The Montessori Method / Scientific Pedagogy as Applied to Child Education in 'The Children's Houses' with Additions and Revisions by the Author

by Maria Montessori

"This rational analysis of design, from which writing will spring, is so essential in all its parts, that a child who, before being confided to my care, already wrote many of the letters, has taken six days to learn to draw a perpendicular or a horizontal line; he spent fifteen days before imitating a curve and an oblique. Indeed the greater number of my pupils, are for a long time incapable of even imitating the movements of my hand upon the paper, before attempting to draw a line in a determined direction. The most imitative, or the least stupid ones, produce a sign diametrically opposite to that which I show them and all of them confound the points of conjunction of two lines no matter how evident this is. It is true that the thorough knowledge I have given them of lines and of configuration helps them to make the connection which must be established between the plane and the various marks with which they must cover the surface, but in the study rendered necessary by the deficiency of my pupils, the progression in the matter of the vertical, the horizontal, the oblique, and the curve must be determined by the consideration of the difficulty of comprehension and of execution which each offers to a torpid intelligence and to a weak unsteady hand.

"I do not speak here of merely having them perform a difficult thing, since I have them surmount a series of difficulties and for this reason I ask myself if some of these difficulties are not greater and some less, and if they do not grow one from the other, like theorems. Here are the ideas which have guided me in this respect.

"The vertical is a line which the eye and the hand follow directly, going up and down. The horizontal line is not natural to the eye, nor to the hand, which lowers itself and follows a curve (like the horizon from which it has taken its name), starting from the centre and going to the lateral extremity of the plane.

"The oblique line presupposes more complex comparative ideas, and the curve demands such firmness and so many differences in its relation to the plane that we would only lose time in taking up the study of these lines. The most simple line then, is the vertical, and this is how I have given my pupils an idea of it.

"The first geometric formula is this: only straight lines may be drawn from one given point to another.

"Starting from this axiom, which the hand alone can demonstrate, I have fixed two points upon the blackboard and have connected them by means of a vertical. My pupils try to do the same between the dots they have upon their paper, but with some the vertical descends to the right of the point and with others, to the left, to say nothing of those whose hand diverges in all directions. To arrest these various deviations which are often far more defects of the intelligence and of the vision, than of the hand, I have thought it wise to restrict the field of the plane, drawing two vertical lines to left and right of the points which the child is to join by means of a parallel line half way between the two enclosing lines. If these two lines are not enough, I place two rulers vertically upon the paper, which arrest the deviations of the hand absolutely. These material barriers are not, however, useful for very long. We first suppress the rulers and return to the two parallel lines, between which the idiot learns to draw the third line. We then take away one of the guiding lines, and leave, sometimes that on the right, sometimes that on the left, finally taking away this last line and at last, the dots, beginning by erasing the one at the top which indicates the starting point of the line and of the hand. The child thus learns to draw a vertical without material control, without points of comparison.

"The same method, the same difficulty, the same means of direction are used for the straight horizontal lines. If, by chance, these lines begin well, we must await until the child curves them, departing from the centre and proceeding to the extremity as nature commands him, and because of the reason which I have explained. If the two dots do not suffice to sustain the hand, we keep it from deviating by means of the parallel lines or of the rulers.

"Finally, have him trace a horizontal line, and by uniting with it a vertical ruler we form a right angles. The child will begin to understand, in this way, what the vertical and horizontal lines really are, and will see the relation of these two ideas as he traces a figure.

"In the sequence of the development of lines, it would seem that the study of the oblique should immediately follow that of the vertical and the horizontal, but this is not so! The oblique which partakes of the vertical in its inclination, and of the horizontal in its direction, and which partakes of both in its nature (since it is a straight line), presents perhaps, because of its relation to other lines, an idea too complex to be appreciated without preparation."

Thus Séguin goes on through many pages, to speak of the oblique in all directions, which he has his pupils trace between two parallels. He then tells of the four curves which he has them draw to right and left of a vertical and above and below a horizontal, and concludes: "So we find the solution of the problems for which we sought—the vertical line, the horizontal, the oblique, and the four curves, whose union forms the circle, contain all possible lines, all writing.