A Prescient Letter from Ralph A. Raimi to Frank Quigley, June 29, 1958.
I reproduce below, complete, verbatim and without amendment of any kind, except that I have here divided the text into more paragraphs than had been signalled in the original, a letter I sent to Frank Quigley, then Assistant Professor of mathematics at Yale University. The date of the letter is a few weeks after the inauguration of the School Mathematics Study Group (SMSG), headed by E.G.Begle, then a professor at Yale. For details on the exact chronology of the events of 1957-1958 that preceded the formation of SMSG, see William Wooton’s, SMSG: The Making of a Curriculum (Yale University Press, 1965), especially pages 9-16.
I had spent a postdoctoral year at Yale in 1955‑56, and was in 1958 back at Rochester as Assistant Professor of mathematics. But I still took an interest in events at Yale and I had been reading in the newspapers about the what I took to be the imminent formation of SMSG or something like it. I thought Quigley was going to be associated with the project, whose exact coutours and (needless to say) ultimate fate were not yet known to me. In particular, I didn’t quite realize that by the time of this letter the SMSG had already been established, with an initial grant of $100,000 from the NSF to get the office work started, and that the first summer’s writing project was already under way at Yale, with the participation of mathematicians, professors of education and school teachers, to establish policy for what was to become the major “New Math” project of the era, that policy being political as well as pedagogical. At that time, SMSG was still a hurried response to Sputnik, and intended only to compose a curriculum and textbooks for college-intending high school students, those who would become our scientists and technicians. It was on this assumption that NSF, acting on the intellectual recommendations of the CEEB report of that year, and on the cold war recommendations of the President and Congress, had decided to finance the entry of the mathematics community into what had traditionally been the domain of local school districts and, at most, the education departments of our several states.
The NSF consulted with Richard Brauer, President of the AMS, and secured the cooperation of all the mathematics organizations including the MAA (Mathematical Association of America) and the NCTM (National Council of Teachers of Mathematics), before appointing Professor Begle of Yale to head the project and approving the selection of several committees for specified supervisory tasks: an Executive Committee, a Council, and the several teams to write high school textbook material for algebra, geometry, etc.
My letter opens with a reference to a newspaper article about a meeting at Yale, a meeting I cannot now identify because it must have been one of very many that were happening at that time, in the course of setting up SMSG and collecting participants. Clearly it was a meeting to which I had been invited via an open advertisement in some organ of AMS or MAA, not an open meeting to inform the public, just as ordinary scheduled meetings of the organizations themselves are announced in their journals. In other words, my being “invited” did not distinguish me from any other member of the mathematical societies. Not knowing even the name, “SMSG”, let alone how far it was advanced, I imagined the meeting to which I did not go was exploratory, Begle looking for advice from whoever showed up, and I expected that those right in New Haven, as Quigley still was, would naturally attend. As may be deduced from my phrase, “a bunch of Yale professors”, I did not yet understand the magnitude of the project Begle was to head.
Frank Quigley had been a good friend during my Yale year 1955-1956, and I still maintained a slight correspondence with him. He left Yale about 1960 and became a professor of mathematics at Tulane University. So far as I know he never had any connection with SMSG, though he and I both knew Begle quite well from our time at Yale.
The footnotes of course are not in the original, and are added here to explain some personal references, since the letter is being quoted verbatim.
Today is the eleventh anniversary of my marriage, which is the reason I did not attend the educationists' meeting . That seems to make my wedding as important as an Orange Bowl game . But it is education I wish to write about, not weddings.
I was truly very sorry not to have been at the meeting, and even sorrier not to be at Yale, where, I read in the newspapers, something is being done about mathematical education. I take it you are a member of Begle's project, however, and I am pleased that a competent authority on division facts is in on it. It is important to keep the MAT boys at Yale out , especially L__, at this stage of the game, but Begle is capable of handling such necessary exclusions with his own stony grace, and he knows L__.
If you do not know L__ (and if he is still at Yale), you must meet him, perhaps under the pretext of asking his advice on something connected with your project. The full magnitude of the problem you face can only be appreciated if you get to know those who teach the teachers. L__ is clearly a superior intellect among these, and has read enough 'anti‑educationist' literature to impress a scholar, at first, as a remarkably reasonable man. Later, when you see the true convictions, and lack of understanding, which underlie this veneer of sense, you will see that hope does not lie in that direction.
The remodeling of elementary education cannot be revolutionary. All the violent revolutions of the past have generated their own reactions; I have 1789 and 1917 particularly in mind. One should contrast these failures with the success of the evolution of English democracy and justice. There is a cybernetic problem involved: not to build a perfect machine, but to build a stable one, capable of correcting its own mistakes in a stable way, and capable of growing towards perfection. The first stage of a revolution should be so constructed that while it may fall far short of the goal, it renders inevitable that the next step will be taken in the right direction, whoever may be around to take that step.
In the evolution of English law, this was done by insisting on proper procedure, long before the particular statutory provisions, which the procedure, after all, served, could have been called just. It is sad that witchcraft should have been called a crime, but it would have been much sadder if witches had not been tried with all due process. It was inevitable that mankind should discover the non‑existence of witchcraft, but by no means inevitable that it should rediscover the value of due process. Preservation of due process, were a choice necessary, was better than a fiat of the non‑existence of witchcraft, given by a wise autocrat, for then the next step in the evolution of official justice was necessarily a good one.
Well, I don't wish to push this figure too far; I'd rather speak specifically of our present concern. We are faced not merely with an outmoded, too slow, often false school curriculum, but with a staff of teachers unable to teach a better one, headed by a bureaucracy which doesn't want to, backed by a public which, having come from such schools, doesn't much care. If this were the precise picture, as it was ten years ago, no action by a bunch of Yale professors could do any good. But there has been a break: the public now thinks it cares. There is a great deal to be said for lip‑service to a fine ideal; it permits underground labor in behalf of that ideal some chance of freedom.
The public now demands better education. It doesn't know what good education is, and it fears every particular manifestation of it, but it is so far committed that it will accept, if only for a while, a certain number of genuine reforms. When enough of these reforms have been adopted, the public will feel free to call it a day. The job, they will say, is done.
Precisely this has happened once before: 1900‑1950. A transition from public education for a few to public education for all was demanded, and the noble ideal of equal opportunity was in the air. The reformers had their chance, and made some startling innovations, often on the basis of good theory. But their reforms did not carry any built‑in guarantees of further progress. By 1930 an entrenched officialdom had taken over, declared the revolution complete, and proceeded to deform the tenets of that revolution to suit their own convenience.
If we are not careful, we will find a similar rigidity of doctrine arising fifteen years from now. The only difference will be that a certain amount of mindless Boolean algebra will have replaced a certain few pages of mindless trigonometric tables. Our first task must be to establish the procedure of reform beyond the possibility of repeal, even at the cost of perpetuating a few barbarisms in the actual curriculum. A constant, continuous examination of the curriculum by the scholarly community must be accompanied by a tradition of due honor to the examiners; otherwise we shall have failed.
Of course this cannot be done in a vacuum; besides, it is not what the public is currently demanding. They pretend they want a better curriculum, now; we must pretend we are giving it to them, now. And we must, in fact, change it, and do what we can towards changing the training of teachers, and all the rest of what is needed. But we must not forget that our first purpose is to change the climate in the hierarchy of education, so that our descendants will also be able to advance the true cause. Thus we must, in all our public utterances, and in all our textbook prefaces, and in all our conferences with educational leaders and politicos, stupid or wise, emphasize the length and continuing nature of our present effort.
There is great danger in this possibility: On a given occasion we may propose a certain kind of textbook, or a certain set of rules for teacher certification, and encounter strong opposition. In overcoming this opposition we may be tempted to argue so persuasively the merits of this particular proposal, and win in such a blaze of glory, that the cowed opposition will mutter to itself, "OK, buddy, you won this time, but this book, or set of rules, had better do the trick."
"Oh, it will, it must," we will have argued (otherwise, why so fierce a struggle?), and for good or bad, our day will be ended. We ourselves will have been committed to rigidity, and to the vindication of our momentary beliefs.
The public asks what to take for its educational malaise. We must answer, as the medicos do, “Take advice, and come back every two weeks thereafter.” This is the first advice they must take.
Sonya, Jessica, Diana, and I are well. I hope to see you at the Summer Meeting. Would you like to take a weekend trip to Rochester this summer? We have a room, a piano, a flute, a shortwave radio, and lots of good food and drink.
 I'm not sure what meeting this was. The initial grant of $100,000 from the NSF was dated May 7, and Begle's Advisory Committee was already in place. The meeting I missed was a more public affair than a simple initial gathering of SMSG personnel, though I believe it included that.
 This is a personal reference of no importance.
 I was mistaken in this.
 When I was at Yale (1955‑56), one of the younger professors, perhaps Quigley himself, had found in a used book store a book about teaching arithmetic in the schools. In it were gravely listed the "number facts" a child ought to know by this or that age. Some of them were called "division facts," e.g. that fifteen divided by five is three. Of course there were also addition facts, subtraction facts, etc. At the end of each chapter the author summed up the total number of facts that constituted, apparently, a satisfactory accomplishment. So it went. We passed the book around among ourselves at the time, making merry with it and its whole philosophy of school mathematics, challenging each other (for example) to "number fact" duels. That book was a superb example of the kind of idiocy that SMSG was later to attempt to remedy.
 "L__" in my letter refers to a man who happened to be an across‑the‑street neighbor of mine in Branford that year. He was a young professor in science education, and the MAT (“Master of Arts in Teaching”) program at Yale. As my letter indicated, I considered him a menace in 1956.
 Begle's 'stony grace' was well‑known, but I was quite wrong about the exclusion. SMSG welcomed the folk I characterized in my letter as "the educationists", and I did not then understand why. In later years Begle complained, though never in public, that math education had been taken over by the "psychologists", by which he meant mainly behaviorists. He did once say (publicly, I think) that on every occasion that he included some person for politic reasons it turned out a mistake. It might just have been as a diplomatic necessity that Begle's teams had to be "3 from Group A, 2 from Group B,..." My own present view is that he thereby got the intersection of all the talents in each group, and it appears I believed so in 1958, since I was crediting Begle with the same view.
 Fifteen years! A startling (though conditional) prediction. SMSG was disbanded 14 years after its founding, and the official death‑knell, Morris Kline's *Why Johnny Can't Add", was published the following year.
 I clearly already understood the formalist drift the new programs would take, for Max Beberman’s UICSM had been in existence for several years, with much public debate about what was already called “The New Math”. Still, I was not yet arguing against such subject matter in this letter, though the sentence contains a warning about converting abstract mathematics into a pointless catechism.