Using the “between-grade levels” regression discontinuity design, this study examined the hypothesized differential sensitivity of logico-mathematical (LM) and infralogical (IL) operational tasks to the effects of chronological age and first grade schooling in a sample of 580 1st and 2nd grade Israeli children. The results indicate that the development of logico-mathematical operational skills (classification, class inclusion and transitivity) is mainly attributable to schooling. In contrast, the effect of schooling on the development of conservation of mass, liquid quantity and number (clearly an infralogical task) is negligible; acquisition of conservation is almost exclusively due to maturation and out-of-school experiences. The results support the theoretical predictions derived from French-Swiss research of the last two decades and are inconsistent with claims regarding the specificity of schooling effects to tasks that are taught in school.