| Competence in many domains requires that children develop both conceptual understanding and procedural skill. I propose an iterative model for understanding the development of these two types of knowledge and include change in problem representation as one mechanism underlying this development. My dissertation evaluated this iterative model in the context of children learning about decimal fractions. In two experiments, fifth- and sixth-grade students completed assessments of their conceptual and procedural knowledge of decimal fractions, both before and after a problem-solving session. During the problem-solving session, they placed decimal fractions on number lines, received accuracy feedback, and were prompted to try to explain the correct solutions. The results of Experiment 1 provided correlational support for the iterative model. Children's prior conceptual knowledge supported gains in procedural knowledge, and in turn, these gains in procedural knowledge supported improvements in conceptual knowledge. Further, correct problem representation mediated the relation between conceptual knowledge and improved procedural knowledge. The results of Experiment 2 provided causal evidence for the link from improved problem representation to improved procedural knowledge. Children who received representational support represented more problems correctly and made greater gains in procedural knowledge. General math ability had inconsistent influences on learning across the two experiments. Overall, the results supported the iterative model for the development of conceptual and procedural knowledge and suggested potential mechanisms underlying this development. This research also has important implications for mathematics instruction. |
