An examination of the relationship between conceptual understanding of mathematics? commutative and associative properties and procedural skills, an examination of the relationship between those skills and ages of children, and a study of the relationship between the role of the integration or absence of number words and concrete references to problem solving ability on a task, for 18 3- and 4-year-olds and 24 4- and 5-year-olds from two preschools and four child care centers in Australia