This study aimed at investigating the developmental process of the conception of number and finding the necessary instruction procedure for accelerating its acquisition. Test items, concerning (1) the equivalence of perceptually different sets, and (2) conservation of number, were administered to 4- and 5-year-old children. The results were as follows : 1) Children's comparative judgment of two sets were dominated by perceptual configurations. 2) It was relatively easy for them to know the equivalence of two perceptually different sets. Most of them, however, could not know the invariant relation of two sets, if one of the two was transformed. It was the most difficult to grasp invariance of a set before and after transformations. 3) Children, who were on the way to acquisition of number concept, could recite numbers, count objects and know that the final number word represented the quantity of the set, finally relied upon perceptual cues at thecomparative judgment. Then, an experimental education was undertaken to develop children's conception of equivalence of sets and conservation of number. Program A (4 children) : to make the comparison of sets by one-to-one correspondence and to have an image of interrelations of unmber. Program B (4 children) : to develop unmder concept by the mediation of the number words. The instruction was administered individually and about ten minutes lesson was given to each child 8 or 9 times. The observation of the instructional process suggested that : 1) A gr. children mastered to use one-to-one correspondence in comparison of two sets, and this eliminated the perceptual cues which had been obstacles in cognition of equality.