Children's profiles of addition and subtraction understanding

Abstract

The current research explored children's ability to recognize and explain different concepts both with and without reference to physical objects so as to provide insight into the development of children's addition and subtraction understanding. In Study 1, 72 7- to 9-year-olds judged and explained a puppet's activities involving three conceptual relations: (a) a + b = c, b + a = c; (b) a - b = c, a - c = b; and (c) a + b = c, c - b = a. In Study 2, the self-reports and problem-solving accuracy of 60 5- to 7-year-olds were recorded for three-term inverse problems (i.e., a + b - b = ?), pairs of complementary addition and subtraction problems (i.e., a + b = c, c - b = ?), and unrelated additio..