Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Dual-process theories have been proposed to explain normative and heuristic responses to reasoning and decision-making problems. Standard unitary and dual-process theories predict that normative responses should increase with age. However, research has focused recently on exceptions to this standard pattern, including developmental increases in…

Predictive relationships among perceived family processes, intrinsic and extrinsic motivation, incremental beliefs about intelligence, confidence in intelligence, and creative problem-solving practices in mathematics and science were examined. Participants were 733 scientifically talented Korean students in fourth through twelfth grades as well as…

Strategies used to solve two-digit addition problems (e.g., 27 + 48, Experiment 1) and two-digit subtraction problems (e.g., 73 - 59, Experiment 2) were investigated in adults and in children from Grades 3, 5, and 7. Participants were tested in choice and no-choice conditions. Results showed that (a) participants used the full decomposition…

Two studies investigated children's metacognition about everyday reasoning, assessing how they distinguish reasoning from nonreasoning and "good" reasoning from "bad." In Study 1, 80 1st graders (6-7 years), 3rd graders (8-9 years), 5th graders (10-11 years), and adults (18+ years) evaluated scenarios where people (a) used reasoning, (b) solved…