Adolescents' understanding of inversion and associativity

Abstract

The present study investigated when an understanding of the mathematical concepts of inversion and associativity matures and whether the application of these concepts to problem solving requires the interruption of computational strategies (e.g., Siegler & Araya, 2005). In the study, 40 adolescent participants per grade from Grades 7, 9, and 11 and 40 adult participants solved multiplication and division inversion and associativity problems and completed a task that measured whether the execution of the inversion shortcut or associativity strategy prevents the execution of competing computational strategies. Inversion shortcut use approached adult levels in Grade 9. Associativity strategy use significantly increase in early adulthood. Also, there was considerable individual variability in strategy use. Finally, the execution of both conceptually-based strategies interrupted computational strategies. Thus, adolescence is an important developmental period for understanding multiplicative concepts and applying conceptual mathematical knowledge to problem solving may require the interruption of procedural knowledge.