The Montessori Method, 2nd Edition - Restoration # Chapter 15 Intellectual Education > **...To lead the child from the education of the senses to ideas.** > > *Edward Séguin.* ## [15.1 Sense exercises a species of auto-education](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.1-sense-exercises-a-species-of-auto-education (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) The sense exercises constitute a species of auto-education, which, if these exercises are many times repeated, leads to a perfecting of the child's psycho-sensory processes. The directress must intervene to lead the child from sensations to ideas–from the concrete to the abstract, and to the association of ideas. For this, she should use a method tending to isolate the inner attention of the child and to fix it upon the perceptions–as in the first lessons his objective attention was fixed, through isolation, upon single stimuli. The teacher, in other words, when she gives a lesson must seek to limit the field of the child's consciousness to the object of the lesson, as, for example, during sense education, she isolated the sense which she wished the child to exercise. For this, knowledge of a special technique is necessary. The educator must, "***to the greatest possible extent, limit his intervention; yet he must not allow the child to weary himself in an undue effort of auto-education.***" It is here, that the factor of individual limitation and differing degrees of perception are most keenly felt in the teacher. In other words, in the quality of this intervention lies the art which makes up the individuality of the teacher. A definite and undoubted part of the teacher's work is that of teaching an exact nomenclature. She should, in most cases, pronounce the necessary names and adjectives without adding anything further. These words she should pronounce distinctly, and in a clear strong voice, so that the various sounds composing the word may be distinctly and plainly perceived by the child. So, for example, touching the smooth and rough cards in the first tactile exercise, she should say, "This is smooth. This is rough," repeating the words with varying modulations of the voice, always letting the tones be clear and the enunciation very distinct. "Smooth, smooth, smooth. Rough, rough, rough." In the same way, when treating the sensations of heat and cold, she must say, "This is cold." "This is hot." "This is ice-cold." "This is tepid." She may then begin to use the generic terms, "heat," "more heat," "less heat," etc. ## [15.2 Importance of an exact nomenclature, and how to teach it](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.2-importance-of-an-exact-nomenclature%2C-and-how-to-teach-it (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) * ***First**.* "The lessons in nomenclature must consist simply in provoking the association of the name with the object, or with the abstract idea which the name represents." Thus the ***object*** and the ***name*** must be united when they are received by the child's mind, and this makes it most necessary that no other word besides the name be spoken. * ***Second**.* The teacher must always ***test*** whether or not her lesson has attained the end she had in view, and her tests must be made to come within the restricted field of consciousness, provoked by the lesson on nomenclature. The first test will be to find whether the name is still associated in the child's mind with the object. She must allow the necessary time to elapse, letting a short period of silence intervene between the lesson and the test. Then she may ask the child, pronouncing slowly and very clearly the name or the adjective she has taught: "**Which is *smooth?* Which is *rough?***" The child will point to the object with his finger, and the teacher will know that he has made the desired association. But if he has not done this, that is, if he makes a mistake, ***she must not correct him***, but must suspend her lesson, to take it up again another day. Indeed, why correct him? If the child has not succeeded in associating the name with the object, the only way in which to succeed would be to ***repeat*** both the action of the sense stimuli and the ***name***; in other words, to repeat the lesson. But when the child has failed we should know that he was not at that instant ready for the psychic association which we wished to provoke in him, and we must therefore choose another moment. If we should say, in correcting the child "No, you have made a mistake," all these words, which, being in the form of reproof, would strike him more forcibly than others (such as smooth or rough), would remain in the mind of the child, retarding the learning of the names. On the contrary, the ***silence*** which follows the error leaves the field of consciousness clear, and the next lesson may successfully follow the first. In fact, by revealing the error we may lead the child to make an undue ***effort*** to remember, or we may discourage him, and it is our duty to avoid as much as possible all unnatural efforts and all depression. * ***Third**.* If the child has not committed any error, the teacher may provoke the motor activity corresponding to the idea of the object: that is, to the ***pronunciation of the name.*** She may ask him, "What is this?" and the child should respond, "Smooth." The teacher may then interrupt, teaching him how to pronounce the word correctly and distinctly, first, drawing a deep breath and, then, saying in a rather loud voice, "Smooth." When he does this the teacher may note his particular speech defect or the special form of baby talk to which he may be addicted. Regarding the ***generalization*** of the ideas received, and by that I mean the application of these ideas to his environment, I do not advise any lessons of this sort for a certain length of time, even for some months. There will be children who, after having touched a few times the kinds of stuff, or merely the smooth and rough cards, ***will quite spontaneously touch the various surfaces about them***, repeating "Smooth! Rough! It is velvet! etc." In dealing with normal children, we must ***await*** this spontaneous investigation of the surroundings, or, as I like to call it, this ***voluntary explosion*** of the exploring spirit. In such cases, the children experience joy at each ***fresh discovery**.* They are conscious of a sense of dignity and satisfaction which encourages them to seek new sensations from their environment and to make themselves spontaneous ***observers**.* The teacher should ***watch*** with the most solicitous care to see when and how the child arrives at this generalization of ideas. For example, one of our little four-year-olds while running about in the court one day suddenly stood still and cried out, "Oh! the sky is blue!" and stood for some time looking up into the blue expanse of the sky. ## [15.3 Spontaneous progress of the child the greatest triumph of Scientific Pedagogy](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.3-spontaneous-progress-of-the-child-the-greatest-triumph-of-scientific-pedagogy (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) One day, when I entered one of the "Children's Houses," five or six little ones gathered quietly about me and began caressing, lightly, my hands, and my clothing, saying, "It is smooth." "It is velvet." "This is rough." Several others came near and began with serious and intent faces to repeat the same words, touching me as they did so. The directress wished to interfere to release me, but I signed to her to be quiet, and I did not move, but remained silent, admiring this spontaneous intellectual activity of my little ones. The greatest triumph of our educational method should always be this: ***to bring about the spontaneous progress of the child**.* One day, a little boy, following one of our exercises in design, had chosen to fill in with colored pencils the outline of a tree. To color the trunk he laid hold upon a red crayon. The teacher wished to interfere, saying, "Do you think trees have red trunks?" I held her back and allowed the child to color the tree red. This design was precious to us; it showed that the child was not yet an observer of his surroundings. ***My way of treating this was to encourage the child to make use of the games for the chromatic sense**.* He went daily into the garden with the other children, and could at any time see the tree trunks. When the sense exercises should have succeeded in attracting the child's spontaneous attention to colors about him, then, in some ***happy moment*** he would become aware that the tree trunks were not red, just as the other child during his play had become conscious of the fact that the sky was blue. In fact, the teacher continued to give the child outlines of trees to fill in. He one day chose a brown pencil with which to color the trunk, and made the branches and leaves green. Later, he made the branches brown, also, using green only for the leaves. Thus we have ***the test*** the child's intellectual progress. We can not create observers by saying, "***observe***," but by giving them the power and the means for this observation, and these means are procured through education of the senses. Once we have ***aroused*** such activity, auto-education is assured, for refined well-trained senses lead us to a closer observation of the environment, and this, with its infinite variety, attracts the attention and continues the psycho-sensory education. If, on the other hand, in this matter of sense education we single out definite concepts of the quality of certain objects, these very objects become associated with, or a part of, the training, which is in this way limited to those concepts taken and recorded. So the sense training remains unfruitful. When, for example, a teacher has given in the old way a lesson on the names of the colors, she has imparted an idea concerning that particular ***quality***, but she has not educated the chromatic sense. The child will superficially know these colors, forgetting them from time to time; and at best his appreciation of them will lie within the limits prescribed by the teacher. When, therefore, the teacher of the old methods shall have provoked the generalization of the idea, saying, for example, "What is the color of this flower?" "of this ribbon?" the attention of the child will in all probability remain torpidly fixed upon the examples suggested by her. We may liken the child to a clock and may say that with the old-time way it is very much as if we were to hold the wheels of the clock quiet and move the hands about the clock face with our fingers. The hands will continue to circle the dial just so long as we apply, through our fingers, the necessary motor force. Even so, is it with that sort of culture which is limited to the work which the teacher does with the child? The new method, instead, may be compared to the process of winding, which sets the entire mechanism in motion. This motion is in direct relation to the machine, and not with the work of winding. So the spontaneous psychic development of the child continues indefinitely and is in direct relation to the psychic potentiality of the child himself, and not with the work of the teacher. The movement or the ***spontaneous psychic activity*** starts in our case from the education of the senses and is maintained by observing intelligence. Thus, for example, the hunting dog receives his ability, not from the education given by his master, but from the ***special acuteness*** of his senses; and as soon as this physiological quality is applied to the right environment, the ***exercise of hunting***, the increasing refinement of the sense perceptions, gives the dog the pleasure and then the passion for the chase. The same is true of the pianist who, refining at the same time his musical sense and the agility of his hand, comes to love more and more to draw new harmonies from the instrument. This double perfection proceeds until at last the pianist is launched upon a course that will be limited only by the personality which lies within him. Now a student of physics may know all the laws, of harmony which form a part of his scientific culture, and yet he may not know how to follow a most simple musical composition. His culture, however vast, will be bound by the definite limits of his science. Our educational aim with very young children must be to ***aid the spontaneous development of the mental, spiritual, and physical personality***, and not to make the child a cultured individual in the commonly accepted sense of the term. So, after we have offered to the child such didactic material as is adapted to provoke the development of his senses, we must wait until the activity known as observation develops. And herein lies the ***art of the educator***; in knowing how to measure the action by which we help the young child's personality to develop. To one whose attitude is right, little children soon reveal ***profound individual differences*** which call for very different kinds of help from the teacher. Some of them require almost no intervention on her part, while others demand actual ***teaching**.* It is necessary, therefore, that the teaching shall be rigorously guided by the principle of limiting to the greatest possible point the active intervention of the educator. Here are some games and problems which we have used effectively in trying to follow this principle. ## [15.4 Games of the blind](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.4-games-of-the-blind (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) The Games of the Blind are used for the most part as exercises in general sensibility as follows: ***The Stuff**.* We have in our didactic material a pretty little chest composed of drawers within which are arranged rectangular pieces of stuff in great variety. There are velvet, satin, silk, cotton, linen, etc. We have the child touch each of these pieces, teaching the appropriate nomenclature and adding something regarding the quality, such as coarse, fine, and soft. Then, we call the child and seat him at one of the tables where he can be seen by his companions, blindfold him, and offer him the stuff one by one. He touches them, smooths them, crushes them between his fingers, and decides, "It is velvet, It is fine linen, It is rough cloth," etc. This exercise provokes general interest. When we offer the child some unexpected foreign object, such as example, a sheet of paper, or a veil, the little assembly trembles as it awaits his response. ***Weight**.* We place the child in the same position, call his attention to the tablets used for the education of the sense of weight, have him notice again the already well-known differences in weight, and then tell him to put all the dark tablets, which are the heavier ones, at the right, and all the light ones, which are the lighter, to the left. We then blindfold him and he proceeds to the game, taking each time two tablets. Sometimes he takes two of the same color, sometimes two of different colors, but in a position opposite to that in which he must arrange them on his desk. These exercises are most exciting; when, for example, the child has in his hands two dark tablets and changes them from one hand to the other uncertain, and finally places them together on the right, the children watch in a state of intense eagerness, and a great sigh often expresses their final relief. The shouts of the audience when the entire game is followed without an error give the impression that their little friend sees *with his hands* the colors of the tablets. ***Dimension and Form**.* We use games similar to the preceding one, having the child distinguish between different coins, the cubes and bricks of Froebel, and dry seeds, such as beans and peas. But such games never awaken the intense interest aroused by the preceding ones. They are, however, useful and serve to associate with the various objects those qualities peculiar to them, and also to fix the nomenclature. ## [15.5 Application of the visual sense to the observation of the environment](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.5-application-of-the-visual-sense-to-the-observation-of-the-environment (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) ***Nomenclature**.* This is one of the most important phases of education. Indeed, nomenclature prepares for ***exactness*** in the use of language which is not always met within our schools. Many children, for example, use interchangeably the words thick and big, long and high. With the methods already described, the teacher may easily establish, utilizing the didactic material, ideas that are very exact and clear, and may associate the proper word with these ideas. ## [15.6 Method of using didactic material: dimensions, form, design](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.6-method-of-using-didactic-material%3A-dimensions%2C-form%2C-design (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) ***Dimensions***. The directress, after the child has played for a long time with the three sets of solid insets and has acquired security in the performance of the exercise, takes out all the cylinders of equal height and places them in a horizontal position on the table, one beside the other. Then she selects the two extremes, saying, "This is the ***thickest***, This is the ***thinnest***." She places them side by side so that the comparison may be more marked, and then taking them by the little button, she compares the bases, calling attention to the great difference. She then places them again beside each other in a vertical position to show that they are equal in height, and repeats several times, "thick–thin." Having done this, she should follow it with the test, asking, "Give me the thickest, Give me the thinnest," and finally she should proceed to the test of nomenclature, asking, "What is this?" In the lessons which follow this, the directress may take away the two extreme pieces and may repeat the lesson with the two pieces remaining at the extremities, and so on until she has used all the pieces. She may then take these up at random, saying, "Give me one a little thicker than this one," or "Give me one a little thinner than this one." With the second set of solid insets, she proceeds in the same way. Here she stands the pieces upright, as each one has a base sufficiently broad to maintain it in this position, saying, "This is the highest" and "This is the lowest." Then place the two extreme pieces side by side she may take them out of the line and compare the bases, showing that they are equal. From the extremes she may proceed as before, selecting each time the two remaining pieces most strongly contrasted. With the third solid inset, the directress, when she has arranged the pieces in gradation, calls the child's attention to the first one, saying, "This is the largest," and to the last one, saying, "This is the smallest." Then she places them side by side and observes how they differ both in height and in base. She then proceeds in the same way as in the other two exercises. Similar lessons may be given with the series of graduated prisms, rods, and cubes. The prisms are ***thick*** and ***thin*** and of equal ***length***. The rods are ***long*** and ***short*** and of equal ***thickness***. The cubes are *big* and *little* and differ in size and in height. The application of these ideas to the environment will come most easily when we measure the children with the anthropometer. They will begin among themselves to make comparisons, saying, "I am taller, you are thicker." These comparisons are also made when the children hold out their little hands to show that they are clean, and the directress stretches hers out also, to show that she, too, has clean hands. Often the contrast between the dimensions of the hands calls forth laughter. The children make a perfect game of measuring themselves. They stand side by side; they look at each other; they decide. Often they place themselves beside grown persons and observe with curiosity and interest the greatest height difference. ***Form***. When the child shows that he can with security distinguish the forms of the plane geometric insets, the directress may begin the lessons in nomenclature. She should begin with two strongly-contrasted forms, the square, and the circle, and should follow the usual method, using the three periods of Séguin. We do not teach all the names relative to the geometric figures, giving only those of the most familiar forms, such as square, circle, rectangle, triangle, and oval. We now call attention to the fact that there are ***rectangles that are narrow and long***, and others which are ***broad and short***, while the ***squares*** are equal on all sides and can be only big and little. These things are most easily shown with the insets, for, though we turn the square about, it still enters its frame, while the rectangle, if placed across the opening, will not enter. The child is much interested in this exercise, for which we arrange in the frame a square and a series of rectangles, having the longest side equal to the side of the square, the other side gradually decreasing in the five pieces. In the same way, we proceed to show the difference between the oval, the ellipse, and the circle. The circle enters no matter how it is placed, or turned about; the ellipse does not enter when placed transversely, but if placed lengthwise will enter even if turned upside down. The oval, however, not only cannot enter the frame if placed transversely, but not even when turned upside down; it must be placed with the *large* curve toward the large part of the opening, and with the ***narrow*** curve toward the ***narrow*** portion of the opening. The circles, ***big*** and ***little***, enter their frames no matter how they are turned about. I do not reveal the difference between the oval and the ellipse until a very late stage of the child's education, and then not to all children, but only to those who show a special interest in the forms by choosing the game often, or by asking about the differences. I prefer that such differences should be recognized later by the child, spontaneously, perhaps in elementary school. It seems to many persons that in teaching these forms we are teaching ***geometry*** and that this is premature in schools for such young children. Others feel that, if we wish to present geometric forms, we should use ***solids***, as being more concrete. I feel that I should say a word here to combat such prejudices. To ***observe*** a geometric form is not to ***analyze*** it, and in the analysis, geometry begins. When, for example, we speak to the child about sides and angles and explain these to him, even though with objective methods, as Froebel advocates (for example, the square has four sides and can be constructed with four sticks of equal length), then indeed we do enter the field of geometry, and I believe that little children are too immature for these steps. But the ***observation of the form*** cannot be too advanced for a child at this age. The plane of the table at which the child sits while eating his supper is probably a rectangle; the plate which contains his food is a circle, and we certainly do not consider that the child is too ***immature*** to be allowed to look at the table and the plate. The insets which we present simply call attention to a given ***form***. As to the name, it is analogous to other names by which the child learns to call things. Why should we consider it premature to teach the child the words ***circle, square, and oval,*** when in his home he repeatedly hears the word ***round*** used in connection with plates, etc.? He will hear his parents speak of the ***square*** table, the ***oval*** table, etc., and these words in common use will remain for a long time ***confused*** in his mind and in his speech if we do not interpose such help as that we give in the teaching of forms. We should reflect upon the fact that many times a child, left to himself, makes an undue effort to comprehend the language of the adults and the meaning of the things about him. Opportune and rational instruction ***prevents*** such an effort, and therefore does not ***weary***, but ***relieves***, the child and satisfies his desire for knowledge. Indeed, he shows his contentment through various expressions of pleasure. At the same time, his attention is called to the word which, if he is allowed to pronounce it badly, develops in him an imperfect use of language. This often arises from an effort on his part to imitate the careless speech of persons about him, while the teacher, by pronouncing clearly the word referring to the object which arouses the child's curiosity, prevents such effort and such imperfections. Here, also, we face a widespread prejudice; namely, the belief that the child left to himself gives absolute repose to his mind. If this were so he would remain a stranger to the world, and, instead, we see him, little by little, spontaneously conquer various ideas and words. He is a traveler through life, who observes the new things among which he journeys, and who tries to understand the unknown tongue spoken by those about him. Indeed, he makes a great and ***voluntary effort*** to understand and imitate. The instruction given to little children should be so directed as to ***lessen this expenditure*** of poorly directed effort, converting it instead into the enjoyment of conquest made easy and infinitely broadened. We are ***the guides*** of these travelers just entering the great world of human thought. We should see to it that we are intelligent and cultured guides, not losing ourselves in vain discourse, but illustrating briefly and concisely the work of art in which the traveler shows himself interested, and we should then respectfully allow him to observe it as long as he wishes to. It is our privilege to lead him to observe the most important and the most beautiful things of life in such a way that he does not lose energy and time in useless things but shall find pleasure and satisfaction throughout his pilgrimage. I have already referred to the prejudice that it is more suitable to present the geometric forms to the child in the ***solid*** rather than in the ***plane***, giving him, for example, the ***cube***, the ***sphere***, and the ***prism***. Let us put aside the physiological side of the question showing that the visual recognition of the solid figure is more complex than that of the plane, and let us view the question only from the more purely pedagogical standpoint of ***practical life***. The greater number of objects which we look upon every day present more nearly the aspect of our plane geometric insets. In fact, doors, window-frames, framed pictures, and the wooden or marble top of a table, are indeed ***solid*** objects, but with one of the dimensions greatly reduced, and with the two dimensions determining the form of the plane surface made most evident. When the plane form prevails, we say that the window is rectangular, the picture frame oval, this table square, etc. ***Solids having a determined form prevailing in the plane surface*** are almost the only ones that come to our notice. And such solids are clearly represented by our ***plane geometric insets***. The child will ***very often*** recognize in his environment forms that he has learned in this way, but he will rarely recognize the ***solid geometric forms***. That the table leg is a prism, or a truncated cone, or an elongated cylinder, will come to his knowledge long after he has observed that the top of the table upon which he places things is rectangular. We do not, therefore, speak of the fact of recognizing that a house is a prism or a cube. Indeed, the pure solid geometric forms never exist in the ordinary objects about us; these present, instead, a ***combination of forms***. So, putting aside the difficulty of taking in at a glance the complex form of a house, the child recognizes it, not as an ***identity*** of form, but as an ***analogy***. He will, however, see the plane geometric forms perfectly represented in windows and doors, and in the faces of many solid objects in use at home. Thus the knowledge of the forms given to him in the plane geometric insets will be for him a species of magic ***key***. opening the external world, and making him feel that he knows its secrets. I was walking one day upon Pincian Hill with a boy from the elementary school. He studied geometric design and understood the analysis of plane geometric figures. As we reached the highest terrace from which we could see the Piazza del Popolo with the city stretching away behind it, I stretched out my hand saying, "Look, all the works of man are a great mass of geometric figures;" and, indeed, rectangles, ovals, triangles, and semicircles, perforated, or ornamented, in a hundred different ways the grey rectangular façades of the various buildings. Such uniformity in such an expanse of buildings seemed to prove the ***limitation*** of human intelligence, while in an adjoining garden plot the shrubs and flowers spoke eloquently of the infinite variety of forms in nature. The boy had never made these observations; he had studied the angles, the sides, and the construction of outlined geometric figures, but without thinking beyond this, and feeling only annoyance at this arid work. At first, he laughed at the idea of man's massing geometric figures together, then he became interested, looked long at the buildings before him, and an expression of lively and thoughtful interest came into his face. To the right of the Ponte, Margherita was a factory building in the process of construction, and its steel framework delineated a series of rectangles. "What tedious work!" said the boy, alluding to the workmen. And, then, as we drew near the garden, and stood for a moment in silence admiring the grass and the flowers which sprang so freely from the earth, "It is beautiful!" he said. But that word "beautiful" referred to the inner awakening of his own soul. This experience made me think that in the observation of the plane geometric forms, and in that of the plants which they saw growing in their own little gardens, there existed for the children precious sources of spiritual as well as intellectual education. For this reason, I have wished to make my work broad, leading the child, not only to observe the forms about him, but to distinguish the work of man from that of nature, and to appreciate the fruits of human labor. * (*a*) ***Free Design***. I give the child a sheet of white paper and a pencil, telling him that he may draw whatever he wishes to. Such drawings have long been of interest to experimental psychologists. Their importance lies in the fact that they reveal the ***capacity*** of the child for observing, and also show his individual tendencies. Generally, the first drawings are unformed and confused, and the teacher should ask the child ***what he wished to draw*** and should write it underneath the design so that it may be a record. Little by little, the drawings become more intelligible and verily reveal the progress that the child makes in the observation of the forms about him. Often the most minute details of an object have been observed and recorded in the crude sketch. And, since the child draws what he wishes, he reveals to us which are the objects that most strongly attract his attention. * (*b*) ***Design Consisting of the Filling in Outlined Figures***. These designs are most important as they constitute "the preparation for writing." They do for the color sense what ***free design*** does for the sense of ***form***. In other words, they reveal the capacity of the child in ***the matter of observation of colors***, as the free design showed us the extent to which he was an observer of form in the objects surrounding him. I shall speak more fully of this work in the chapter on ***writing***. The exercises consist in filling in with colored pencil, certain outlines drawn in black. These outlines present the simple geometric figures and various objects with which the child is familiar in the schoolroom, the home, and the garden. The child must ***select*** his color, and in doing so he shows us whether he has observed the colors of the things surrounding him. ## [15.7 Free plastic work](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.7-free-plastic-work (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) These exercises are analogous to those in free design and in the filling in of figures with colored pencils. Here the child makes whatever he wishes with ***clay***; that is, he models those objects which he remembers most distinctly and which have impressed him most deeply. We give the child a wooden tray containing a piece of clay, and then we await his work. We possess some very remarkable pieces of clay work done by our little ones. Some of them reproduce, with a surprising minuteness of detail, objects that they have seen. And what is most surprising, these models often record not only the form but even the ***dimensions*** of the objects which the child handled in school. Many little ones model the objects which they have seen at home, especially kitchen furniture, water jugs, pots, and pans. Sometimes, we are shown a simple cradle containing a baby brother or sister. At first, it is necessary to place written descriptions upon these objects, as it is necessary to do with the free design. Later on, however, the models are easily recognizable, and the children learn to reproduce the geometric solids. These clay models are undoubtedly very valuable material for the teacher, and make clear many individual differences, thus helping her to understand her children more fully. In our method, they are also valuable as psychological manifestations of development according to age. Such designs are precious guides also for the teacher in the matter of her intervention in the child's education. The children who, in this work reveal themselves as observers, will probably become spontaneous observers of all the world about them and maybe led toward such a goal by the indirect help of exercises tending to fix and make more exact the various sensations and ideas. These children will also be those who arrive most quickly at the act of ***spontaneous writing***. Those whose clay work remains unformed and indefinite will probably need the direct revelation of the directress, who will need to call their attention in some material manner to the objects around them. ## [15.8 Geometric Analysis of Figures: Sides, Angles, Centre, Base](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.8-geometric-analysis-of-figures%3A-sides%2C-angles%2C-centre%2C-base (Link to Montessori.Zone's Translation Base Text "The Montessori Method")) The geometric analysis of figures is not adapted to very young children. I have tried a means for the ***introduction*** of such analysis, limiting this work to the *rectangle* and making use of a game that includes the analysis without fixing the attention of the child upon it. This game presents the concept most clearly. The ***rectangle*** of which I make use is the plane of one of the children's tables, and the game consists in laying the table for a meal. I have in each of the "Children's Houses" a collection of toy table-furnishings, such as may be found in any toy store. Among these are dinner plates, soup plates, soup-tureen, saltcellars, glasses, decanters, little knives, forks, spoons, etc. I have them lay the table for six, putting ***two places*** on each of the longer sides, and one place on each of the shorter sides. One of the children takes the objects and places them as I indicate. I tell him to place the soup tureen in the ***center*** of the table; this napkin in a ***corner***. "Place this plate in the center of the short ***side***." Then I have the child look at the table, and I say, "Something is lacking in this ***corner***. We want another glass on this *side*. Now let us see if we have everything properly placed on the two longer sides. Is everything ready on the two shorter sides? Is there anything lacking in the four corners?" I do not believe that we may proceed to any more complex analysis than this before the age of six years, for I believe that the child should one day take up one of the plane insets and ***spontaneously*** begin to count the sides and the angles. Certainly, if we taught them such ideas they would be able to learn, but it would be mere learning of formulae, and not applied experience. ## [15.9 Exercises in the Chromatic Sense](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education#15.9-exercises-in-the-chromatic-sense) I have already indicated what color exercises we follow. Here I wish to indicate more definitely the succession of these exercises and to describe them more fully. ***Designs and Pictures***. We have prepared some outline drawings which the children are to fill in with colored pencil, and, later on, with a brush, preparing for themselves the water-color tints which they will use. The first designs are of flowers, butterflies, trees, and animals, and we then pass to simple landscapes containing grass, sky, houses, and human figures. These designs help us in our study of the natural development of the child as an observer of his surroundings that is, regarding color. The children ***select the colors*** and are left entirely free in their work. If, for example, they color a chicken red or a cow green, this shows that they have not yet become observers. But I have already spoken of this in the general discussion of the method. These designs also reveal the effect of the education of the chromatic sense. As the child selects delicate and harmonious tints or strong and contrasting ones, we can judge the progress he has made in the refinement of his color sense. The fact that the child must ***remember*** the color of the objects represented in the design encourages him to observe those things which are about him. And then, too, he wishes to be able to fill in more difficult designs. Only those children who know how to keep the color ***within*** the outline and to reproduce the ***right colors*** may proceed to the more ambitious work. These designs are very easy, and often very effective, sometimes displaying real artistic work. The directress of the school in Mexico, who studied for a long time with me, sent me two designs; one representing a cliff in which the stones were colored most harmoniously in light violet and shades of brown, trees in two shades of green, and the sky a soft blue. The other represented a horse with a chestnut coat and black mane and tail. > ##### **The License of this page:** > > This page is part of the “**Montessori Restoration and Translation Project**”.\ > Please [support](https://ko-fi.com/montessori) our “**All-Inclusive Montessori Education for All 0-100+ Worldwide**” initiative. We create open, free, and affordable resources available for everybody interested in Montessori Education. We transform people and environments to be authentic Montessori worldwide. Thank You! > > [](http://creativecommons.org/licenses/by-nc-sa/4.0/) > > **License:** This work with all its restoration edits and translations is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/). > > Check out the **Page History** of each wiki page in the right column to learn more about all contributors and edits, restorations, and translations done on this page. > > [Contributions](https://ko-fi.com/montessori) and [Sponsors](https://ko-fi.com/montessori) are welcome and very appreciated! * [The Montessori Method, 2nd Edition](https://montessori-international.com/s/the-montessori-method/wiki/+Chapter+Index+-+The+Montessori+Method%2C+2nd+Edition+-+Restoration+-+Open+Library#the-montessori-method%2C-2nd-edition---restoration---open-library "The Montessori Method on Montessori Zone - English Language") - English Restoration - [Archive.Org](https://archive.org/details/montessorimethod00montuoft/ "The Montessori Method on Aechive.Org") - [Open Library](https://openlibrary.org/books/OL7089223M/The_Montessori_method "The Montessori Method on Open Library") * [Chapter Index](https://montessori-international.com/s/the-montessori-method/wiki/+Chapter+Index+-+The+Montessori+Method%2C+2nd+Edition+-+Restoration+-+Open+Library) * [Chapter 00 - Dedication, Acknowledgements, Preface to the American Edition, Introduction](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+00+-+Dedication%2C+Acknowledgements%2C+Preface+to+the+American+Edition%2C+Introduction) * [Chapter 01 - A critical consideration of the new pedagogy in its relation to modern science](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+01+-+A+critical+consideration+of+the+new+pedagogy+in+its+relation+to+modern+science) * [Chapter 02 - History of Methods](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+02+-+History+of+Methods) * [Chapter 03 - Inaugural address delivered on the occasion of the opening of one of the “Children’s Houses”](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+03+-+Inaugural+address+delivered+on+the+occasion+of+the+opening+of+one+of+the+%E2%80%9CChildren%E2%80%99s+Houses%E2%80%9D) * [Chapter 04 - Pedagogical Methods used in the “Children’s Houses”](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+04+-+Pedagogical+Methods+used+in+the+%E2%80%9CChildren%E2%80%99s+Houses%E2%80%9D) * [Chapter 05 - Discipline](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+05+-+Discipline) * [Chapter 06 - How the lesson should be given](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+06+-+How+the+lesson+should+be+given) * [Chapter 07 - Exercises for Practical Life](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+07+-+Exercises+for+Practical+Life) * [Chapter 08 - Reflection the Child’s diet](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+08+-+Reflection+the+Child%E2%80%99s+diet) * [Chapter 09 - Muscular education gymnastics](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+09+-+Muscular+education+gymnastics) * [Chapter 10 - Nature in education agricultural labor: Culture of plants and animals](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+10+-+Nature+in+education+agricultural+labor%3A+Culture+of+plants+and+animals) * [Chapter 11 - Manual labor the potter’s art, and building](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+11+-+Manual+labor+the+potter%E2%80%99s+art%2C+and+building) * [Chapter 12 - Education of the senses](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+12+-+Education+of+the+senses) * [Chapter 13 - Education of the senses and illustrations of the didactic material: General sensibility: The tactile, thermic, basic, and stereo gnostic senses](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+13+-+Education+of+the+senses+and+illustrations+of+the+didactic+material%3A+General+sensibility%3A+The+tactile%2C+thermic%2C+basic%2C+and+stereo+gnostic+senses) * [Chapter 14 - General notes on the education of the senses](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+14+-+General+notes+on+the+education+of+the+senses) * [Chapter 15 - Intellectual education](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+15+-+Intellectual+education) * [Chapter 16 - Method for the teaching of reading and writing](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+16+-+Method+for+the+teaching+of+reading+and+writing) * [Chapter 17 - Description of the method and didactic material used](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+17+-+Description+of+the+method+and+didactic+material+used) * [Chapter 18 - Language in childhood](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+18+-+Language+in+childhood) * [Chapter 19 - Teaching of numeration: Introduction to arithmetic](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+19+-+Teaching+of+numeration%3A+Introduction+to+arithmetic) * [Chapter 20 - Sequence of exercise](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+20+-+Sequence+of+exercise) * [Chapter 21 - General review of discipline](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+21+-+General+review+of+discipline) * [Chapter 22 - Conclusions and impressions](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+22+-+Conclusions+and+impressions) * [Chapter 23 - Illustrations](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+23+-+Illustrations)