Two experiments were carried out to examine the effect of training on children's numerical behavior in comparing 2 coilections. The curriculum of the training was to enable children to grasp interrelations of number ((k+1)=(k)+(1), (k-1)=(k) -(1), ect. ) by associating a quantitative image to each numeral,and to use counting as a quantifying operation. (A child has a quantifying operation when assigned numerals to a set imply various relations to other numerals. ) In the Ist expetiment, 11 4-year-old children received 10 training sessions. Children showed a marked and statistically signiLicant progress in the numerical iudgment of 2 collections. Their performance improved significantly even when a collection had more elements than were dealt with in the training session. Furthermore, many of them also acquired number conservation, for which no direct instruction was given. Effects of the training dimi nished only slightly 6 months later.