Is Conservation of Number a Necessary Condition for Mathematical Understanding?
This study investigated the importance of conservation of number as a prerequisite skill for arithmetic instruction. Piaget's theory maintains that the child's ability to conserve number constitutes a prerequisite to arithmetic understanding. 116 Ss (ages 4 to 6) were homogeneously grouped on the basis of a conservation of number pretest and randomly assigned to experimental and control groups. The experimental group was trained in arithmetic concepts, while the controls played a game under similar conditions. The 2 groups were posttested on arithmetic and number conservation tasks. The regression of arithmetic posttest scores on the conservation dimension was plotted separately for the experimental group and for the control group. The homogeneity of regression analysis showed that the 2 regression lines were separated but essentially parallel. In other words, although training had an effect, it did not have a differential (interaction) effect on nonconservers and conservers. Thus, the results failed to confirm the hypothesis that conservation of number is necessary for the understanding of arithmetic.