Efficacy and teaching mathematics by telling: A challenge for reform

Abstract

This paper analyzes the tension between the traditional foundation of efficacy in teaching mathematics and current reform efforts in mathematics education. Drawing substantially on their experiences in learning mathematics, many teachers are disposed to teach mathematics by "telling": by stating facts and demonstrating procedures to their students. Clear and accurate telling provides a foundation for teachers' sense of efficacy - the belief that they can affect student learning - because the direct demonstration of mathematics is taken to be necessary for student learning. A strong sense of efficacy supports teachers' efforts to face difficult challenges and persist in the face of adversity. But current reforms that de-emphasize telling and focus on enabling students' mathematical activity undermine this basis of efficacy. For the current reform to generate deep and lasting changes, teachers must find new foundations for building durable efficacy beliefs that are consistent with reform-based teaching practices. Although productive new "moorings" for efficacy exist, research has not examined how practicing teachers' sense of efficacy shifts as they attempt to align their practice with reform principles. Suggestions for research to chart the development of, and change in, mathematics teachers' sense of efficacy are presented.