Mary Putnam-Jacobi

“ It is upon forms and colors, therefore, that both perception and memory must first be exercised. The visual impression should be amplified up to the point at which it is able to fix itself on the mind by its own momentum; therefore, without conscious effort. When the mind has accumulated a stock of reminiscences which can not be forgotten, it will, by so much, have enriched its structure and enlarged its furniture. ”

“ 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!" ”

“ Without such power the mind becomes inevitably the prey to a skepticism generated much less by contradictions in the outside world, than by the weakness of its internal organism. What other result should logically be produced, when, to the opening mind, as it turns eagerly to the wonderful world in which it awakens and finds itself, we offer for contemplation, exercise, and earliest sustenance, the alphabet, the abstruse structure of words to be spelled, the grammar of sentences to be construed, the complex gymnastics of copies to be written? ”

“ The art was thus approached as all arts should be, from the stand-point of its real genesis, and tended to place itself in the same relative position in the child's mind that it had occupied in the real history of the world. ”

“ 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. ”

“ IN modern times education has been recognized to be something more than an elegant luxury, designed exclusively for the benefit of the "upper classes." It is a force, and a potent and indisputable means, not only for the training but for the evocation of forces. ”

“ Of this, literature and other art is one and only one portion. The work of the professions, of the upper regions of industry, commerce, and finance, the work of scientific and of political life, is the work appropriate to the intelligences which have proved themselves equal to a course of training at once complex and severe. A person destined to receive a superior education is expected to develop more vigorous mental force, to have a larger mental horizon, to handle more complex masses of ideas, than another. ”

“ To study words before things tends to impress the mind with a fatal belief in their superior importance. To study expression before subjects of thought have been accumulated, is to cultivate the habit, always prevalent in civilized life, of talking fluently without having anything to say. To direct attention to sets of arbitrary signs before attention has been trained by contemplation of real objects, teaches the mind to place conventional and contingent facts on the same level with necessary truths. ”

“ In the earliest training, contemplation of an object is insufficient to fix its outlines on the mind: it must be handled as well as seen. In my own experiment with a child of four, Froebel's building blocks were used to construct definite models; but these, once framed, were repeated from memory. Sometimes the details of an exciting story, as that of "Blue-Beard," were associated with the different details of the model, so that these were more vividly remembered. ”

“ The final ends of education are efficiency and repose. The educated person is he who knows how to get what he wants, and how to enjoy it when he has got it.
When a "higher education" is demanded, for any class of persons—as women—it means that it has become desirable to train their faculties for more difficult work than that traditionally assigned to them, and also that it is desirable to enable them to get more enjoyment out of any work that they do. The necessary correlative of the possession of powers is the opportunity for their exercise. ”

“ 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. ”

“ 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. ”

“ Habits of rich association of ideas must be formed, and of pleasure in their contemplation. And very early must be offered to the child problems to be solved, either by purely mental exertion, or by that combined with manual labor. And all this care must be taken for girls as well as for boys, so soon as it is seriously agreed that girls may be admitted to a superior as well as to a primary education.
The first intellectual faculties to be trained are perception and memory. ”

“ Froude remarks, men of genius always have tenacious memories. Conversely, the relatively feeble mind of the young child requires a large object to awaken its prehensile faculties. If the memory of children for what has once impressed them is often remarkable, it is because the infantile period of mental development bears much analogy with the character of genius. ”

“ The outlines of the object itself may be magnified, and at the same time roughened, by being copied with sticks, as may be done in the first attempts at map-drawing. The copy substitutes a schematic outline for the real one, but by the very fact blends a mental conception with the simple visual image. This necessity for amplification is very important, and, as it seems to me, very often overlooked. It is strictly in accordance with the physiological law in neuro-dynamics, that a stimulating impression must vary in intensity inversely to the susceptibility of the nerve-element to be impressed. ”

“ 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. ”

“ But because this science is based upon an abstraction, and not upon a direct perception, it should be made to follow, and not, as is usually the case, precede geometry." Again, "the earliest suggestions of motion reveal to us time as well as space. But space is external to the mind; time enters into our spiritual consciousness, and measures our flow of thought." ”

“ But the study of ordinary, i. e., of complex objects, is necessarily empirical, whereas geometric forms can be at once submitted to scientific generalizations, can therefore at once initiate the child into scientific method. Dr. Hill recommends the study of geometry to be begun at the age of eight. The child upon which my own experiment was performed began the study of geometric elements before she was four. Some details of her education may perhaps be quoted as the best way of illustrating certain abstract principles. ”

“ The child, when just six, began to draw maps from this globe. On a single very large piece of paper would be represented whatever outlines were discoverable at the maximum distance and at a certain aspect of the globe. The latter was then revolved somewhat, the child remaining at the same distance, and a new map outlined as before, and so on until the entire globe had been, in the major outlines, copied by the child. It was reserved for months of future study to fill in the details in proportion to their successive natural, not political, importance. ”

“ 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. ”

“ In considering space we are led to imitate the act of the Divine Intellect, which has geometrized from eternity. Geometry is the earliest and simplest of all possible sciences." The writer proceeds to point out that "the earliest abstraction from the idea of form is that of number, and out of this idea is evolved the earliest of the truly abstract sciences, namely, arithmetic. ”

“ Space conceptions are objective, static; time conceptions, from the beginning subjective, are at first successive, then become progressive, finally causal, dynamic—when the conception of cause arises from consideration of the sum of antecedent events. ”

“ When the child has once learned to handle present existences, he will be prepared to understand the reflections of a past life in language. When he has had some experience in framing complex abstractions, he can then appreciate the complex abstractions of speech. ”

“ President Hill, in his eloquent little book on the "True Order of Studies," emphatically insists on the necessity for a selection of studies which differ widely from the conventional programme. "We awake to consciousness," he observes, "through the fact of motion which reveals to us an outer world, and a universe of space and time in which that world of matter moves. ”

“ Not speech abstractions, the highest conquest of the mind, but the development of the visual conceptions, which are its earliest spontaneous achievement, should be the first object of systematic training. Forms and colors are the elements of all visual impressions ”

“ Deliberate study of the arts of expression, which is equivalent to the study of literature, rhetoric, and style, was reserved until after many years of study of things should have accumulated impressions and ideas which spontaneously sought an outlet. ”

“ It seems to me that for several years no abstract statements should be made to a child, except such as may be, at least schematically, represented by tangible objects, and at every new point of even advanced studies recurrence to such schemas may be usefully made. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ These space and time relations are the earliest objects of distinctly conscious intellection; the first objects concerning which our knowledge takes a scientific form. This was true of the race, and it is true of the individual. Before the child has a clearly intellectual life on any other subjects, it attains a very definite power to distinguish the square, the circle, the oval, the spiral ”