Expertise in mathematics instruction: Subject matter knowledge.

Abstract

The relationship between expert teachers' classroom behavior and their subject matter knowledge has not been examined extensively. To begin such an examination, one topic, fraction knowledge, was explored in depth as it occurred in natural teaching settings. Fractions are one of the more difficult topics in elementary arithmetic; much of this difficulty is attributable to the complex relationships among the meanings and representations of fractions and basic arithmetic operations. Despite these difficulties, many teachers are quite proficient at teaching children to perform operations with fractions. We examined expert teachers' knowledge by using extensive protocols to investigate the content and organization of teachers' knowledge of fractions. These protocols involved interviews, card-sorting tasks, and transcriptions of videotaped lessons. Semantic nets that reflected their knowledge of fractions were developed for individual teachers. Comparisons of these semantic nets showed wide variations among the knowledge of expert teachers. Some teachers displayed relatively rich conceptual knowledge of fractions, although others relied on precise knowledge of algorithms. Implications of these knowledge differences are discussed.This article explores the organization and content of subject matter knowledge of expert arithmetic teachers. Teaching is a cognitive skill and, as such, is amenable to analysis in ways similar to other cognitive skills (Leinhardt & Greeno, 1984). The expertise involved in the cognitive aspects of teaching can be seen as emerging from two core areas of knowledge: lesson structure and subject matter. Lesson structure knowledge includes the skills needed to plan and run a lesson smoothly, to pass easily from one segment to another, and to explain

Interaction between a First-Year Elementary School Teacher and Students in Mathematics Class

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“…In particular, Leinhardt & Smith (1985) compared knowledge of novice and expert teachers for fraction instruction. They found…”

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