1. The point made concrete, which forms the tenth and last of Froebel's gifts, is represented by many natural objects, by beans, lentils, pebbles, shells, leaves, and buds of flowers, by seeds of various kinds, as well as by tiny spheres of clay and bits of wood and cork.
2. We have been moving by gradual analysis from the solid through the divided solid, the plane and the line, and thus have reached in logical sequence the point, into a series of which the line may be resolved.
3. The point which was visible in the preceding gifts, but inseparable from them, now in the tenth gift has an existence of its own. Although it is an imaginary quantity having neither length, breadth, nor thickness, yet it is here illustrated by tangible objects which the child can handle. By its very lack of individuality, it lends itself to many charming plays and transformations.
4. By the use of the point the child learns practically the composition of the line, that its direction is determined by two points, that the shortest distance between two points is a straight line, and that a curved line is one which changes its direction at every point. The gift closes the series of objects obtained by analysis from the solid, and prepares for the occupations which are developed by synthesis from the point.
5. The outlines of all geometrical plane figures both rectilinear and curvilinear may be illustrated with the point as well as straight and curved lines and angles of every degree.
6. The law of mediation of contrasts is no longer illustrated in the gift itself, but simply governs the use of the material. All lines and outlines of planes made with a series of dots show its workings, and the symmetrical figures, as we have noted from the first, owe to it their very existence.
Meeting-Place of Gifts and Occupations.
When we begin upon a consideration of the tenth gift, the last link in the chain of objects which Froebel devised to "produce an all-sided development of the child," we see at once that the meeting-place of gift and occupation has been reached. The two series are now in fact so nearly one that the point is much more often used for occupation work than as a gift. This convergence of the series in regard to their practical use was first noted in the tablets, and has grown more and more marked with each succeeding object.
Though the point is in truth the last step which the child takes in the sequence of gifts as he journeys toward the abstract, yet we are met at once in practice by the apparently inconsistent fact that it is one of the first presented in the kindergarten. This can only be explained by the statement that it is in truth quite as much of an occupation as a gift, and is used in the former sense among the child's first work-materials as a preparation for later point-making (perforating), and as an exercise in eye-training and accuracy of measurement. It is not an occupation, of course, for the reason that permanent results cannot be produced with it, and because no transformation of its material is possible.