Development of an Expert Explanation: An Analysis of a Sequence of Subtraction Lessons

This article documents the teaching and learning that occurred during an 8-day unit on subtraction with regrouping in an expert teacher's second-grade classroom. Students in this study were found to be not only highly skilled in computation at the end of the sequence, but also to have, in some cases, unusual skill in solving problems beyond the range of instruction. Detailed analyses of the expert lessons that led to such high levels of student performance and understanding focused both on the explanations the teacher provided and on students' knowledge growth throughout the sequence. Two aspects of the teacher's explanations were analyzed: the subject-matter content and the explanational plan. Semantic nets were used to portray the teacher's subject-matter knowledge displayed in each lesson and were compared with corresponding nets of student knowledge for each day. All explanations were structurally analyzed to develop a network of goal states and action schemas, similar to other cognitive planning nets...