Popular Science Monthly/Volume 27/September 1885/An Experiment in Primary Education II
|AN EXPERIMENT IN PRIMARY EDUCATION.|
ONLY one attempt was made during this year to teach the child the meaning of words. It was done through a simple generalization which had become indispensable in the study of geometry, when she passed from plane to solid figures. By means of wooden models she learned, in addition to the cube—the sphere, ovoid, oblate, cylinder, prism, tetrahedron, octahedron, and dodecahedron. She then was led to make parallel lines of plane and solid figures with a corresponding number of sides or angles, then to abstract the Greek numerals tri, tetra, penta, hexa, etc., found to belong to both columns, and set this in the center, with the syllable gon on one side, and hedron on the other. An hour was required to complete the setting out of these figures, and arranging these titles with movable letters, which for the first time the child learned to use for spelling. The exercise was, of course, repeated again and again, until every step was perfectly familiar. From the beginning the child had no difficulty in connecting the plane and solid figures, nor in learning the numerals appropriate to each. The new effort at abstraction and classification was at first somewhat hard, but soon became easy. The facility with which the impression of forms may be made upon a child's mind, when this is as yet uncrowded by notions on the other qualities of objects, was shown by a little incident at this period. A few weeks after having made her first acquaintance with the oblate, she saw at dinner for the first time some small stewed onions. "Oh!" she exclaimed, "they have brought us some oblates for dinner." Another day, when she accidentally pulled the cord of a window-shade in a certain position she observed that she had thus made "two scalene triangles." Looking at the ceiling above a lamp, she called to me to notice how the light made three "beautiful concentric circles."
One other study during the year was made upon the intrinsic meaning of words. In the course of some observations on plants the child had learned to recognize the ovary and ovule, and to herself dissect them out of a flower. When this had been done, the analogy between the vegetable ovule and chicken-egg or ovum was easily pointed out, and the relation of the latter to the geometric ovoid. The four objects were then placed in a row on the table, the names of each spelled with movable letters, and then the common root ov described and taken out. The important and fundamental idea was thus grasped that there was an intrinsic meaning to at least some words, and also that objects associated by a common name, whose specific variations were of subordinate importance, must be classed together as deeply related, notwithstanding superficial difference of aspect. But this idea, once distinctly enunciated and understood, was then set aside for a season. That the idea was understood, I tested in the following way: At table the child remarked that a particular potato was "shaped like an egg." "What shall we then call it?" I asked. "An ovoid," was the reply. "Very good. Do you know what I thought you might call it?" "An ovum," she answered, with an air of mischievous triumph. "And why did you not?" "Because it is not an egg, but only shaped like an egg" I tempted the child with the suggestion that she should tease the waiter by asking him to bring us some ovules instead of eggs; but the instinctive modesty of childhood recoiled from the pedantic proposition.
The necessity for precision in the use of terms, thus initiation into scientific terminology, was enforced incidentally on another occasion. A playfellow much older than the child picked up a piece of mica and called it isinglass. This conventional inaccuracy I strongly rebuked, and, procuring a piece of real isinglass, led the child to note its difference, and to condemn in private and without malice the slovenly language of her presumably untaught comrade. Now, the child had a doll called Rosa, and was in the habit of illustrating any absurdity by pretending that Rosa was guilty of it. Some time after the conversation on the isinglass she was watching a stream of water falling in the sunlight from a hose. She exclaimed: "See the beautiful silver water coming from the old gray hose. Rosa would have called that mica!"
When the box of wooden geometric models was thoroughly mastered, after about six months' study, I procured for the child a set of models of crystals, such as are used for studying mineralogy. About half of these proved too complex for study, but the child easily learned to recognize and distinguish twenty-six, partly simple, partly compound forms. As each face of the crystal showed some plane figure which she had already learned, and as she was also familiar with the Greek numerals from three to twelve, it was generally easy for the child to devise the name of the crystal, even when apparently so repelling as a scalenhedron, rhombic dodecahedron, right rhombic pyramid, etc. It was interesting to notice her capacity to discern the general outline of a crystal and thus its generic features, and afterward to distinguish the secondary divisions of its sides, or the specific characters; thus in a four-faced cube, a three-or six-faced tetrahedron, a three-faced octahedron, etc. The forms in the four systems of crystallization were learned by repeated handling of the models, until the child's perceptions had become saturated with them, and she could, for instance, discover for herself four-faced cubes in the curved molding on staircases. Then, at the beginning of the second year, the crystals began to be copied in clay, and opportunity then afforded for studying their axes, or the basis of their classification, by means of long pins thrust through the soft model in appropriate direction.
Arithmetic, the second science in Dr. Hill's category, was begun several months after the first studies of form and outline. Instead of the beans so frequently recommended, the child used sticks of different sizes and colors. For two or three months she studied such numbers as seem almost to form natural complex entities, and hence have often been sacred numbers, thus: four, nine, ten, twelve, twenty-four, thirty-six. The child was exercised in dividing these up into symmetrical groups, whose resemblances she was trained to tell at a glance by the eye, before enumeration. Thus she learned to form groups of threes, fours, and sixes, and to unite them in as many fantastic combinations as could be invented. The object was to effect the transition from the perception of form to the conception of number by a series of visual impressions as vivid as possible. The breaking up of a whole into parts really precedes in facility the additioning of parts into a whole, for the reason that the power of destruction in a child obviously precedes the power of construction. Froebel's fifth gift of cubical blocks has its first application on this fact, since the entire mass forming a cube may be broken up into twenty-seven smaller cubes. When we reached the number twenty-seven, I told the child it was the smallest cube that existed. But she having a year previously, when only four years old, learned to handle these same cubes, corrected my error, and demonstrated triumphantly that eight blocks would make a still smaller cube. The incident shows the tenacity of ideas once implanted in the right way and at the right time.
It is much more difficult to teach a child to subtract than to add, a fact upon which Warren Colburn sagaciously comments. In the discussion of practical problems, a hitch often occurs in the child's mind which may be quite unsuspected by the teacher. Thus, if Henry and Arthur go to buy a ball which costs sixteen cents, and one boy had six cents and the other seven, I found the child unable to solve the problem as to how many more cents were needed, because, as she said, she could not take thirteen from sixteen, since the very trouble was that the boys did not have sixteen cents. It was necessary to use sticks, and with the distinct formal agreement that those of one color should be known to represent an imaginary number, those of another color the number of actual things manipulated. But what a stride for a young child's mind to make, into a sphere neither real nor imaginary, but where the existent and the non-existent are indissolubly associated in an ordinary practical affair of every-day life!
From the beginning the decimal system imposed itself spontaneously upon the child's mind, on account of the facility of visibly recognizing groups of five and ten sticks, and of verbally recognizing their successive additions. In this way the multiplication-table the famous despair of little Marjorie Fleming—was mastered with great ease by this far less gifted child. Every one remembers the fierce vehemence of Pet Marjorie's protest, "But 7 times 9 is devilish, and what Nature itself can't endure!" It is so, if presented as an isolated fact. The child I taught, however, discovered of herself that the successive addition of tens was as easy as that of ones. After that, when she came to add (or multiply by) nines, she would say, first add ten, then say, and nine was one less. If it were eight, it was two less, etc. After a fortnight of these exercises, she was asked one day out of study hours what was the sum of 14 and 19, and answered immediately 33. Upon being asked to explain the process, she said, "10 and 19 makes 29, then I must add 4 more, and 1 and 29 are 30, and 3 more are 33." When three decimals were reached, a somewhat laborious exercise was performed. Thus, to operate with 138, the number 100 was constructed out of ten packages of purple sticks, each package containing ten sticks. These packages were placed in a row; underneath was a second row, containing, to represent the number 30, three packages of yellow sticks, each containing ten; finally, a third row of eight units was made with green sticks in a single series. In this exercise the sticks were all of the same size; in another, later, a hundred was represented by a single long stick, usually purple, a ten by a yellow stick next in size, a unit by a stick still smaller and green. Thus the original and clumsier representation was condensed by the substitution of an expressive sign for the literal numbers, and as soon as the sticks became used as signs, and not as the objects really to be counted, the mutual relation of their respective sizes also ceased to be literally exact, and became merely schematic. Thus was gradually managed a transition to the use of pure written signs or symbols. The transition initiated and enlarged the condensation of Roman into Arabic numerals. Knowledge of the process of subtraction, especially in three and more decimals, was essentially facilitated by this device with sticks, and the terrible difficulty of borrowing ten quite overcome. Thus, if the number 288 were to be taken from 362, the larger number would be represented by three long purple sticks, six shorter yellow sticks, and two green sticks, the shortest of all. These colors were always selected because harmonizing so well with each other. Then, similarly, the 288 was represented by two purple, eight yellow, and eight green sticks. It was easily recognized by the child, that one of the yellow sticks could be removed from the ten sections of the 362, and ten green sticks substituted, bringing the entire number of units up to twelve, from which the eight of the lower figures could be taken. It was also obvious that, when one yellow stick had been taken away, only seven remained. There was no need, therefore, to employ the usual confusing statement that a ten must be borrowed from the upper figures, and later restored to a different place in the lower.
The study of abstract numbers, with Colburn's arithmetic, was begun when the child was five and a half years. At the end of a year she had thoroughly mastered the first four rules, including both "short" and "long" division, and was considerably advanced in the study of fractions, proper and improper.
The last study entered upon during this year was that of natural objects, and, for obvious reasons, plants were chosen for this purpose. I suppose that most persons seriously interested in education are acquainted with Miss Youmans's admirable little "First Lessons in Botany," and the plea she makes for this science as a typical means of training the observing powers of children. According to her plan, the first object studied is the leaf—and the pupil is taught at once, not only to draw the leaf, but to fill out a schedule of description of it. Much may be said in favor of this method, which proceeds from the simple to the complex form, but it is by no means the only possible one; the writing part of the scheme is, moreover, impossible for a child who has not yet learned how to write. There is another method which consists in seizing at once upon the most striking aspect of the subject, and which shall make the most vivid impression upon the imagination. For this purpose the leaf is the least useful, the flower the most so. The earliest botanical classifications are based upon the corolla, and, in accordance with a principle already enunciated, a child may often best approach a science through the series of ideas that attended its genesis. The conditions are different for an adult, who requires to get the latest results; the child's mind is always remote from these, but often singularly near to the conceptions entertained by the first observers. Again, it is unnatural to enter upon the beautiful world of plants by the study of forms and outlines—which is much better pursued when abstracted from all other circumstances, as in models of pure mathematical figures. But with plants comes a new idea—that of life, of change, of evolution. It is fitting that this tremendous idea make a profound impression on the child's mind; and this impression may be best secured by watching the continuous growth of a plant from the seed. The study of life is a study of events, of dynamics, of catastrophes. The earliest observation perceives the extraordinary influence of the surrounding medium upon the destinies of the living organism. It is not difficult to surround these destinies with such a halo of imagination as shall impress on the mind a sense of the mystery, sanctity—I may add, the necessary calamities of life—before it has become absorbed in the consideration of living personalities.
I trust it will not seem a piece of bathos when I add that I initiated the pursuit of these objects by making the child watch the growth of seven beans on a saucer of cotton-wool. A specimen bean was first dissected, and its principal parts named—the cotyledons, the embryo with its radicle and plumula, the episperm. The daily reference to these terms speedily rendered the child quite familiar with them. To seven other beans were given appropriate names, as of a band of brothers, and they were then planted on cotton-wool by the child. A daily journal of events was opened, in which I wrote each day or two, at the child's dictation. As she had learned the Arabic numerals, she inserted these herself in the protocol whenever necessary. The entire history of each bean was thus written out, and the successive steps of its development, from the thrilling moment when the radicle first peeped out, to the time when, after transplantation to a flower-pot, the plumula had developed to a long, trailing vine. The rate of growth of this vine was measured day by day exactly, with a rule, the number of leaves counted, etc. But the mathematical considerations were here subordinated to a larger idea, that of the succession of events. Some of the beans molded early in their career, and the relations of this catastrophe to the accidental differences of position, moisture, etc., were carefully studied. On one occasion the child dictated to me the following entry for the journal: "The episperm, on the under surface of Tertius, is all black, and has split, leaving a space the shape of an equilateral triangle, with the apex pointing to the convex edge of the cotyledons." In the summer, when flowers could be obtained from the woods in abundance, the child made collections of ovaries and ovules, and was never tired of finding the latter asleep in their beds, in so many differently shaped houses. At this time the static considerations were allowed to predominate, and the child rather forgot the function of the embryo seeds—so much so that, upon seeing some small pieces of ice lying in half a musk-melon, she said that these were like the ovules in an ovary. At the beginning of the second year, the study of plant-growth was resumed with seven hyacinths, that received appropriate names, as seven sisters. The first lessons in written expression coincided with the beginning of this new study; for now the child was allowed to write the plant-journal herself. The exercise was complex. The child first examined the hyacinths, and noted whether anything had transpired since the last observation. She then framed a spoken sentence, in which such an event was accurately described. She then dictated the writing of this sentence as a whole, which she was afterward to copy. During this dictation, some knowledge of spelling was incidentally acquired; for the child was led to spell by sound, and without reference to silent letters. The words she had not yet seen. Finally, when fairly at work at the writing, the meaning of the sentence was temporarily ignored, and attention closely concentrated upon the forms of the letters, and no mercy shown to inaccurate imitation of them. Thus, one day she entered the observation that Blanche, in a blue glass, had grown much more vigorously than Aura, in a dark one; and a blue glass was given to the less favored sister, in the hope that she would improve. She noted that the tips of the white roots were gray and conoid in shape (making the observation herself independently), and was allowed to demonstrate the function of these tips by cutting one off and seeing the growth of that root arrested. On another day she first discovered, then described, then wrote down, that the first broad leaves of Blanche had split open, showing two others at right angles to them. This was her first perception of this remarkable law of phyllotaxy, and she herself illustrated it by making two loops with the thumb and finger of each hand, and making them intersect each other. The previous acquisition of mathematical conceptions was constantly shown to facilitate and render precise her observations of complex objects.
It was rather as a concession to a prevailing prejudice that at this time the child was taught to read. This study, usually made of the most importance, was held for this child to be quite subordinate and easy, and little stress laid upon it. The child was allowed to follow her own inclination, to divine the subject of the chapter from the picture at the head of it, and, to a considerable extent, the words in each sentence from the context; when the wrong word was thus suggested, she was obliged to spell out the real word by sounds, always seeking first the central or predominant sound, and building up the word around it, instead of enumerating the letters in order. Thus in the word scratch she took out the letters a t, as the central nucleus, preceding the first by the sound of r, then of c, then of s; then, when the sound scrat was complete, adding that of ch. She was made to read as much and as rapidly as possible, relying upon constant repetition and association of ideas to secure familiarity. Thus unconsciously the conception was continued, that written as well as spoken language was an outgrowth of thought before the attempt was made to study it as an object of thought. This method is like that of learning to walk before studying the laws of Weber on locomotion.
This method may seem slovenly, but, after all, it is both the natural and scientific method of studying an unknown tongue, which must be deciphered by the context. How else did Champollion read the Rosetta stone, or Eliot find a written language for his Indian Bible? Throughout this period the task of reading was treated as something so easy as to be insignificant, and was so regarded by the child herself. The main intellectual work of the day's lessons (whose duration was never more than an hour and a half) was concentrated upon the arithmetic, map-drawing, analysis of flowers, and the geometrical studies, that she now pursued by the help of Hill's "First Lessons," and Spencer's "Inventional Geometry." She studied angles, vertical and adjacent, the relations of angles and circles, and the measurement of the former by the latter. Exercises in these were practiced daily with compass and ruler; and, when lines drawn with the pencil failed to give a large enough visual impression, they were designed with colored sticks. This enlargement of the material illustration never failed to clear up any obscurities. At the time these notes cease, the child was six and a half years old.
I have tried to make clear in these few notes the outlines of a (single) experiment, which seems to me to show that the mental education of even a very young child may be imbued with scientific methods and even ideas which should furnish suitable preparation for advanced scientific studies. It can not be a matter of indifference that 'such habits of mind are acquired from the beginning, or only after much previous faulty training. What comes first will always remain the most important, will always dominate the rest. Experience in the medical education of women has repeatedly brought home to me the difficulty of teaching such an art as medicine to persons who come to it through the prevailing systems of school discipline, especially those which are applied to girls. Experience with one little girl at least convinces me that the aptitude for vivid and accurate perception, and for scientific method in ideas, often exists where unsuspected, and only demanding proper cultivation.
As an illustration of the method described in the text, when carried into more complete studies, I insert an exercise written by the child when six and a quarter years old. It is a description of a wild Iris, which she analyzed herself on successive days, writing down the results from memory on the next day. She was never told anything, but obliged to discover for herself each fact, to compose the sentence describing it, and to spell by ear the words of the sentence without copy. She was allowed to insert in her description whatever fancies occurred to her. The headings and order of evolution of the subject were alone dictated. With nearly all the technical terms she was, however, already familiar; two only were told—"perianth," as opposed to corolla, and "blade." Before analyzing the Iris she was obliged to take a long walk to the woods for it, and first to draw a map showing the way, and by means of the compass. Two intersecting lines from sight-objects were dictated by me, and the fact learned by this and another previous experiment which had failed, that to locate an object in space at least two lines are required. The final description, whose writing occupied two or three weeks, was as follows:
The Rainbow Family.—(This name was given as a literal translation of Iridaceæ, and as a return in a spiral to the first natural object studied eighteen months before, the rainbow. The way was also prepared for the future historical study of the myth of Iris.)
Iris Tricolor.—(The numeral was already familiar.)
Perianth = 6 Petals. (The algebraic signs and numbers were used to indicate that in a scientific document, not a flowing style, but the fewest words and most concise expressions were required.)
These stand on top of a long tube in which the style is locked in. There are two kinds of petals: 1. Three which are the biggest, and have three colors. There are two parts to each the upper broad part called the blade, and the lower long narrow part. (The term "blade" was here taught for the first time.) The blade is first purple; in the middle is a gold stripe which runs into the narrow part. (At this point, the child drew and painted from memory, on the margin of her protocol, a picture of the petal.) Between the purple and gold the blade is white. These petals curve outward and downward, so that the gold stripe comes on top. The bees see it and come for the pollen. (First introduction of a Darwinian law.) 2. Three petals, which are entirely purple, are vertical, smaller, and stand between the others. (The child made another drawing by opening the flower on the page and tracing its outlines.) It is as if six girls were standing in a circle (here was introduced a botanical outline of the whorl, instinctively devised by the child, the circle being drawn accurately, with compasses). Every other one leans back and stretches her arms out horizontally, as if to show her gold bracelet. The three others lean forward, and hold their arms up above their heads. (Prolonged contemplation of this lovely group tended to evoke such instinctive æsthetic conceptions as are at the basis of many pieces of statuary, notably Thorwaldsen's Graces.) The gold stripe is like the orange feathers on the head of the bee-martin. The bees think it is a flower, and come and settle on the bird's head; then he catches them. (This illustration was suggested by the child, shortly after having seen such a bird which bad been shot. She thus learned to step from one section of natural history to another, and also to seek analogies of organs in their functions.) Mamma says (here knowledge by testimony is distinguished from that obtained by personal observation, which has not yet reached so far) that all flowers that want the bees to visit them have bright colors. This is like ladies who want the gentlemen to visit them, and then put on their finest clothes.
The Great Mistake.—We thought there were three more petals in the middle of the corolla. These were smaller than the others, and divided at the top like a funny M. (The child then made a drawing in illustration.) Each stands inside a gold-striped petal, and has a groove on the outer side like a bath-tub. In this a princess is bathing. She is a stamen, with a long, whitish anther like a veil over her head. So there were three stamens inserted with the petals.
How we found out the Truth.—(This process is introduced with some solemnity, as befits its importance.) 1. We looked to see how the pollen got on the stigma. (Introduction to the biological method of studying structure in association with function.) 2. We noticed that the pollen could slip down the groove into the tube leading to the ovary. 8. We saw that the petal-like pieces were fastened together in the middle of the perianth, making a solid white cylinder which passed into the green tube. (Another drawing from memory illustrated this.) 4. It was plain that the white cylinder was the style, because it went to the ovary. 5. Then mamma said (recognition of authority and testimony again) that the petal-like pieces were the stigma, immensely big. (The incident showed the function of the reason in unraveling the deceptions imposed by the senses and the superficial aspect of things.)
Ovary—at the bottom of the tube (ovary inferior)—has three lodges and a great many ovules.
(Thus the botanical analysis was rigidly accurate and complete. But, instead of being a dry schedule, it comprised a mass of vivid, glowing impressions destined to remain forever as a typical group of ideas in the child's mind. The prolonged, patient, sympathetic study of the individual preceded the abstract study of a class of flowers. In the future it was intended that the child should construct her own classes from among the botanical individuals she should really learn to know.)
- What is easy, when taken instinctively, may be incredibly difficult when itself becomes the object of thought and study.