空間概念の形成に関する実験的研究

抄録

For the solution of Piaget's “three mountain's task” by children, it seems necessary for them to acquire three-dimensional coordinates reference system and the action of projection. The purposes of the present study are to try to form the action of projection with three-dimensional coordinates reference system in first and second grade school children under the experimentally constructed training programs and to discuss the possibilities of their learning.
In the first preparatory program, made of 6 steps of training, children learn the action of identification of left-right relationship of objects (dolls) on the base of three-dimensional reference system (left-right, upward downward, before-behind of objects). At the first step children are allowed to use their bodies as reference system in order to identify the right or left hand of dolls presented concretely in different postures, but at the final step they have to do it with the dolls verbally and imaginarily presented, depending only on internalized reference system. In the second main program, which contains 20 steps of training, we use a three-dimensional coordinates frame (Fig. 1), by which we can give children concrete tasks of projection of points or of objects on the 4 vertical planes. In the first stage of training (step 1-14) children learn to measure and express the projection of points on each of 4 vertical planes in two-dimensional coordinates; at first they are allowed to move themselves to the front of each plane of the frame and measure Y- and Y-coordinates of each projected point, but after-wards they must do them all, remaining on the same position. After learning of the action of projection of points, in the second stages (15-18 steps), they learn to draw projection of objects (piles of colored wooden blocks, a beer jug, a coffee pot and others) on each of 4 plahes, making use of projection of points of markeres of objects as reference points of drawing. Then in the last stage of training (step 19-20), aiming at promoting internalization of action, the coordinates frame are taken off, children learn to draw projections of objects (a coffee cup, a cap, a kettle and others) on the imagined planes without the help of coordinates frame and reference markeres.
For the period of 8 months,. 4first and second grade school children (training group) were trained under tarese programs and the progress of their performances with the “three mountain's tasks” were compared with the. change of performances with the same tasks of 5 third and fourth grade school children (comparative group), who had participated in the training only under the preparatory program.
As the steps of training advancd on, especjally after the training of steps 15-17, the performances with the “three mountain's tasks” of training group's children began to change gradually. And finally the results of control tests showed that 3 of 4 training group children had completely acquired the action of projection of objects with the three-dime ntional coordinates reference system, which was ehough for the successful solution of the “three-mountain's tasks” and the remaining one with his action ungeneralized. It was also showed that mean performances or progresses on these tasks of training group approximately corresponded to that of com- parative grogp, which showed gradual progresses for 6 months after training under the preparatory program.
Data obtained in these experiment ssuggest high possibilities of learning of Euclidian three-dimensional coordinates reference system and the action of projection by lower and middle grade school children, when their actions are nicely organized at their first stage of education at the level of materialized concrete actions, as suggested by the theory of stage-by-stage formatlon of mental action.