NOTES.

-The fame of most writers was made in middle life. Prescott finished his "Ferdinand and Isabella" in his forty-first year; Motley was forty-one when he finished "The Dutch Republic." Longfellow and Bryant were famous before they were forty. Bryant wrote his "Thanatopsis" at eighteen. Everett was a very popular preacher at nineteen. Lowell was twenty eight when he wrote the Bigelow papers, and Holmes' "Old Ironsides" came hot from his pen at twenty.one.

-It is sometimes queried whether type has not weakened memory.

Among the ancients, Mithridates was noted for his extraordinary command of languages, and it was said that he knew every soldier in his army by his name, and the same legend was current about Julius Cæsar. In more modern times Frederick the Great's librarian, a certain Lacroze, possessed the same faculty. On one occasion he recited before Leibnitz twelve verses in eleven different languages, and which he only heard repeated once. When he was asked where a given subject was treated he would cite not only the book, but the page and even the line, and in addition to knowing every European language, Latin, Greek and Hebrew, to please Leibnitz he added Chinese to his other accomplishments. M. Blanchard

points out that an extraordinary memory does DEAFNESS & HEAD NOISES CURED

not necessarily imply a great intellect. Cardinal Mezzofanti, who knew seventy-eight languages, and could learn a new dialect in about ten days, was in no way remarkable either as a churchman or as a man. But the greatest phenomenon of the kind ever known seems to have been a certain Verdet, who, born in Nimes, 1824, came out first on the list of the pupils of L'Ecole Normale when only eighteen years of age. With him work was entirely a question of memory. He remembered, word

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Volume XI

Number 8

High School Graduates.

Quite a number of fathers and mothers of Boston have petitioned the School Board of that city to allow pupils to graduate from the Latin School without a knowledge of Greek. In the petition, it is asserted that the requirements for graduation are such, that in each of two years, selected at random, only two pupils out of twenty or more who began were able to graduate; not, however, because of poor scholarship, but because the physical strain was too great. The truth of these statements we cannot vouch for; but they suggest to us a thought or two. There is

no doubt but that the public secondary schools exact more of the average pupil than the private schools of the same grade. Think, for instance, of only two pupils out of thirty who may have begun together, graduating at any of the private preparatory schools, Andover, for instance, or Williston. And yet, probably the average of scholastic ability in either of these schools would not be superior to that in the Latin schools (boy's or girl's) of Boston. What makes the difference? Well, we can only hazard a reason. The temptation of the principal of the public schools is to graduate only those who, he feels sure, will enter college without conditions. If he be a man who measures his value, and, we were about to say, his hope of heaven, by the success of his graduates in passing college examinations, then the number of his graduates will be very small. His salary is

assured in any case, and so he can place his standard where he pleases, not being concerned about having a sufficiently large balance on the right side of the ledger. But how about the rights of the public? Can any public school which so organizes and carries out its course of instruction that only a number approximating to very near zero are physicaly able to accomplish it, justify its right to exist? It is not a great while ago that the lower schools were dominated by the same selfish spirit. The graduates were few. Attendance, good conduct, disposition towards work, went for nothing. Children who should have graduated and entered higher schools were debarred by intellectual barriers, set up by the selfishness and pedantry of their judges. But a change has come. It is being believed that the schools are for the children; that it is the alpha and omega of the teacher's work to train. It is well to impart information, especially to the young mind, but that is not the main object. The secondary schools are not yet dominated by the new, unselfish spirit. We have no doubt that the standards set up by the colleges and technical schools, and the examinations insisted upon by the more prominent institutions, are to be very much blamed for this undesirable condition. But not wholly. The private institutions graduate the great majority of the students who enter them. Of course it would materially reduce their income were it otherwise. But it is to be noted that these graduates, as a whole, have no difficulty in gaining admittance to the colleges and scientific schools. There may be conditions - many of them. What of it? Physical health is there, ambition is there, and experience tells us that often these "conditioned" students are in the end the pride of their alma mater. The public schools should give their students the same opportunity. There might be more pupils conditioned by college pedants, but we venture to say that the average intellectual ability of these schools would be decidedly higher.

One Way.

An Illinois Supt. would neutralize the evils of the graded system by treating each child as a unit, to be instructed according to his own powers, needs and attainments. His theory, as he describes it, is this: -"Let a course of study be agreed upon. This should constitute a highway of culture that each pupil must travel. This road should be divided up into sections, and those assigned to the several teachers employed. In the grade there should be no class organization." This gentleman thinks that in a short time the grade would naturally fall into groups of greater or less number, who accomplish about the same amount in the same time. But the teacher - what must necessarily be his or her skill and ability? Here is what our theorist says: Each teacher must be a pedagogical Napoleon, a born leader. She must be able to inspire every pupil with that stubborn determination that laughs at defeat." True enough; but there's the rub. When those who select the teaching corps are moved by high motives, and an intelligent will, and when, in consequence, in every room are "born leaders," then it may be possible for the "immediate goal" of the teacher's endeavor to be the "highest possible development of John Smith." But that time, we fear, is about as far off as the millenium.

Reading.

Perhaps more nonsense has been preached about the ways of teaching reading to little folks than concerning any other school study. Or perhaps it would be better to say that the importance of this or that method has been ridiculously exaggerated. Very little time has been lost in teaching reading, no matter what method was used. And all the talk about the superiority of this method or that because, ia the one, the child "reads the idea," and in the others not, is again, largely imaginative. The

old alphabet method was not the best method; no one doubts that. But the great intellects of the past learned to read that way; scholarship, quite as profound as to-day, did not criticize the method; and there is no evidence that it ever palsied anybody's ability to get at the ideas on a printed page. For ourselves, we believe that the word method and sentence method are more cumbersome than the alphabet method unless there goes with either the teaching of the sounds of the letters.

The author of the "Evolution of Dodd" tells the readers of the Illinois School Journal, in his inimitable way, just what he found out on this question of teaching reading, through a couple of questions which he sent to schools at random in some twelve different states."

66

"To begin " he says, "at the beginning (and let me say, right here, that my report will, for the most part, like all other census reports, merely state things as I have found them, leaving other folks to form conclusions therefrom), I started out with the purpose of asking primary teachers just two questions, the first of these being, What method of teaching reading do you use? and the second, Will you tell me your own private opinion about the real merits of such method, based on your own experience, and unbiased by anyone else's opinion or say-so? With these two questions formulated I set out on my census pilgrimage.

I had almost no trouble at all in getting prompt and unequivocal answers to the first of my questions. Whenever I propounded the same, the reply would come back to me as a ball comes back from the bat, and always straight at me. There were no 'fouls' made, no 'strikes' called. It was a straight pitch and a square bat, every time.

And in almost every case, north, south, east, or west, in city, town, or country, I got one or two replies. Either my respondent would say, 'I use the word-method of teaching,' or 'I use the sentence-method.' There were some slight variations in these replies, some teachers working in a personal adjective in their answers, as I use Brown's word-method;' or 'I use Jones's sentence-method;' but this seemed to be a small matter, so far as the general trend of methods was concerned. In one or two cases I got a reply, albeit from rather old-fashioned folks, I use the alphabet-method;' but the great bulk, at least ninety-five per cent of the teachers I put the question to, answered either wordmethod' or sentence-method.'

And so my census on this first question seems to have determined this fact, that the great bulk of our primary teaching of reading is now done by the 'word-method,' or the sentencemethod.' I consider that point fairly established. I make no comments; I only record the fact.

But when I propounded my second question, then came the rub. To return to my base ball figure of speech, it seemed almost impossible for me, at first, to get anybody to 'bat to my pitching' at all. Some would strike towards what I said, but would take great pains not to hit the real issue by so much as a " 'tick." Others would swipe' my interrogation clear out of bounds on a foul,' and baffle all my efforts to get them to really play ball.' But I finally got what I wanted. I'm not a Mason, but by

working the 'never'll tell,' secret service system on my reluctant non-respondents, I finally began to get results. These results I am glad I am now able to make public without betraying those who reposed their confidence in me, since all the pledge I gave them (and, indeed, all they asked me to give them), was that, in anything I might hereafter say, I would not reveal the identity of my informant. Curious fact, that; that we all hesitate to give an honest personal opinion unless we can run to cover under an in cog!

Well, when I had finally found the way to get any replies at all to my second question, the answers came with a uniformity that was somewhat remarkable, to say the least; especially in view of the reluctance to respond, noted above. With a very few exceptions, which I can readily account for, the replies all agreed on the following points, namely, that these two systems of teaching reading tend to make excellent vocal readers of reading matter, the words or sentences of which have been told to the children to start on; but the pupils thus taught do not read new matter well, and that they do not spell well."

That is just what we should expect. And for the reason stated in the article from which we quote: "And just here," says the author, "will you kindly oblige me by pronouncing instantly, and at first sight, by either the word or sentence method, whichever you prefer, and without having anyone tell you what the word is, so that you can say it over after them, the following: Honorificabilitudinity!

And if you fail to fetch it on sight the first time, I wish you would reflect just a little as to how you will finally "down it.” For you will finally down it. And when you have done so, just stand off a little ways so that you can put the act into perspective, and see how it was that you did it. And then will you please ask yourself if the methods of teaching primary reading that you are using in your school are enabling your pupils to down' new words when they come to them, without someone's telling them what they are? Just think it over, that's all."

Vermont to Oregon.

Editor of POPULAR EDUCATOR:

Dear Sir: -I merely rise to say I appoint myself a committee of one to hold an indignation meeting over that ridiculous letter of one Ernest Darling, published in your March issue. Ernest Darling indeed! Very earnest and very darling he must be if his life is inspired with the tone of his letter. He reminds me of a lazy five-year-old who severely announced concerning my methods, "I don't like her; she tries too hard to make me learn." This 'earnest darling" also reminds me of the old gentleman who thanked the Lord for what he did not know; the dear Lord only knows how very much he had to be greatful for.

66

As for

I find your paper a constant help and inspiration. marches and drills, my brightest, most satisfactory pupils are clamoring for them, especially for something that can be used in a room where desks occupy the center of the floor.

Your science lessons, history devices, language work, character sketches, and arithmetic papers all help me, also penmanship, drawing, memory gems, and examination papers. Indeed, now that I am on the war-path, I would like to tell that "earnest darling" I derive much pleasure and profit from reading your advertisements.

As for being "led round by the nose," if any teacher has not back bone enough to stick to her own methods if she thinks them better than the plans of the educational papers, then of course she ought to be glad and thankful for the privilege of being led. Very sincerely,

A GREEN MOUNTAINEER.

The Psychology of the Fundamental Arithmetical Operations.

BY PROF. JOHN DEWEY, University of Michigan.

IN the February number of this Journal, I tried to show that number is a synthetic-analytic process, and to derive the main features of number from the nature of this process. The key to the conception advanced, as distinct from that which underlies much that goes by the name of the Grube method, is the distinction between unity and a unit. Every act performed constitutes a unity or a whole; every object grasped in a single act is a unity. The unity, therefore is never a fixed thing; it varies with the mental act. It may be a tree, a leaf, a cell of a leaf, or a molecule in a cell. One which is a unity at one time will be a hundred at another time, a thousand at a second, and indefinite millions at a third but it always is itself a unity the moment attention is paid to it. When we say it may be a hundred or a thousand, we are evidently introducing another kind of idea from that implied in calling everything a unity. We are introducing the idea of t! ● value of that unity. Now value obviously implies measurement; measurement, in turn, a measure — a standard of reference, a unit of value. All these expressions are absolutely synonymous. Number, then, a unit or units, arises from the process of stating the value of some whole. It implies, first, something which is to be measured the whole or group

under consideration; secondly, a unit which measures, and thirdly, the process of bringing the unit of measure into connection with the whole to be measured-the act of measuring. And this brings me again to the synthesis-analysis; measurement, from the standpoint of the breaking up of the original undefined, of unmeasured whole, being analytic, from the standpoint of the value thus obtained synthetic. All number, in other words, expresses both how many and how much; telling how many units (analysis) are in a given thing at the same time it tells how much the whole amounts to (synthesis).

If the foregoing account is correct, it is obvious that all number must be taught so as to bring out the process and all the factors in it. The ruling (or Grube) method in arithmetic must then be indicted for neglecting this fundamental psychological nature of number. In the first place it starts with a unit, a numerical one, instead of with a whole or concrete one.

It takes the unit, 1, 2, 3, etc., to be an entity or thing in itself, instead of simply a standard of reference in fixing valve. The result is that the child is kept for six months drilling from one up to five, a year from five to ten; while numbers which are a great deal more significant, as twelve (hours, a dozen) twenty (the entire number of fingers and toes), one hundred (cents, etc), are kept out of sight. The final result is that processes like addition and subtraction which logically go together are separated, while division and fractions are made utterly unintelligible - even, as recent articles would seem to indicate, to those who attempt to expound them.

I propose, in this article, to show that fundamental operations are not simply something which happen to do with number, but are the necessary and successive phases of the evolution of number itself, and thus to indicate how, in a method of teaching based upon the psychology of number, the performance of any process so implies the others as to prep re the way for them. mean to show that when number is taught in accordance with a true psychology, the mind when it comes upon subtraction, division, r tio is not introduc d to a new field, but is simply becoming conscious of operations with which it has been prac

I

tically —if not reflectively — familiar before. The right method, once more is as follows: First, the presentation of a whole, or group, a concrete unity, not a mere unit; second, the presentation of the unit which serves to measure the whole; and third, the process of analysis-synthesis; breaking up the whole into a definite number of such units as parts, and the building up of the whole out of such parts.

At the outset we may notice that all arithmetical processes fall into two groups-those in which we mea-ure the value of a w.cle by the ue of a unit which is not itself accurately measured or defined, and those in which the unit is itself definitely valued or measured. The frst group is evidently crude; we cannot fix value accurately until we know the value of our standard. Or inarily, therefore, we reserve the term measurement to denote the latter of the two types of operations, and call t'e other counting merely. But it should be noticed that the operations of addition and subtraction belong in type to counting and not to defined measuring: that is, in addition and subt action of themselves there is nothing to fix the value of the units with which we deal. We may, to be sure, add and subtract quantities which are perfectly definite or measured in themselves, as when we add feet or subtract dollars, but that is because the operation of fractions (multiplication-division) has already been performed upon them.

I shall now take up the process of counting and show how all the operations, namely, addition, subtraction, multiplication, division, (and accordingly, ratio and fractions) are involved in it. According to the form of the Grube method current in schools, and regarded by so many educators as the acme of wisdom, counting is simply the operation of piling units on top of each other; we begin with 1, a fixed thing, put on another 1 and thus get 2; and so on indefiuitely. This method goes against the radical mathematical idea - that of limit. There is absolutely nothing here to give any reason for the counting or to set any limit to it. The thing to be measured the qualitative whole is left out; it is Hamlet with the Prince of Denmark left out. The result is that the various processes have absolutely no relation to each other; counting is the simplest form of addition, but subtraction is another and new thing. But if the educational theorist would only bear in mind the fact that the child always learns to count something, that he takes a group or whole, like the hand, he would get started right. One unit is not the natural beginning, but one whole, and the unit is simply one part of that whole, having absolutely no meaning except as a part (analytically) and a standard of reference synthetically. Let us, then, start in our account of counting as the child starts in the actual counting - with the group or whole, Suppose we begin with the hand. One finger is the obvious unit, or standard of reference the basis of fixing the numerical value of the whole group. The successive counts made, 1, 2, 3, 4, 5, are the simplest form of addition. So far the ordinary theory of counting goes, but here it stops. But it must be remembered that the 1, 2, 3, etc., are not fixed snd independent units; they are stages in the process of enumerating, or telling the value of the whole group. The moment we recognize this fact, that moment we see that the other processes are involved as much as addition. Four is not absolute 4; it is 4 in 5 as a whole. Here we have subtraction as well as addition; we must refer 4 not only back to 1, but forward to 5 to see its value. In other words, in counting a group, (instead of counting in the air, as according to the Grube theory) the mind is going both backward and forward. In counting the fingers on the hand, 4 is referred not only to 1, but also to 5; its value as fixed by reference to 1 is addition; as fixed by reference to 5 it is subtraction, and one reference is just as