Chapter 18 - Language in childhood
The Montessori Method, 2nd Edition - Restoration
# Chapter 18 - Language in childhood
## [18.1 The physiological importance of graphic language](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+18+-+Language+in+childhood#18.1-the-physiological-importance-of-graphic-language (Link to Montessori.Zone's Translation Base Text "The Montessori Method"))
Graphic language, comprising dictation and reading, contains articulate language in its complete mechanism (auditory channels, central channels, motor channels), and, in the manner of development called forth by my method, is based essentially on articulate language.
Graphic language, therefore, may be considered from two points of view:
* (a) That of the conquest of a new language of eminent social importance which adds itself to the articulate language of the natural man; and this is the cultural significance which is commonly given to graphic language, which is therefore taught in the schools without any consideration of its relation to spoken language, but solely with the intention of offering to the social being a necessary instrument in his relations with his fellows.
* (b) That of the relation between graphic and articulate language and, in this relation, of an eventual possibility of utilizing the written language to perfect the spoken: a new consideration upon which I wish to insist and which gives to graphic language ***a physiological importance**.*
Moreover, as spoken language is at the same time a ***natural function*** of man and an instrument that he utilizes for social ends, so written language may be considered in itself, in its ***formation***, as an organic ***ensemble*** of new mechanisms which are established in the nervous system, and as an instrument which may be utilized for social ends.
In short, it is a question of giving written language not only physiological importance but also a ***period of development*** independent of the high functions that it is destined to perform later.
It seems to me that graphic language bristles with difficulties in its beginning, not only because it has heretofore been taught by irrational methods, but because we have tried to make it perform, as soon as it has been acquired, the high function of teaching ***the written language*** which has been fixed by centuries of perfecting in a civilized people.
Think how irrational have been the methods we have used! We have analyzed the graphic signs rather than the physiological acts necessary to produce the alphabetical signs, and this without considering that ***any graphic sign*** is difficult to achieve because the visual representation of the signs has no hereditary connection with the motor representations necessary for producing them; as, for example, the auditory representations of the word have with the motor mechanism of the articulate language. It is, therefore, always a difficult thing to provoke a stimulative motor action unless we have already established the movement before the visual representation of the sign is made. It is a difficult thing to arouse an activity that shall produce a motion unless that motion shall have been previously established by practice and by the power of habit.
Thus, for example, the analysis of writing into ***little straight lines and curves*** has brought us to present to the child a sign without significance, which therefore does not interest him, and whose representation is incapable of determining a spontaneous motor impulse. The artificial act constituted, therefore, an ***effort*** of the will that resulted in the child in rapid exhaustion exhibited in the form of boredom and suffering. To this effort was added the effort of constituting ***synchronously*** the muscular associations coordinating the movements necessary for holding and manipulating the instrument of writing.
## [18.2 Two periods in the development of language](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+18+-+Language+in+childhood#18.2-two-periods-in-the-development-of-language (Link to Montessori.Zone's Translation Base Text "The Montessori Method"))
All sorts of ***depressing*** feelings accompanied such efforts and conduced to the production of imperfect and erroneous signs which the teachers had to correct, discouraging the child still more with the constant criticism of the error and of the imperfection of the signs traced. Thus, while the child was urged to make an effort, the teacher depressed rather than revived his psychical forces.
Although such a mistaken course was followed, the graphic language, so painfully learned, was nevertheless to be ***immediately*** utilized for social ends; and, still imperfect and immature, was made to do service in the ***syntactical construction of the language***, and in the ideal expression of the superior psychic centers. One must remember that in nature the spoken language is formed gradually; and it is already established in ***words*** when the superior psychic centers use these words in what Kussmaul calls ***dictorium***, in the syntactical grammatical formation of language which is necessary to the expression of complex ideas; that is, in the language of the ***logical mind**.*
In short, the mechanism of language is a necessary antecedent of the higher psychic activities which are to ***utilize it**.*
There are, therefore, two periods in the development of language: a lower one which prepares the nervous channel and the central mechanisms which are to put the sensory channels in relation with the motor channels; and a higher one determined by the higher psychic activities which are ***exteriorized*** using the preformed mechanisms of language.
![](https://digital.library.upenn.edu/women/montessori/method/313-1.gif)
Thus for example in the scheme which Kussmaul gives on the mechanism of articulate language we must, first of all, distinguish a sort of cerebral diastaltic arc (representing the pure mechanism of the word), which is established in the first formation of the spoken language. Let E be the ear, and T the motor organs of speech, taken as a whole and here represented by the tongue, A the auditory center of speech, and M the motor center. The channels EA and MT are peripheral channels, the former centripetal and the latter centrifugal, and the channel AM is the inter-central channel of association.
![](https://digital.library.upenn.edu/women/montessori/method/313-2.gif)
The center A in which reside the auditive images of words may be again subdivided into three, as in the following scheme, viz.: Sound (So), syllables (Sy), and words (W).
That partial centers for sounds and syllables can really be formed, the pathology of language seems to establish, for, in some forms of centro-sensory dysphasia, the patients can pronounce only sounds, or at most sounds and syllables.
Small children, too, are, in the beginning, particularly sensitive to simple sounds of language, with which indeed, and especially with *s*, their mothers caress them and attract their attention; while later the child is sensitive to syllables, with which also the mother caresses him, saying: "***ba, ba, punf, tuf!***"
![](https://digital.library.upenn.edu/women/montessori/method/314-1.gif)
Finally, it is the simple word, dissyllabic in most cases, which attracts the child's attention.
But for the motor centers also the same thing may be repeated; the child utters at the beginning simple or double sounds, such as example ***bl, gl, ch,*** an expression which the mother greets with joy; then distinctly syllabic sounds begin to manifest themselves in the child: ***ga, ba;*** and, finally, the dissyllabic word, usually labial: ***mama**.*
![](https://digital.library.upenn.edu/women/montessori/method/314-2.gif)
We say that the spoken language begins with the child when the word pronounced by him signifies an idea; when for example, sees his mother and recognizes her he says "***mamma;***" and seeing a dog says, "***tettè;***" and wishing to eat says: "***pappa.***"
Thus we consider ***language** begun* when it is established with perception; while the language itself is still, in its psycho-motor mechanism, perfectly rudimentary.
That is when above the diastatic arc where the mechanical formation of the language is still unconscious, the recognition of the word takes place, that is, the word is perceived and associated with the object which it represents, and language is considered to have begun.
On this level, ***later***, language continues the process of perfecting in proportion as the hearing perceives better the component sounds of the words, and the psycho-motor channels become more permeable to articulation.
This is the first stage of spoken language, which has its own beginning and its own development, leading, through the perceptions, to the ***perfecting*** of the primordial mechanism of the language itself; and at this stage precisely is established what we call ***articulate language***, which will later be the means which the adult will have at his disposal to express his own thoughts, and which the adult will have great difficulty in perfecting or correcting when it has once been established: in fact, a high stage of culture sometimes accompanies an imperfect articulate language which prevents the aesthetic expression of one's thought.
The development of articulate language takes place in the period between the age of two and the age of seven: the age of ***perceptions*** in which the attention of the child is spontaneously turned towards external objects, and the memory is particularly tenacious. It is the age also of ***motility*** in which all the psycho-motor channels are becoming permeable and the muscular mechanisms establish themselves. In this period of life by the mysterious bond between the auditory channel and the motor channel of the spoken language, it would seem that the auditory perceptions have the direct power of ***provoking*** the complicated movements of articulate speech which develop instinctively after such stimuli as if awaking from the slumber of heredity. It is well known that it is only at this age that it is possible to acquire all the characteristic modulations of a language which it would be vain to attempt to establish later. The mother tongue alone is well pronounced because it was established in the period of childhood, and the adult who learns to speak a new language must bring to it the imperfections characteristic of the foreigner's speech: only children under the age of seven years learn several languages at the same time can receive and reproduce all the characteristic mannerisms of accent and pronunciation. \`
Thus also the ***defects*** acquired in childhood such as dialectic defects or those established by bad habits, become indelible in the adult.
What develops later, the ***superior*** language, the ***dictorium***, no longer has its origin in the mechanism of language but in the intellectual development which makes use of the mechanical language. As the articulate language develops by the exercise of its mechanism and is enriched by perception, the ***dictorium*** develops with syntax and is enriched by ***intellectual culture**.*
![](https://digital.library.upenn.edu/women/montessori/method/316.gif)
Going back to the scheme of language we see that above the arc which defines the lower language, is established the ***dictorium, D***, from which now come the motor impulses of speech which is established as ***a spoken language*** fit to manifest the ideation of the intelligent man; this language will be enriched little by little by intellectual culture and perfected by the grammatical study of syntax.
Hitherto, as a result of a preconception, it has been believed that written language should enter only into the development of the ***dictorium***, as the suitable means for the acquisition of culture and of permitting grammatical analysis and construction of the language. Since "spoken words have wings" it has been admitted that intellectual culture could only proceed with the aid of a language that was stable, objective, and capable of being analyzed, such as graphic language.
But why, when we acknowledge the graphic language as a precious, nay indispensable, instrument of intellectual education, for the reason that it ***fixes the ideas*** of men and permits their analysis and of their assimilation in books, where they remain indelibly written as an ineffaceable memory of words which are therefore always present and by which we can analyze the syntactical structure of the language, why shall we not acknowledge that it is ***useful*** in the more humble task of ***fixing*** the ***words*** which represent perception and of analyzing their component sounds?
Compelled by a pedagogical prejudice we are unable to separate the idea of a graphic language from that of a function which heretofore we have made it exclusively perform, and it seems to us that by teaching such a language to children still in the age of simple perceptions and of motility we are committing a serious psychological and pedagogical error.
But let us rid ourselves of this prejudice and consider the graphic language in itself, reconstructing its psycho-physiological mechanism. It is far more simple than the psycho-physiological mechanism of the articulate language and is far more directly accessible to education.
***Writing*** especially is surprisingly simple. Let us consider ***dictated*** writing: we have a perfect parallel with spoken language since a *motor* action must correspond with *heard* speech. Here there does not exist, to be sure, the mysterious hereditary relations between the heard speech and the articulate speech; but the movements of writing are far simpler than those necessary to the spoken word, and are performed by large muscles, all external, ***upon which we can directly act***, rendering the motor channels permeable, and establishing psycho-muscular mechanisms.
This indeed is what is done by my method, which ***prepares the movements directly**;* so that the psycho-motor impulse of the heard speech ***finds the motor channels already established*** and is manifested in the act of writing, like an explosion.
The real difficulty is in the ***interpretation of the graphic signs**;* but we must remember that we are in the age of ***perceptions***, where the sensations and the memory, as well as the primitive associations, are involved precisely in the characteristic progress of natural development. Moreover, our children are already prepared by various exercises of the senses, and by methodical construction of ideas and mental associations to perceive the graphic signs; something like a patrimony of perceptive ideas offers material to the language in the process of development. The child who recognizes a triangle and calls it a triangle can recognize a letter *s* and denominate it by the sound ***s***. This is obvious.
![](https://digital.library.upenn.edu/women/montessori/method/318.gif)
Let us not talk of premature teaching; ridding ourselves of prejudices, let us appeal to experience which shows that in reality, children proceed without effort, nay rather with evident manifestations of pleasure to the recognition of graphic signs presented as objects.
And with this premise let us consider the relations between the mechanisms of the two languages.
The child of three or four has already long begun his articulate language according to our scheme. But he finds himself in the period in which ***the mechanism of articulate language is being perfected**;* a period contemporary with that in which he is acquiring the content of language along with the patrimony of perception.
## [18.3 Analysis of speech necessary](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+18+-+Language+in+childhood#18.3-analysis-of-speech-necessary (Link to Montessori.Zone's Translation Base Text "The Montessori Method"))
The child has perhaps not heard perfectly in all their component parts the words which he pronounces, and, if he has heard them perfectly, they may have been pronounced badly, and consequently have left an erroneous auditory perception. It would be well that the child, by exercising the motor channels of articulate language should establish exactly the movements necessary to a perfect articulation, ***before*** the age of easy motor adaptations is passed, and, by the fixation of erroneous mechanisms, the defects become incorrigible.
To this end the ***analysis of speech*** is necessary. As when we wish to perfect the language we first start children with composition and then pass to grammatical study; and when we wish to perfect the style we first teach them to write grammatically and then come to the analysis of style so when we wish to perfect the *speech* it is first necessary that the speech ***exist***, and then it is proper to proceed to its analysis. When, therefore, the child ***speaks***, but before the completion of the development of speech which renders it fixed in mechanisms already established, the speech should be analyzed to perfect it.
Now, as grammar and rhetoric are not possible with the spoken language but demand recourse to the written language which keeps ever before the eye the discourse to be analyzed, so it is with speech.
The analysis of the transient is impossible.
The language must be materialized and made stable. Hence the necessity of the written word or the word represented by graphic signs.
![](https://digital.library.upenn.edu/women/montessori/method/320-1.gif)
The third stage of my method for writing, that is, the composition of speech, is included the ***analysis of the word*** not only into signs but into the component sounds; the signs representing its translation. The child, that is, ***divides*** the heard word which he perceives integrally **as *a word***, knowing also its meanings, into sounds and syllables.
Let me call attention to the following diagram which represents the interrelation of the two mechanisms for writing and for articulate speech.
![](https://digital.library.upenn.edu/women/montessori/method/320-2.gif)
The peripheric channels are indicated by heavy lines; the central channels of association by dotted lines; and those referring to the association concerning the development of the heard speech by light lines.
***E*** ear; ***So*** auditory center of sounds; ***Sy*** auditory center of syllables; ***W*** auditory center of the word; ***M*** motor center of articulate speech; ***T*** external organs of articulate speech (tongue); ***H*** external organs of writing (hand); ***MC*** motor center of writing; ***VC*** visual center of graphic signs; ***V*** organ of vision.
Whereas in the development of spoken language the sound composing the word might be imperfectly perceived, here in the teaching of the graphic sign corresponding to the sound (which teaching consists in presenting to the child a sandpaper letter, naming it ***distinctly*** and making the child *see* it and ***touch*** it), not only is the perception of the heard sound ***clearly*** fixed–separately and clearly but this perception is associated with two others: the centro-motor perception and the centro-visual perception of the written sign.
The triangle ***VC, MC,*** and ***So*** represents the association of three sensations concerning the analysis of speech.
When the letter is presented to the child and he is made to touch and see it, while it is being named, the centripetal channels ***ESo; H, MC, So; V, VC, So*** are acting and when the child is made to name the letter, alone or accompanied by a vowel, the external stimulus acts in ***V*** and passes through the channels ***V, VC, So, M, T; and V, CV, So, Sy, M. T.***
When these channels of the association have been established by presenting visual stimuli in the graphic sign, the corresponding movements of articulate language can be provoked and studied one by one in their defects; while, by maintaining the visual stimulus of the graphic sign which provokes articulation and accompanying it by the auditory stimulus of the corresponding ***sound*** uttered by the teacher, their articulation can be perfected; this articulation is by innate conditions connected with the heard speech; that is, in the course of the pronunciation provoked by the visual stimulus, and during the repetition of the relative movements of the organs of language, the auditory stimulus which is introduced into the exercise contributes to the perfecting of the pronunciation of the isolated or syllabic sounds composing the spoken word.
When later the child writes under dictation, translating into signs the sounds of speech, he analyses the heard speech into its sounds, translating them into graphic movements through channels already rendered permeable by the corresponding muscular sensations.
## [18.4 Defects of language due to education](https://montessori-international.com/s/the-montessori-method/wiki/Chapter+18+-+Language+in+childhood#18.4-defects-of-language-due-to-education (Link to Montessori.Zone's Translation Base Text "The Montessori Method"))
Defects and imperfections of language are in part due to organic causes, consisting of malformations or in pathological alterations of the nervous system; but in part, they are connected with functional defects acquired in the period of the formation of language and consist in an erratic pronunciation of the component sounds of the spoken word. Such errors are acquired by the child who hears words imperfectly pronounced or ***hears bad speech**.* The dialectic accent enters into this category, but there are also vicious habits that make the natural defects of the articulate language of childhood persist in the child, or which provoke him by imitating the defects of language peculiar to the persons who surrounded him in his childhood.
The normal defects of child language are because the complicated muscular agencies of the organs of articulate language do not yet function well and are consequently incapable of reproducing the *sound* which was the sensory stimulus of a certain innate movement. The association of the movements necessary to the articulation of the spoken words is established little by little. The result is a language made of words with sounds that are imperfect and often lacking (whence incomplete words). Such defects are grouped under the name ***bloesitas*** and are especially because the child is not yet capable of directing the movements of his tongue. They comprise chiefly: ***stigmatism*** or imperfect pronunciation of ***s; rhotacism*** or imperfect pronunciation of ***r; lambdacism*** or imperfect pronunciation of ***l; gammacism*** or imperfect pronunciation of ***g; iotacism***, defective pronunciation of the gutturals; ***mogilalia***, imperfect pronunciation of the labials, and according to some authors, as Preyer, mogilalia is made to include also the suppression of the first sound of a word.
Some defects of pronunciation that concern the utterance of the vowel sound, as well as that of the consonant, are because the child ***reproduces perfectly*** sounds imperfectly heard.
In the first case, then, it is a matter of functional insufficiencies of the peripheral motor organ and hence of the nervous channels, and the cause lies in the individual; whereas in the second case the error is caused by the auditory stimulus and the cause lies outside.
These defects often persist, however, attenuated, in the boy and the adult: and produce finally an erroneous language which will later be added in writing orthographical errors, such example as dialectic orthographical errors.
If one considers the charm of human speech one is bound to acknowledge the inferiority of one who does not possess a correct spoken language, and an aesthetic conception in education cannot be imagined unless special care is devoted to perfecting the articulate language. Although the Greeks had transmitted to Rome the art of educating in language, this practice was not resumed by Humanism which cared more for the aesthetics of the environment and the revival of artistic works than for the perfecting of the man.
Today we are just beginning to introduce the practice of correcting by pedagogical methods the serious defects of language, such as stammering; but the idea of ***linguistic gymnastics*** tending to its perfection has not yet penetrated into our schools as a ***universal method*** and as a detail of the great work of the aesthetic perfecting of man.
Some teachers of deaf-mutes and intelligent devotees of orthophony are trying nowadays with small practical success to introduce into the elementary schools the correction of the various forms of ***bloesitas***, as a result of statistical studies which have demonstrated the wide diffusion of such defects among the pupils. The exercises consist essentially of ***silence*** cures which procure calm and repose for the organs of language, and inpatient ***repetition*** of the ***separate*** vowel and consonant ***sounds**;* to these exercises is added also respiratory gymnastics. This is not the place to describe in detail the methods of these exercises which are long and patient and quite out of harmony with the teachings of the school. But in my methods are to be found all exercises for the corrections of language:
* (a) ***Exercises of Silence***, which prepares the nervous channels of language to receive new stimuli perfectly;
* (b) *Lessons* which consist first of the distinct pronunciation by the teacher of ***a few words*** (especially of nouns which must be associated with a concrete idea); by this means clear and perfect ***auditory stimuli*** of language are started, stimuli which are *repeated* by the teacher when the child has conceived the idea of the object represented by the word (recognition of the object); finally of the provocation of articulate language on the part of the child who must repeat *that word alone* aloud, pronouncing its separate sounds;
* (c) ***Exercises in Graphic Language***, which analyzes the sounds of speech and causes them to be repeated separately in several ways: that is, when the child learns the separate letters of the alphabet and when he composes or writes words, repeating their sounds which he translates separately into composed or written speech;
* (d) ***Gymnastic Exercises***, which comprise, as we have seen, both ***respiratory exercises*** and those of ***articulation**.*
I believe that in the schools of the future the conception will disappear which is beginning today of "***correcting in elementary schools***" the defects of language, and will be replaced by the more rational one of ***avoiding them by caring for the development of language*** in the "Children's Houses"; that is, in the very age in which language is being established in the child.
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* [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)