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…

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…

The present study tested the hypothesis that children's fluency with basic number facts and knowledge of computational strategies, derived from early arithmetic experience, predicts their performance on complex arithmetic problems. First-grade students from United States and Taiwan (N = 152, mean age: 7.3 years) were presented with problems that…

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…

Examined the performance of kindergartners from middle- and low-income families on arithmetic calculations presented in a nonverbal format and in three verbal formats. Children from middle-income families performed better than those from low-income families on verbal calculation tasks but not on the nonverbal task. (BC)