It Wasn't Done That Way When I Was A Child
( Originally Published 1924 )
ANY teacher whose methods are even approximately modern is likely to have heard this cry many times. Strangely enough, it is not, as one might suppose, an appreciation of progress. It is rather the last word in utter condemnation.
If the teacher replies that every activity of life is changing, that automobiles, airplanes, and thou-sands of other — I had almost said — "necessities" are of recent development, it often only serves to bring out the list of iniquities of which the school is guilty.
The complaint of the mother is likely to be: "My little girl is reading, and she can't spell a word ! Why, she does n't even know her letters ! When I was a girl we learned our letters so we knew them forward and backward before we even began reading. How can anyone read without even knowing the letters? I was one of the best spellers in my class, and I don't see how Mary is even going to be able to look up a word in the dictionary !"
The teacher's attempt to explain about "word method" or "sentence method" often falls on deaf ears, and the mother goes away shaking her head, fearful that her child will be permanently handicapped by such teaching.
The father, as befits a wage-earner, is more likely to complain about arithmetic. From the man who can barely figure his due for overtime to the one who was a "crack mathematician when he was in college," they question the "newfangled" ways of dealing with numbers.
It all results from trying to help Johnny with his lessons. Despite the warnings of schools, despite their own grumbling about doing the school's work at home, parents as a class do delight in helping their children with their lessons. Whether it comes from the pleasure of watching the opening up of a human mind, — always a fascination, — or the desire to push Johnny along a little faster than the neighbor's boy can go, or just the natural wish of the parents to give and obtain every advantage for one they love, is immaterial. The fact remains that parents do try to help.
So father starts an example with Johnny, and Johnny does n't put it down the way father would, he does n't subtract the same way, he may even multiply backward. Is it any wonder that father criticizes and Johnny defends himself for doing it the way he was taught, and the evening is entirely spoiled ?
Sometimes the complaint, from either parent, concerns the less formal ways of learning that are being increasingly used. The "grown-ups" pull long faces and deplore the loss of the old drill (which they cordially hated when it was applied to themselves !) and fear that the coming generation will not be well grounded in the fundamentals and will never have had the experience of "being made to do really disagreeable tasks."
It goes to prove that education is not yet recognized as a profession. The intelligent layman would hesitate to tell a physician how to diagnose or to treat a case of sickness. Witness the sigh of relief that comes from a household when the summoned doctor arrives. Neither would the average man direct a lawyer how to handle the intricacies of a case in court.
But where is the man or woman so humble as not to know more about his or her child and his upbringing than any teacher or school ? All of us have attended school, we know many teachers, and don't think too highly — more's the pity — of some of them, our children go to school and tell us all about it (even though what they tell is unintentionally inaccurate to an unbelievable degree), some of us have even taught, if no more than by giving a few lectures in law or medical or business school. So, of course, as it is all so simple and plain to see, we can, with perfect confidence in our infallibility, say, "Well, it wasn't done that way when I was a child."
I should be the last to discourage the parents' interest in the details of the work of the school, or to decry honest, intelligent, constructive criticism. It is a truism to say that it is only by the backing and cooperation of the home that the school can exist. Parents should recognize, however, that education is a most intricate and difficult profession. There has begun to be a science of teaching, and men and women are devoting their lives to its study. It deals with human beings, no two just alike and the same individual changing from day to day, with a world whose conditions are constantly varying, with changing demands, and changing ideals. Not only is there the experience of the past to affect its methods, but experimenters in considerable numbers have been and are now at work, trying this method and that, comparing results, searching out weaknesses, improving the technic of teaching, broadening its scope, defining its aims. Educational magazines by the score, books by the hundreds bring their material, contributions from experience and from laboratory experiments, from practice and from theory, for the busy teacher to assimilate and to use where it can strengthen her work. It is not too much to say that no one who is not making a life-work of teaching can really be in full touch with its progress, and, as a matter of fact, the pace of improvement is too fast even for many of those who are !
This means that the mere fact of being a father or mother cannot automatically qualify one as an expert on children - on either their feeding, their schooling, or any other side of their upbringing. In fact, the parent has one decided handicap. In any normal childhood there are many interesting and wonderful occurrences, some full of possibilities for good, others less welcome. It is difficult, meeting these incidents and events in the family environment, to have the same perspective that comes to a teacher who may have seen the same reactions and stages of development hundreds, if not thousands, of times.
The moral of all of this is twofold: that parents should be particularly open-minded toward changes and developments in this field, and that education should take the public into its confidence from time to time concerning the more evident changes that so naturally puzzle those whose children are affected by them. Such a policy of mutual confidence would give parents a fair basis for judging whether the schools to which they confide their children are living up to their opportunities, and would ensure better understanding and cooperation in educational progress. It is in the hope of adding to this understanding that I shall discuss briefly the questions already raised concerning reading and arithmetic.
Few, even of the best-informed teachers, realize the tremendous importance of reading, or how poorly it has been taught. In school, textbooks — the condensed information on each field — must of course be read. But all through life the sources of our information about the past, about the experiences of others in our own lines of work, about present developments in every kind of endeavor, about the daily occurrences of the world, are in the printed page. In fact, commerce, industry, practically all human activities are dependent to a great degree on interchange of thought through print or writing.
If it could be known how many pupils fail in various subjects in school and college, not from any weakness in those particular subjects, but because they cannot read readily and rapidly, it would shock both parents and teachers. The boy whose geography or history — sometimes even arithmetic — is always lagging be-hind the work of the class may have so much lower reading-speed than he should have that he is hopelessly handicapped in trying to keep up. If there is much class discussion such a pupil may struggle along for a while, but if a teacher depends on as-signed study, sooner or later he will drop back. So with adults: those who on account of their slowness in reading read only the daily papers, — and much of them by the headlines, — those who waste time over the morning's mail, or find their trade journals too heavy to wade through, those to whom any but the lightest reading, liberally illustrated, is a burden, are all likely to be suffering from this same weakness.
Experiments have shown that the great dangers in teaching good reading (by "good reading" is meant the ability to recognize rapidly what is expressed in print or writing, without needing to use conscious attention on the technic of reading instead of on the matter read) are:
Too early attention to the alphabet, phonics, or any other kind of analysis of words.
Oral reading of new matter, after the child begins to acquire silent-reading speed.
Too little silent reading of interesting material. This is likely to be a result if adults read to the child to any great extent.
Of course you see that, if this statement is true, the former methods of teaching reading were surprisingly efficient examples of how not to teach one to read ! Such a statement demands conclusive proof, and fortunately that proof is available.
Moving pictures taken of the eye while reading 1 show that reading is largely a matter of eye-habits; in particular, that: —
1. The eye does not move smoothly across the page, but moves in jumps or steps, pausing at the end of each step long enough to see the next part of the line being read. For example, a reader's eye might pause on each of the plaices marked in this sentence.
2. Poor readers take short eye-steps, good readers long eye-steps. For example : a good silent reader read the following line, on the first reading: —
everything possible for his comfort and for the as-
and on the second reading : —
everything possible for his comfort and for the as-
A poor reader read it the first time: —
everything possible for his comfort and for the as and the second time : —
everything possible a for his comfort and for the as-
The one who made the first two silent readings shown above read it orally :
everything possible for his comfort and for the as-
The poor reader shows wrong eye-habits not only in short steps, but in the uncertainty that forces the eye to go back for another look. This is shown where the numbers on the pauses are not in correct order.
3. Poor readers have not been proved to make longer pauses at the end of each step, but their totals of pauses are much larger and their reading is there-fore much slower.
The total eye-pauses in each of the preceding five examples amounted, in fiftieths of a second, to: —
First good silent reading 1 14/50 sec.
Such differences mean, in actual experience, an intolerable handicap for the poor reader. Suppose a high school expects a pupil to study at home, as many of them do, between two and three hours daily. If this is calculated for the child of good reading-speed, and the poorer reader, as in the example quoted, takes about twice as long to read the material (and probably even more to fix it in mind, as will be shown later), it means that from four to six hours daily would be needed. The alternatives are unprepared lessons, or injured health.
Or to put it in terms of business: Is the competent executive the one who glances over a contract or other paper, sees its salient factors instantly and so can decide quickly, or the one who has to read it several times before he even grasps its bearing? I do not ignore the possible difference of ability in two such men; I am simply pointing out a possible defect that may so handicap one of two men of equal ability as to make him less likely to succeed.
4. Oral reading steps are shorter and pauses are in general longer than for silent reading. This is be-cause the slowness of the tongue holds back the eye.
The example already given shows this condition.
Based on such experiments as this, the teaching of reading is now by the word, phrase, or sentence method, which, simply stated, means that the child is taught to form a mental picture of an entire word or phrase, instead of — as formerly — being taught to recognize a word by the letters in it. I believe that such methods might all be called, if a name must be used, the picture method.
No one, meeting a friend on the street, stops to analyze the features, saying: "He has blue eyes, light hair, a cleft chin, and so on, so he must be Mr. A " ! On the contrary, if the image fits the mental picture of Mr. A as it previously has been formed, there is immediate recognition. As a matter of fact, how many of your own intimate acquaintances can you describe in detail ?
In the same way the child beginning to read can be given a gallery of word- and phrase-pictures that he will instantly recognize again when they occur in his reading. There are many ways of helping to accomplish this, but as they are details of teaching-technic, they will not be considered here.
The child who knows the alphabet is, then, handicapped in learning to read, and will be handicapped for life if poor eye-habits are formed on account of this knowledge. The one who recognizes in immediately has an advantage over the one who must see i and n; the one who can see and recognize in the as a unit has a still greater advantage, while the pupil to whom in the house or in the woods is one reading-step has another gain in reading-efficiency.
A western educator tells the story of one class in a school system that was, by fault of a new teacher, started on the alphabet in commencing reading. Before the end of the first year this was discovered, and every effort was made to correct the pupils' reading habits. In the fourth year this class was still much the poorest reading-class in the city de-spite all the school had been able to do in the mean-time in its effort to correct its poor eye-habits.
"But," you may ask, "may our children not learn the alphabet at all ? How can they spell correctly ? "
Certainly they may, after the eye habits are started correctly. The alphabet, spelling, writing, phonics, — which is simply word-analysis by sounds and is particularly used for the purpose of working out new words, — all become a part of the children's study. Intelligently used, they will not harm the habits that have been started. Overdone too early, especially by the parent who is distressed over a child's inability to spell, they may cause serious harm.
Do not worry about spelling. It may be postponed even to an extreme, and yet come out satisfactorily. The teaching of spelling, which there is not space to take up here, has never been done so well as now, and — even if you do find it hard to believe --children have never been as good spellers as they are now!
The harmful influence of oral reading on silent reading is easy to explain. If a child has reached a point where eye recognition is more rapid than the ability to enunciate, that child will begin to read poorly orally if the material read is at all interesting. His eye and his mind will go along at silent-reading speed, while his tongue stumbles along behind, repeating, not what the eye is reading, but what is remembered of the words read a moment before. Small wonder that words are mispronounced, or even replaced by other words, and that expression is absent. But the remedy is not, as the prescription used to be, more practice in oral reading; it is to stop oral reading entirely as reading-practice. If this is not done, but the conscientious mother or teacher drills the child, stopping him and making him reread for all mistakes, the eye finally may be-come discouraged and settle down to the speed of the tongue, and the result will be a permanent loss of reading-speed.
In testing pupils, even in grammar grades and high school, investigators find many individuals who have only one way of reading — the oral way. The limit of speed is often below one hundred and fifty words a minute, and the habit of oral reading is so established that every word is fully pronounced mentally, if not vocally. Such pupils often cannot succeed well in school work, and reading will always be a slow, laborious process for them, unless they go through the very difficult undertaking of correcting this condition.
Only a short time ago a mother remarked that her daughter's school had asked to have her twelve-year-old child read aloud to her daily during the summer vacation. An inquirer who asked the reason was told that the child was a very poor reader. The answer was that it was almost certain that the child was too good a reader for the teacher's purpose; and so it proved, for she could read silently at about double her oral speed, and consequently was over-running her tongue and stumbling badly. The remedy suggested might have improved her oral reading, but if so, would have accomplished it by the sacrifice of the tremendously important advantage of her rapid silent reading.
The ability to read well orally is, however, a pleasant accomplishment, and the oral use of words in school is necessary for checking pronunciation. Both these aims are 'net by much use of oral composition, public speaking, and reading aloud interesting material that a pupil has read for himself and considers important enough to bring to the class as a contribution to its work. The purpose in all this, or in occasional class-reading of some particularly worth-while book, is to give information and pleasure to others. There is not the same temptation to run ahead of the tongue, and the oral reading is not done to an extent that can form bad habits.
Being read to by others may work harm if it does either of two things: —
Lessens the amount the child will read to himself ; Makes it easier to get information through the ear than through the eye.
Much reading-practice is needed before reading itself ceases to occupy much of the attention and the mind can concentrate on the meaning of what is read. Anything interfering with that practice is detrimental.
Some time ago it was reported that a pupil in the year before high school appeared unable to accomplish her work, although she was very conscientious, and mental tests had shown her to be normal. Examinations of her ability to understand what she was studying showed that she must read each paragraph over and over again before she understood its content, but that she was alert and intelligent in class discussions. Further tests showed that the paragraph she must read over and over again to understand was grasped the first time it was read to her. Inquiry then disclosed the fact that her father had read her books and her lessons to her for years, and in so doing had trained her ear as a source of information, while her eye, having no such practice, was almost helpless as an avenue for learning. Despite very careful efforts made to overcome this defect, the girl was handicapped seriously.
A natural question is, "Why can any of us who were taught by the old methods read well ?" The answer is that great numbers can't ! My own tests of adults have shown reading-speeds from about one hundred and forty words to over eight hundred words a minute. Those who, although taught slow eye-habits, yet can read rapidly now have taught them-selves by silent-reading practice, and have overcome the wrong eye-habits that were started by the school. This was usually done, I believe, by much silent reading at home when oral reading was being taken in school.
One other point : Do not think that slow readers understand better and remember longer. The contrary is more likely to be true. In general, it is the reader who spends no appreciable time on the mechanical process of reading, whose whole mind is on the content, who gets the information most readily. This does not, of course, take into account pauses for consideration and thought, where the text opens up such possibilities, nor does it consider marked differences in native ability.
This explanation will, I hope, make it clear that the changed method of teaching reading is not a fad, but is founded on research and logic. It depends, not on opinion, but on scientific experiment. There is every reason to believe that the newer ways are fundamentally correct, and that the present-day children will be much better readers than their parents were.
In this subject I shall touch on but two topics, sub-traction and multiplication. They are two of the fundamental processes about which any educated person would supposedly be informed, yet they, as well as reading, have surprises in store.
Every mathematical-association committee of which I have found record, that within the last twenty years or so has considered ways of subtracting, has re-ported against the former methods of teaching and using this operation.
Most of us were taught to "borrow" when subtracting a larger digit from a smaller. For example, in 92 — 37 the pupil was told to borrow I from the 9, making 12, to take 7 from this 12, leaving 5, and then to subtract 3 from the 8 remaining from the 9, leaving 5.
The new method says: "What must be added to 7 to make the next higher 2 ?" 5 must be added, and as this makes 12, there is one to carry — as in addition — to the 3, making 4. "What must be added to 4 to make 9 ?" 5; so the answer is 55.
This method is usually spoken of as the "shop method," from its likeness to making change, or the Austrian method. It will be easier to understand if it is considered in various types.
When a child is learning to add, there are forty-five number-combinations, such as I + 3 = 4, 7 + 8 = 15, 2 + 2 = 4, that he must master in order to add readily. Any weakness in these combinations is certain to show later on in his arithmetic. The good teacher uses them not only in the form "7 + 8 = what ?," but also "7 + what = 15 ? " and "What + 8 = 15 ?" so that the coupling of 7 and 8 to make 15 becomes an immediate association.
But this reversed addition is subtraction; and with-out learning new terms, without a struggle with a new subject, the child naturally begins to subtract one-digit numbers.
This same simplicity of approach and use holds as long as the digits subtracted are not larger than the ones from which they are taken. 34 would be done by saying "4 and 5 would make 9, 3 and 4 would make 7, so the answer is 45.
When examples are met that would necessitate "borrowing" by the other method, the child is told to add whatever is needed, carrying as in direct addition. 723 In this example, the work would be as follows: 485 5 and 8 would make 13, carry I; 9 (8 and the I 238 carried) and 3 would make 12, carry I ; 5 (4 and the I carried) and 2 would make 7. This operation is exactly the same as the one that would be performed in adding 485 and 238 to get 723. The only additional need is that the child shall be able to recognize from the total and one part what the other part is: that is, shall know the number-combinations so well that any two numbers of a set will bring to mind the third one.
But the simplicity of learning and using this method is not its only advantage. For one thing, it makes it easy to subtract several numbers from a single one in one operation. In the following example the three lower sums of money are to be taken from the single sum at the top. Starting to add in the usual way, and subtracting from the top row by the $ 1703.03 shop method, the work would be : 3, 12, 20, and 3 makes 23, carry 2; 4, II, and 0 makes II, carry 1; 9, 12, 19, and 3 makes 22, carry 2 ; 4, 8, and 0 makes 8; I, Io, 12 and 7 makes 19, carry I ; 5, 6, 9, and 1 makes Io.
A similar method would be used if it were necessary to take away a certain number of times the quantity to be subtracted, as in taking 7 times 463 from 4876. 7 X 3 = 21 and 5 makes 26, carry 2; 7 X 6 = 42 and 2 carried makes 44 and 3 makes 47, carry 4; 7 X 4 28 and 4 carried makes 32 and 6 makes 38, carry 3; 3 carried and 1 makes 4.
The last operation can be extended to shorten division very markedly, as in the following example. This method would not be given in the usual school arithmetic. but has value in more advanced study of the subject.
In the shortened division, 6 times the divisor 379 is taken from 2487 as in the previous illustration, the remainder, 213, being written below; 5 times 379 is then taken from 2139 (which can be seen to correspond to the operation in the long division) ; 6 times 379 from 2441, and similarly multiples of it from the successive diagonal rows 167o, 1542, 2671, leaving the final remainder 18. One interesting feature of this division is the small space it occupies.
The foregoing illustrations make it clear, I think, that the shop method of subtraction not only gives a more natural approach to the operation for the child, but offers to one skilled in it a more useful way of handling numbers.
In multiplication, reversing the order in which the digits of the multiplier are used offers two advantages with no apparent disadvantage — unless the fact that it differs from past usage may be considered a disadvantage.
The difference lies in the order of multiplying. In the usual order one starts to multiply with the right hand digit of the multiplier, in this case 6, following by each successive digit as one goes to the left. There-fore the products obtained are written so that each one starts one place farther left. In reversed-order multiplication, one starts to multiply by the left hand digit of the multiplier, in this case i, and follows by using each successive figure toward the right, the successive partial products each ending one place farther toward the right.
It is evident that there is no difference in the difficulty of these methods. A child might be taught one or the other with equal ease.
The argument for changing to the "left to right" order — and this too is strongly recommended by mathematical committees — comes from the later use of multiplication in dealing with measurements and other approximations. Suppose that 231.4756 and 182.3421 were to be multiplied, the result being known to be of no value beyond the second decimal place. By the old method, the work would need to be carried through to the bitter end, although a good share of the work and six places of the result were known to be of no use ! Furthermore, the products first written are the ones of least importance in the result. By the natural method, the partial products can be stopped whenever it seems best, and the first partial product is the best single approximation, each succeeding product adding to its accuracy.
Here, each multiplier is used only with the digits that will give results from the second decimal place up. The amount that would be carried from the next place below is, however, added in this illustration, the nearest unit being carried. The left-hand I multiplies all the number 231.4756; the 8 multiplies all but the 6, but it takes into account that 8 X 6 = 48 by carrying 5 (the nearest whole value) to the second decimal place; the 2 leaves off the last two figures, 5 and 6, but takes into account the I secured by carrying from their product; the 3 leaves off 756, but carries 2 from their product by itself, and so on. The last number, 1, will be seen to multiply only the 2, ignoring the 31,4756 because that would all fall to the right of the second decimal place.
Comparing this with the former method, it will be seen that twenty-seven figures are saved in the work and result, with no loss in accuracy if only two decimal places are wanted. A slightly less accurate result could be obtained by omitting the carrying from the unused figures, and simply multiplying one less figure each time.
The justification for the omission of these extra decimal places is that if the given numbers are accurate only to four places, the result cannot be accurate beyond the second place — in fact, it is unlikely to be accurate that far. Suppose these two numbers are approximate measurements; then there are figures not obtained that belong in the fifth decimal places. These figures multiplied out will change every number to the right of the second decimal place, probably will change the second place also, and may affect still others. Is n't it, then, absurd to pretend to ourselves that we are getting a correct result when it cannot possibly be right ? It is much better to get only as much as has value — and to save useless work at the same time.
There are many, of course, who will never have practical use for this shortened form of multiplication. They have, however, sacrificed nothing in learning the reversed-order method, for it has no disadvantage as compared with the other method.
The foregoing are two of the most striking changes that may be met in the actual operations of arithmetic. There are many changes in ways of teaching it, and some of them will be described in another chapter.