Examined the relationship between 6- to 8-year olds' conceptual understanding of additive composition, commutativity, and associativity principles and addition problem-solving procedures. Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving…

Examined patterns of conceptual and procedural knowledge of addition in 5- to 8-year-olds. Found that children were more successful in noticing that addends had been reordered rather than decomposed and in noticing the decomposition of addends presented with objects rather than with symbols. Also found that profiles of procedural competence were…

Investigates children's knowledge of concrete versions of additive composition, commutativity, and associativity. Reports that in study one, four-to five-year-olds (n=24) and five- to six-year-olds (n=25) judged the equivalence of conceptually related addition problems using groups of objects. States that in study two, five- to six-year-olds…