Abstract

The present study was an attempt to understand the nature of young children's self-explanation in the domain of procedural and conceptual knowledge in mathematics. The objective of this study was to examine the relationship between task demands on three outcome variables: (a) quantity of self-explanation, (b) quality of self-explanation (procedural and conceptual), and (c) conceptual knowledge, or an understanding in mathematics of the concepts central to each task. Three different self-explanation tasks were developed for the present study. Each task was based on one of the following theoretical assumptions about the generation of self-explanation: (a) learning through discovery (Self-Explanation Task 1), (b) direct instruction (Self-Explanation Task 2), and (c) effect of surprise (cognitive conflict; Self-Explanation Task 3). Prior knowledge in mathematics was investigated as a possible moderating variable in the analyses. Thirty second-grade students were interviewed four times. In the first interview, the Number Knowledge Test (NKT) was individually administered to participants to measure their prior knowledge of counting, number, and quantity. In the second, third, and fourth interviews, one of the three self-explanation tasks was administered. A near transfer task was administered at the end of each self-explanation task to measure the knowledge of the concepts central to each. The data revealed that the task based on direct instruction produced the highest number of self-explanations compared to each of the other two tasks, regardless of prior knowledge. In addition, a significant interaction was found between task type and prior knowledge on the generation of conceptual self-explanations. Specifically, low prior knowledge students generated higher quality self-explanation (i.e., conceptual self-explanations) on the task based on discovery learning, whereas high prior knowledge students produced better quality self-explanations on the task based on surprise. No such interaction was found for procedural self-explanations, but the data revealed that the task based on direct instruction produced a higher number of procedural self-explanations compared to either of the other two tasks. Finally, the results indicated that there was a significant correlation between task type and conceptual knowledge, with evidence suggesting that the task based on surprise was more effective than the task based on direct instruction in enhancing conceptual understanding of key mathematical principles. A number of implications for the classroom are discussed, not least of which includes the importance of maintaining a prominent place in the mathematics curriculum for procedural instruction