The Sums Are Larger Than Their Natural Number Addends: Relation to Operands Understanding Predicts Growth in Arithmetic/Algebraic Problem Solving.

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal study aimed to address this issue. Two-hundred-and-two Chinese fifth graders (57% boys) were assessed on their RO understanding. Their arithmetic/algebraic problem solving were assessed multiple times over 2 years. Results from latent growth curve modeling showed that RO understanding predicted the growth in arithmetic/algebraic problem solving when other known predictors of arithmetic/algebraic problem solving were controlled. The findings highlight the role of RO understanding in children's mathematical development. Interventions should be developed to enhance children's RO understanding. Public Significance Statement: The relation to operands (RO) principles, which describe the relation between operands and answers in arithmetic problems (e.g., A + B > A for all positive B), have received little attention in the literature. The current findings illustrate that children's understanding of the RO principles is related to the growth in children's arithmetic/algebraic problem solving performance. Educators should pay more attention to this construct and develop relevant interventions to ensure that children understand these arithmetic principles. [ABSTRACT FROM AUTHOR]