Abstract
This paper is the third report of our research carried out in 1959-1963. Here, our pieliminary research programs of experimental education of number concepts are presented.
Ss: 26 three year old children of the kindergarten (Yôji Group) of Tokyo Woman's Christian College. Ss are divided evenly into two groups, the older (G. II) and the younger (G. I).(This grouping system is not entirely adequate for our purpose, but the groups had already been determined.)
Experimental design and teaching method: For G. I, the dice-pattern symbols (from one to five) are used as the teaching instrument. These patterns are supposed to act as representations of some collections of objects, and, as symbols of cardinal numbers. The first main tasks of G. I consist of naming (one, two, three, etc.), associative learning of the names, mutual discrimination, identification, reconstruction and transformation of these patterns, and one to one correspondence between these patterns and various concrete objects. Having mastered them, Ss are taught the operation of addition by summing two patterns, for instance, of two and three, then transforming this sum into the regular pattern of five. Similarly, the operation of subtraction can be taught. Then, our original plan was to introduce the numerical figures (1, 2, 3, etc.) and the signs of plus, minus and equals (+, -, =) and to teach the Ss that the equation (e. g. 2+3=5) or subtraction are parallel to the operations of dice-patterns, and therefore to the operations of collecetions of concrete objects. After this, the range of numbers would be extended to twenty or thirty.
For G. II, teaching devices consist of rote learning of numerical orders, counting of the concrete objects, such as marbles, from one to thirty. The numbers, here, signify the ordinal numbers. Then, calculating operations of addition are taught. This is done by summing the two collections of marbles, for instance, two and three, then counting this sum in order. The operation of subtraction is similarly taught. Then, it was our original plan to introduce numerical figures, signs of plus, minus and equals and the equations, similarly to G. I.
This design is to compare the efficiencies of each two teaching plans of number concept mediated by the cardinal 04 ordinal number.
Procedure: Usually, teaching is done by the method of group learning of 13 Ss and by the particularly trained experimenters, but, occasionally, if the task is too difficult, 13 Ss groups are again divided into 2 or 3 subgroups. The experiment continued from June, 1959, to September, 1960.
Result: The prearranged teaching curriculum was not completly mastered by the Ss. However, this is only the preliminary work. The experiment promised us the effectiveness of both methods or devices, and cleared the way for our main experiment. Also it assured us that the group learning method was applicable even to the 3 year old children. The results of our main experiment will be reported in subsequent papers.
