Peter Gray presents the case for teaching less math in schools, based on some old, forgotten research:

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.This was back in the days when people believed that children shouldn’t have to spend all of their time at school work — that they needed some time to play, to do chores at home, and to be with their families — so there was reason back then to believe that whenever something new is added to the curriculum something else should be dropped.

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.

No arithmetic until *seventh* grade? That seems extreme — especially for an era when most families considered an eighth-grade education as complete. Anyway, 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.

In sum, Benezet showed that kids who received just one year of arithmetic, in sixth grade, performed at least as well on standard calculations and much better on story problems than kids who had received several years of arithmetic training. This was all the more remarkable because of the fact that those who received just one year of training were from the poorest neighborhoods — the neighborhoods that had previously produced the poorest test results.

Gray asks, *Why have almost no educators heard of this experiment?* Let’s not open that can of worms.

Although this research supports the Waldorf approach and a few other alternative schooling styles that Aretae appreciates, he’s not completely on board:

I’m not all the way on board with the approach, though, because I’ve taught a class of 5th & 6th graders algebra, and I’ve helped tutor kids as young as 8 who did very well in college algebra classes. Regardless, it indicates that the scope of the problem with our current system is much bigger than you thought it was, unless you already think (like me) that public schooling is one of the horseman of the apocalypse.

I’m not sure what to make of holding off math instruction, because it seems like many kids might need it, and some certainly don’t. I know most kids are terrified of word problems and see no connection at all between the math they’ve been taught and solving real-world problems, but those problems always struck me as the only interesting ones in the whole assignment.

I know I could have learned much more advanced math much earlier if it had been (a) taught at all, and (b) taught by someone who understood it. Instead we were taught arcane algorithms for random mathematical tasks. When I finally got to algebra, I felt like I’d wasted the last three or four years of math, because I suddenly had simple, *generalizable* rules for fractions, rates, etc. that made all my previous learning obsolete.

I hadn’t really thought through the notion that, as Aretae notes, teaching either before an individual is ready, or before they’re interested, has potential *negative* returns.

Whatever the magnitude of that effect, there’s another simple reason why most math instruction, whatever the methodology, fails spectacularly:

Nothing has worked. There are lots of reasons for this, one of which is that the people who teach in elementary schools are not mathematicians. Most of them are math phobic, just like most people in the larger culture. They, after all, are themselves products of the school system, and one thing the school system does well is to generate a lasting fear and loathing of mathematics in most people who pass through it. No matter what textbooks or worksheets or lesson plans the higher-ups devise for them, the teachers teach math by rote, in the only way they can, and they just pray that no smart-alec student asks them a question such as “Why do we do it that way?” or “What good is this?” The students, of course, pick up on their teachers’ fear, and they learn not to ask or even to think about such questions. They learn to be dumb. They learn, as Benezet would have put it, that a math-schooled mind is a chloroformed mind.In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle.[2] They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn’t figure out that multiplication is used to find the area was evidence to Kenschaft that they didn’t really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.

The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, “It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal ‘home schooling’ of children.”

Sad.