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Abstract: Four sets each consisting of 3 or 5 test-items of different difficultieswere composed. to examine the stability of children's concepts of number,length, area and volume respectively, under both a screened-operation conditionand an unscreened-operation condition. In each of 13 districts throughout thecountry, 3-6-yr olds, with 30 Ss in each age-group, or 7-1l-yr olds, with20-30 Ss in each age-group, were examined individually with the "clinicalmethod". As the general results preliminarily suggest: The stability of children'sconcepts in mathematics, manifesting both in their performances of the examinationand in their cognitive levels of resolving processes, develops with the increaseof age. The stability of one kind of mathematical concepts may emerge earlieror later, depending on the kind and difficulty of test-problems used. Underthe unscreened-operation condition the stability of concepts is higher than thatunder the screened-operation condition. The performance under the screened-operation con-dition may be promoted by the demonstration or enlightenment ofuncreened-operation. Both these two events are more significant during thedeveloping period of concepts. No nationality-or sex-differences are found betweenchildren on the same culture-background. And the stability of concepts seems todevelop in an order of number, length, area and volume. According to theauthors, there exists a developmental process of the concepts from unstableto stable, and stability per se is not absolute, but conditional, it is by nomeans fixed to occur at a certain year of chronological age.

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