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…

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…

Results showed that only 32 percent of adult female shoppers in a supermarket were able to use a proportional reasoning strategy to determine which of two sizes of a common item (size ratio 2:3) was the better buy. Performance declined when the ratio was more complex. (JMB)

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…

Observed gesture and speech to investigate patterns of change in third and fourth graders' strategies for solving mathematical equivalence problems before and after an intervention. Children who received instruction were more likely to generate new strategies. Gradual change was more common. Abrupt strategy change was more common in children who…