Waiting On Math

This article has been on my brain ever since seeing it on a friend's Facebook page a while page. The claim: teaching math can be delayed entirely until junior high and students in the end learn it better.

In 1929, the superintendent of schools in Ithaca, New York, sent out a challenge to his colleagues in other cities. "What," he asked, "can we drop from the elementary school curriculum?" He complained that over the years new subjects were continuously being added and nothing was being subtracted, with the result that the school day was packed with too many subjects and there was little time to reflect seriously on anything....

One of the recipients of this challenge was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who responded with this outrageous proposal: We should drop arithmetic! Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: "For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities." All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children's minds, from common sense, with the result that they could do the calculations as taught to them, but didn't understand what they were doing and couldn't apply the calculations to real life problems. He believed that if arithmetic were not taught until later on--preferably not until seventh grade--the kids would learn it with far less effort and greater understanding.

Benezet followed his outrageous suggestion with an outrageous experiment. He asked the principals and teachers in some of the schools located in the poorest parts of Manchester to drop the third R from the early grades. They would not teach arithmetic--no adding, subtracting, multiplying or dividing. He chose schools in the poorest neighborhoods because he knew that if he tried this in the wealthier neighborhoods, where parents were high school or college graduates, the parents would rebel. As a compromise, to appease the principals who were not willing to go as far as he wished, Benezet decided on a plan in which arithmetic would be introduced in sixth grade.

As part of the plan, he asked the teachers of the earlier grades to devote some of the time that they would normally spend on arithmetic to the new third R--recitation. By "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked 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. This, he thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.

In order to evaluate the experiment, Benezet arranged for a graduate student from Boston University to come up and test the Manchester children at various times in the sixth grade. The results were remarkable. At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement. Of course, at the beginning of sixth grade, those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms. But by the end of sixth grade those in the experimental classes had completely caught up on this and were still way ahead of the others on story problems.

The article goes on to speculate on why this might be, and why it hasn't caught on. In addition to children of younger ages often (I've certainly known extreme exceptions) possessing limited abilities to grasp mathematical concepts, the article seems to lay much blame at the feet of elementary teachers, who are often required to be generalists and often personally do not like math and know little more than what they are trained to teach. (In one example, the author of a recent study goes through an entire elementary teaching staff and fails to find anyone able to explain to him correctly how to calculate the area of a rectangle, despite being responsible for teaching multiplication.)

Also important to note, it seems to me, is that despite the audacity of the overall suggestion, the proposal tested by Benezet did not actually involve not teaching math in the younger grades (at least, not as we would think of it) but rather not doing drill in arithmetical operations (addition, subtraction, multiplication, division, fractions.) Instead, it says he asked his teachers to, as well as focusing on recitation, "give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers." Obviously this kind of more practically focused work has since 1929 become much more common in better classrooms and certainly in the books used by most homeschoolers.

Still, this does tie well with my own reaction to "math class" when I was in parochial school, which was that underneath all the drill we learned very, very little between second grade and fifth. And come to that, very little more was done up until seventh or eight grade when the curriculum started taking baby-steps into algebraic concepts. I wasn't a math wiz, but I was at least able to latch on to what we were doing within the first couple days after a new concept was introduced (up till now you've done "short division" up through twelve, we will now do "long division" of larger numbers) and proceed to be bored for the next two to three months while we repeated it. (We now move to from long division of five digit number to long division of six digit number. And now, we will do word problems involving long division. And now we will do long division of decimal numbers. Buckle your seatbelts!)

Also, at a minimum, this kind of finding strikes me as reassuring as a homeschooling parent, since a couple times a year MrsDarwin and I take time out to sit down and freak out that we aren't getting through enough stuff with the girls. Being assured that there's still plenty of time to get people up to full mastery later is thus a plus.

In the end, though, while the viewpoint it interesting, I'm hesitant to commit to actually holding off on introducing arithmetical concepts (and drill) until that late. Homeschooling parents often see their children as being like those of Lake Wobegon, with all of them above average. And MrsDarwin and I do both know very well how to calculate the area of a rectangle. So surely, we can get these concepts in sooner and avoid the mental chloroform trap, right?

I do, however, find the article very interesting. And I remain convinced there must be something applicable we can get out of it, though I am unsure as to what.

UPDATE: From one of the links The Other Sherry provided, some more info on Benezet's approach:

. . . Benezet in Manchester, N. H., carried out a study from which he concluded "If I had my way, I would omit arithmetic from the first six grades . . . . The whole subject could be postponed until the seventh year . . . and mastered in two years’ study." This led many people to conclude erroneously that all arithmetic could be deferred until the seventh grade. However, closer observation showed that there was much arithmetic taught in grades I to VI. Thiele visited the Manchester, N. H., schools and said: "Firsthand observation leads me to conclude that Benezet did not prove that arithmetic can be taught incidentally . . . . Instead, he provided conclusive evidence that children profit greatly from an organized arithmetic program which stresses number concepts, relations, and meaning. Buswell found that Benezet had only deferred "formal" arithmetic, and that all other aspects of a desirable arithmetic curriculum were present. Of the formal arithmetic, Buswell said, "I should like to eliminate it altogether." On the same topic, "deferred arithmetic," Brueckner says, "From these studies the conclusion should be drawn not that arithmetic should be postponed, [page 18] but that the introduction of social arithmetic in the first few grades does not result in any loss in efficiency when the formal computational aspect of the work is introduced later on, say in grade three." — What does Research say about Arithmetic? By Vincent J. Glennon and C. W. Hunnicutt, National Education Association, Washington D. C., 1952, page 17. [source]