In 1929, superintendent L.P. Benezet decided to omit arithmetic from the elementary school curriculum, because he found it 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 practise 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 asked them to guess what it was, and was not surprised when they identified the location. 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.” Some thought it was Quebec but others knew it was not. I finally told them that it was Queenstown.
I then drew a cross section of the falls, showing the hard layer of rock above and the soft layer eating out underneath, and they told me what it was and why it was that the stone was falling, little by little, from the edge. They told me how this process was going on. 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 practise 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 practise teaching and to which visitors were always sent.
The home superintendent: Boys and girls, would you like to have Superintendent Benezet of Manchester, New Hampshire, ask you some questions about Niagara Falls?
The children express pleasure at the idea.
Mr. Benezet: [Drawing a map on the board] Children, what is this that I have drawn on the blackboard?
Children: The Great Lakes.
Mr. B.: Good. What lakes?
A child: Lake Ontario and Lake Erie.
Mr. B.: Good. What is the river?
Child: The St. Lawrence River.
Mr. B.: That is really correct. It is the St. Lawrence River. But they call it by a different name here. They call it the Niagara River. What have you heard in connection with the Niagara River?
Another child: Niagara Falls are there.
Another child: Niagara Falls are connected with Niagara River.
Mr. B.: Oh! How are they connected?
Child: The water trickles down the Falls and goes into the Niagara River.
Mr. B.: I should call that quite a trickle. Have any of you children seen Niagara Falls?
Three raise their hands.
Mr. B.: How high are the falls? Have you any idea? Are they higher than this room?
Children: Yes [dubiously].
Mr. B.: Well, how high is this room?
Its height is guessed anywhere from 11 feet to 40 feet. The room is actually about 16 feet high. The question of the height of the falls is finally dropped.
Mr. B.: Well, never mind how high the falls are. On this map here I have indicated one spot and marked it “NF,” and another spot and marked it “B.” What does “NF” mean?
Children: Niagara Falls.
Mr. B.: What does “B” stand for?
Another child: Bay.
Mr. B.: No. Remember that Niagara Falls is not only the name of the Falls, but the name of a city.
Child: Baltimore.
After considerable pause, the home superintendent, in the back of the room, tells the class that the name of the city is also the name of an animal.
Child: Buffalo.
Mr. B.: Yes. Now there is another town here that I am going to mark “Q.” It is not Quebec; it is Queenstown. People who have studied this carefully tell us that once upon a time the falls were at Queenstown. Tell me now. What does it mean if I say that I show you the cross section of an apple?
Class is uncertain.
Mr. B.: Suppose that you cut an apple in half with a knife. What do I show you if I hold up one-half?
Child: Half the apple.
Another child: The core of the apple.
Third child: The inside of an apple.
Mr. B.: Tell me. Is the word “section” a new word to the majority of you?
Enthusiastic chorus of “No.”
Mr. B.: Well, a cross-section of an apple means a cut right thru an apple. Why have I said this to you?
Meantime he has drawn on the board a cross-section of Niagara Falls.
Child: Because that is a cross-section of the falls.
Mr. Benezet now explains the two kinds of rock and asks which is the harder. They finally decide that the rock above is the harder. He then shows how the underneath rock rotted away, and that finally there was a shelf of hard rock overhanging. This became too heavy and fell off; and the falls have thereby moved back some ten feet.
Mr. B.: 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 is to 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.
It will be noted that the local superintendent gave them a little hint at the outset, that was not given to the Manchester children, when he said, “Niagara Falls.” They were prepared to identify my map. Also, the Manchester children who had not learned tables but had talked a great deal about distances and dimensions, recognized the fact that 2500 feet was about a half a mile, while the children in the larger city who were fresh from their tables, had little conception of the distance.
I was so delighted with the success of the experiment so far that in the fall of 1930 we started six or seven other rooms along the same line. The formal arithmetic was dropped and emphasis was placed on English expression, on reasoning, and estimating of distances.