Previous research indicates that advancement in acquiring mathematical competencies requires a qualitative leap in conceptual development. Understanding partwhole relationship, which represents the basis for acquiring addition skills, is one of the key advances in conceptual development. Research on the adoption of the basic addition principles – additive composition, commutativity and associativity – provides a better understanding of the part-whole knowledge development. Therefore, the aim of this research was to explore age-related differences in understanding the basic addition principles and to determine whether there are differences in understanding different addition principles. The participants were 4 year old (N = 41), 5 year old (N = 89) and 6 year old (N = 76) preschool children, and 7 year old first grade students (N = 77). Understanding of the addition principles was assessed by presenting addition problems in a concrete context. The main effect of age proved to be significant for all addition principles, with older children performing better than younger children. The results also indicate that there are no differences in understanding different addition principles. In order to determine whether there are qualitative differences in children’s justifications of their answers to the posed problems, they were thoroughly analyzed. Results show that children who are successful in solving addition problems give more elaborated justifications compared to children who are less successful, indicating different levels of conceptual knowledge about addition principles. Overall, the research supports the model proposed by Baroody, Wilkins and Tiilikainen (2003) and the conception of protoquantitative level of mathematical reasoning proposed by Resnick (1992).

conceptual development, additive composition, commutativity, associativity