This study investigated the relationships between first-grade children's performance on Piagetian logical reasoning tasks and an information processing task, and the processes they used to solve verbal addition and subtraction problems. The problems varied systematically in semantic structure, number size, and the availability of objects to aid the solution process. Statistically significant differences in arithmetic performance between the developmental groups were found for some of the cognitive variables. The information processing variable was the cognitive ability most consistently related to accuracy of solution and use of advanced solution strategies. However, none of the cognitive abilities was required to solve the arithmetic problems or to use a given solution strategy. This calls into question the use of these cognitive tasks as readiness variables for arithmetic instruction.