The stick of course is to be regarded in its relation to what comes before and after it,—as the embodied edge of the cube, as the tablet was its embodied face. The child should at last identify his stick, the embodiment of the straight line, with the axis of the sphere, the edge of the cube, and the side of the square.[67] The sticks and rings are, properly speaking, one gift, contrasting the curved and straight lines.
Method and Manner of Lessons.
Although the stick exercises should make their appearance at least once every week after their introduction, they may always be varied by stories, and when occasionally connected with other objects, cut from paper to illustrate some point, are among the pleasantest and most fruitful exercises of the kindergarten.
The sticks may be used for teaching number and elementary geometry, both in the kindergarten and school, or for reviewing and fixing knowledge already gained in these directions, for practice in the elements of designing, for giving a correct idea of outlines of familiar objects, and should constantly serve as an introduction to drawing and sewing lessons, to which they are the natural prelude.
They should be used strictly after the manner of the other gifts, beginning with careful dictations, in which the various positions of one stick should be exhausted before proceeding to a greater number, with coöperative work, and with free invention. These exercises and original designs may be put into permanent form in parquetry, which is furnished for this gift in the various colored papers, as well as for the tablets. The inventions may also be transferred to paper by drawing, and to card-board by sewing.
The exercises may continue from the various simple positions which one stick may assume to really complex dictations requiring from fifteen to twenty-five sticks, and introducing many difficult positions and outlines of new geometrical figures.
Forms of Knowledge and Number Work.
When we consider that the length of the sticks varies from one to six inches, and that the number given to the child is limited only by his capacity for using them successfully, we can see that the outlines of all the rectilinear plane figures can easily be made by their use. Of course in these exercises there must be a great deal of incidental arithmetic, but the gift may also be used for definite number work, and is far better adapted to this purpose than any other in the series, since it presents a number of separate units which may be grouped or combined to suit any simple arithmetical process. Representing the line as it does, it has less bodily substance than any previous gift, and hence comes nearest to the numerical symbols, as the next step to using a line would obviously be making one. It also offers very much the same materials for calculation as were used by the race in its childhood, and hence fits in with the inherited instincts of the undeveloped human being.[68]
Who has not seen him arranging twigs and branches in his play, counting them over and over or simulating the process, and delighting to divide them into groups? So the cave-dweller used them, doubtless, not in play, but in serious earnest, for some such purpose as keeping tally of the wild beasts he had killed, or the number of his enemies vanquished.
"With a few packets of Froebel's sticks," as has been very well said, "the child is provided with an excellent calculating machine." The use of this machine in the primary school in word making as well as in number work is practically unlimited; but in the kindergarten it may very well give a clear, practical understanding of the first four rules of arithmetic,—an understanding which will be based on personal activity and experience.[69]