Should we teach math in elementary school?

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.