has been taught on the theory that since all pictorial representation is a matter of combining straight and curved lines, the simplest procedure is to have the pupil acquire the ability first to draw straight lines in various positions (horizontal, perpendicular, diagonals at various angles), then typical curves; and finally, to combine straight and curved lines in various permutations to construct actual pictures. This seemed to give the ideal "logical" method, beginning with analysis into elements, and then proceeding in regular order to more and more complex syntheses, each element being defined when used, and thereby clearly understood.
Formal method Even when this method in its extreme form is not followed, few schools (especially of the middle or upper elementary grades) are free from an exaggerated attention to forms supposedly employed by the pupil if he gets his result logically. It is thought that there are certain steps arranged in a certain order, which express preëminently an understanding of the subject, and the pupil is made to "analyze" his procedure into these steps, i.e. to learn a certain routine formula of statement. While this method is usually at its height in grammar and arithmetic, it invades also history and even literature, which are then reduced, under plea of intellectual training, to "outlines," diagrams, and schemes of division and subdivision. In memorizing this simulated cut and dried copy of the logic of an adult, the child generally is induced to stultify his own subtle and vital logical movement. The adoption by teachers of this misconception of logical method has probably done more than anything else to bring pedagogy into disrepute; for to many persons "pedagogy" means precisely a set of mechanical, self-conscious devices for replacing by some
