The purpose of the present study was to clarify informal knowledge on equal-whole which magnitude of wholes was the same size for all ratios. Participants in this study were 58 students in the 4th grades and 57 students in the 5th grades who had not stadied ratios yet, and 69 students in the 6th grade who had learned ratios already. There were two kinds of problems in Equal-whole, the problems in which the base quantities were the same, and those which the base quantities were different. The children were asked to compare the magnitudes of the comparison quantity and the ratios in the problems with same and different of base amounts. The results showed that the judgment of magnitudes of comparison quantity showed superior performance irrespective of the type of problem, whereas the problems for the judgment of ratios showed low performance in the problems with different base quantities. It was suggested that children acquired informal knowledge of comparison quantity in the equal-whole through experience of everyday life.

View full abstract

[in Japanese]

View full abstract

[in Japanese]

View full abstract