perhaps not as accelerated. So that’s a lot of kids who did pretty well with the conventional teaching of math starting at age 6 (or earlier), and didn’t learn to hate math, or hate learning. I’d daresay that of the middle 50%, quite a lot disliked math, but that wasn’t the universal response, and at least through 8th grade, most of them learned it adequately.

But anyway, the anonymous hubpages article is a pretty weak attempt at refuting Bluedorn.

Anthony,

I would have to say the same thing about your response to the Hubpages article. You are making a very weak attempt at refuting the Hubpages article and seem to be misrepresenting what that writer is saying.

The article on Hubpages largely covers the claim that children could learn 6 years of math in a matter of months. I think the article makes a very good case that this would not work. Few students could learn 6 years of math in less than a few years.

Why do you call the woman in the library retarded? What makes you think she was? You weren’t there? Isn’t it much more likely that she is one of the millions of Americans who were failed by our K-12 school system?

[…] year, they had ‘caught up’… an article talked about in this blog critiquing it: http://larrysanger.org/2011/06/should-we-teach-math-in-elementary-school/ and with regards to reading, not everybody worries about 5 year old readers, in Finland schooling […]