To develop their logico-mathematical foundation of number as described by Piaget (1947/1950, 1967/1971, 1971/1974), 26 low-performing, low-SES first graders were given physical-knowledge activities (e.g., Pick-Up Sticks and "bowling") during the math hour instead of math instruction. During the second half of the school year, when they showed "readiness" for arithmetic, the children were given arithmetic games and word problems that stimulated the exchange of viewpoints. At the end of the year, the children in the experimental group were compared with a similar (low-performing, low-SES) group of 20 first graders who received traditional exercises focusing narrowly on number (e.g., counting objects, making one-to-one correspondences, and answering questions like 2 + 2). The experimental group was found to be superior both in mental arithmetic and in logical reasoning as revealed by word problems. (Contains 3 figures and 6 tables.)