Scientific Methods As Applied To Child Education In "the Children's Houses"

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" 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 gRometric 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
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