AN EXPERIMENTAL STUDY ON THE CHILD'S CONCEPTION OF NUMBER

Abstract

The purpose of this study is to analyse the child's conception of number from two aspects, one is the magnitude of the number and the other is a set of tasks which are given under different stimulus condition.
The number1, 2, 3, 4, 5, 6, 8, and10are used. And the tasks used are as follows.
(1) Comparative judgement of the number of the two aggregates which comprise the different number of elements or the same number of elements.
(2) Estimation of the number of an aggregate under the different stimulus pattern.
(3) Division of the aggregate into the smaller ones which comprise the same number of elements.
(4) Construction of the given number of an aggregate out of elements.
(5) Taking into account the change in number of an aggregate produced by the addition and subtraction of an element.
(6) Reproduction of the figures which comprise a regular pattern, a circular pattern and an irregular pattern with “go” pieces.
(7) Taking into account the change in the number of an aggregate produced by the perceptual change of an aggregate.
(8) Tasks with respect to the seriation and ordinal number.
A total of200Ss are tested in this investigation, they are divided into tow groups by half year intervals, from5: 0to5: 5, and from5: 6to5: 11.With respect to sex, each group comprises50boys and 50girls.
The results are as follows
(1) In general, the elder group is more successful on each task than the younger group.
(2) When they compare the number of two aggregates, Ss are influenced by the perceptual configuration and they can not judge them by means of the mediator (a numeral word).
(3) Both the magnitude of numbers and the set of tasks are, to a certain degree, scalable, according to the order of difficulty.This is analysed by means of the “index of reproducibility”.
(4) The tasks which can be responsed easily from the perceptual point of view do not always distribute in accordance with the magnitude of the number.
(5) There is some difference between the large numbers and the small numbers with respect to the difficulty of the tasks.
(6) Comparing the stimulus conditions which comprise the same numbers of elements with the different numbers of elements, the type of response is different according to the magnitude of number and each task.
(7) One-to-one correspondence seems to be more related to the acqusition of the conservation concept than the numeral word.
(8) The Ss can neither segregate the aggregate of elements nor reconstruct them.They can not composite the two different aggregates into one aggregate, either.