Math Lessons: A Contrast of Novice and Expert Competence

Abstract

Three important elements needed for constructing expert mathematics lessons are identified and described: rich agendas, consistent but flexible lesson structures, and explanations that meet the goals of clarifying concepts and procedures and having students learn and understand them. Each element is discussed in terms of its hypothetical characteristics and then tested by comparing two novice and four expert elementary mathematics teachers. Information about the teachers' agendas was gathered from preclass interviews; data on the structure of their lessons and on the characteristics of the explanations they gave came from lesson videotapes and related interviews. The novice-expert contrast highlighted the nature of the competencies expert teachers possessed and suggested some areas of instruction for future teachers.