Thursday, October 19, 2006

Better Late than Early

a series of three articles written by L. P. Benezet, the superintendent of public schools in Manchester, New Hampshire, in the late '20s and '30s (see http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html). For reasons he explains at the beginning of the first article, at http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html, Benezet writes,
In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to Read, to Reason, and to Recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade. I asked the teachers if they would be willing to try the experiment. They were young teachers with perhaps an average of four years' experience. I picked them carefully, but more carefully than I picked the teachers, I selected the schools. Three of the four schoolhouses involved [two of the rooms were in the same building] were located in districts where not one parent in ten spoke English as his mother tongue. I sent home a notice to the parents and told them about the experiment that we were going to try, and asked any of them who objected to it to speak to me about it. I had no protests. Of course, I was fairly sure of this when I sent the notice out. Had I gone into other schools in the city where the parents were high school and college graduates, I would have had a storm of protest and the experiment would never have been tried. I had several talks with the teachers and they entered into the new scheme with enthusiasm. The children in these rooms were encouraged to do a great deal of oral composition. They reported on books that they had read, on incidents which they had seen, on visits that they had made. They told the stories of movies that they had attended and they made up romances on the spur of the moment. . . . At the end of eight months I took a stenographer and went into every fourth-grade room in the city. . . . The contrast was remarkable. In the traditional fourth grades when I asked children to tell me what they had been reading, they were hesitant, embarrassed, and diffident. In one fourth grade I could not find a single child who would admit that he had committed the sin of reading. I did not have a single volunteer, and when I tried to draft them, the children stood up, shook their heads, and sat down again. In the four experimental fourth grades the children fairly fought for a chance to tell me what they had been reading. The hour closed, in each case, with a dozen hands waving in the air and little faces crestfallen, because we had not gotten around to hear what they had to tell.

...

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 faculties. There was a certain problem which I tried out, not once but a hundred times, in grades six, seven, and eight. Here is the problem: "If I can walk a hundred yards in a minute [and I can], how many miles can I walk in an hour, keeping up the same rate of speed?" In nineteen cases out of twenty the answer given me would be six thousand, and if I beamed approval and smiled, the class settled back, well satisfied. But if I should happen to say, "I see. That means that I could walk from here to San Francisco and back in an hour" there would invariably be a laugh and the children would look foolish. I, therefore, told the teachers of these experimental rooms that I would expect them to give the children much practice in estimating heights, lengths, areas, distances, and the like. At the end of a year of this kind of work, I visited the experimental room which had had a combination of third- and fourth-grade children, who now were fourth and fifth graders. I drew on the board a rough map of the western end of Lake Ontario, the eastern end of Lake Erie, and the Niagara River. . . . I then labeled three spots along the river with the letters "Q," "NF," and "B." They identified Niagara Falls and Buffalo without any difficulty, but were puzzled by the "Q." . . . I finally told them that it was Queenstown. . . . I then made the statement that in 1680, when white men had first seen the falls, the falls were 2500 feet lower down than they are at present. I then asked them at what rate the falls were retreating upstream. These children, who had had no formal arithmetic for a year but who had been given practice in thinking, told me that it was 250 years since white men had first seen the falls and that, therefore, the falls were retreating upstream at the rate of ten feet a year. I then remarked that science had decided that the falls had originally started at Queenstown, and, indicating that Queenstown was now ten miles down the river, I asked them how many years the falls had been retreating. They told me that if it had taken the falls 250 years to retreat about a half mile, it would be at the rate of 500 years to the mile, or 5000 years for the retreat from Queenstown. The map had been drawn so as to show the distance from Niagara Falls to Buffalo as approximately twice the distance from Queenstown to Niagara Falls. Then I asked these children whether they had any idea how long it would be before the falls would retreat to Buffalo and drain the lake. They told me that it would not happen for another ten thousand years. I asked them how they got that and they told me that the map indicated that it was twenty miles from Niagara Falls to Buffalo, or thereabouts, and that this was twice the distance from Queenstown to Niagara Falls! It so happened that a few days after this incident I was visiting a large New England city with five of my brother superintendents. Our host was interested in my description of this incident and suggested that I try the same problem on a fifth grade in one of his schools. With the other superintendents as audience, I stood before an advanced fifth grade in what was known as the Demonstration School, the school used for practice teaching and to which visitors were always sent. . . . Mr. Benezet: [Draws the same map on the board] . . . People who have studied this carefully tell us that once upon a time the [Niagara F]alls were at Queenstown. . . . Now, when white men first saw the falls in 1680 [placing this date on the board], the falls were further down the river than they are now, and it is estimated that since that time they have moved back upstream about 2500 feet. Now how long ago was it that white men first saw the falls? Child: Four hundred years. Another child: Two hundred years. Third child: Three hundred years. Guesses range anywhere between 110 years and 450 years. One boy says it was about the time that Columbus sailed to America; another says that it was about the time of the Pilgrims and the Puritans. Mr. B.: Well, how are we going to find out? General bewilderment for a while. Finally: Child: Take 1930 and subtract it from 1680. Mr. B.: Fine. He writes on the blackboard: 1680 1930 Mr. B.: Now take a look and tell me how many years that was. See if you can tell me before we subtract it, figure by figure. It [should] be noted that not one child called attention to the wrong position of the two sets of figures. They guess 350 years, 200 years, 400 years. Mr. B.: Well, let's subtract it figure by figure. Child: Zero from 0 equals 0. Three from 8 equals 5. Nine from 6 equals 3. Three hundred fifty years is the answer. Mr. B.: How many think that 350 years is right? About two-thirds of the hands go up. Finally two or three think that it is wrong. Mr. B.: All right, correct it. Child: It should have been 9 from 16 equals 7. Mr. Benezet thereupon puts down 750 for the answer. When he asks how many in the room agree that this is right, practically every hand is raised. By this time the local superintendent was pacing the door at the rear of the room and throwing up his hands in dismay at this showing on the part of his prize pupils. After a time, as Mr. Benezet looks a little puzzled, the children gradually become a little puzzled also. One little girl, Elsie Miller, finally comes to the board, reverses the figures, subtracts, and says the answer is 250 years. Mr. B.: All right. If the falls have retreated 2500 feet in 250 years, how many feet a year have the falls moved upstream? Child: Two feet. Mr. Benezet registers complete satisfaction and asks how many in the class agree. Practically the whole class put hands up again. Mr. B.: Well, has anyone a different answer? Child: Eight feet. Another child: Twenty feet. Finally Elsie Miller again gets up, and says the answer is ten feet. Mr. B.: What? Ten feet? (Registering great surprise) The class, at this, bursts into a roar of laughter. Elsie Miller sticks to her answer, and is invited by Mr. Benezet to come up and prove it. He says that it seems queer that Elsie is so obstinate when everyone is against her. She finally proves her point, and Mr. Benezet admits to the class that all the rest were wrong. Mr. B.: Now, what fraction of a mile is it that the falls have retreated during the last 250 years? Children guess 3/2, 3/4, 2/3, 1/20, 7/8 - everything except 1/2. The bell for dismissal rings and the session is over.

...

As with what we have heard from the Moores concerning reading (Raymond & Dorothy Moore, Better Late Than Early), so with arithmetic: children who are raised in literature-rich and intellectually-stimulating environments, even without formal instruction in reading or formal instruction in arithmetic, can "catch up" and, actually, surpass their heavily-practiced peers in a very short time indeed.

Writes Benezet:
One of our high school teachers was working for her master's degree at Boston University and as part of her work [Professor Guy Wilson of Boston University] assigned her the task of giving tests in arithmetic to 200 sixth grade children in the Manchester schools. . . . Half of them had had no arithmetic until beginning the sixth grade and the other half had had it throughout the course, beginning with the [second half of third grade]. In the earlier tests the traditionally trained people excelled, as was to be expected, for the tests involved not reasoning but simply the manipulation of the four fundamental processes. By the middle of April, however, all the classes were practically on a par and when the last test was given in June, it was one of the experimental groups that led the city. In other words these children, by avoiding the early drill on combinations, tables, and that sort of thing, had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill.

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