Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily?

TLDR

The article examines a classroom lesson in which a student teacher failed to provide a conceptually based justification for the division‑of‑fractions algorithm, noting that her conception of good mathematics teaching aligned with current effective teaching views. The study seeks to explain the lesson’s failure, its insights into learning to teach, and implications for mathematics teacher education. The authors analyze the student teacher’s beliefs about good teaching, her knowledge of division of fractions, and her learning‑to‑teach beliefs, alongside the mathematics methods course she attended, noting that the course did not prompt her to reassess her knowledge or beliefs. The study finds that without a stronger conceptual knowledge base and greater commitment to resource use and hard thinking, the student teacher’s beliefs were difficult to realize, indicating that teacher education programs should rethink how they deliver subject knowledge and challenge existing beliefs.

Abstract

This article analyzes from several vantage points a classroom lesson in which a student teacher was unsuccessful in providing a conceptually based justification for the standard division-of-fractions algorithm. We attempt to understand why the lesson failed, what it reveals about learning to teach, and what the implications are for mathematics teacher education. We focus on (a) the student teacher's beliefs about good mathematics teaching, her knowledge related to division of fractions, and her beliefs about learning to teach; and (b) the treatment of division of fractions in the mathematics methods course she took. The student teacher's conception of good mathematics teaching included components compatible with current views of effective mathematics teaching. However, these beliefs are difficult to achieve without a stronger conceptual knowledge base and a greater commitment to use available resources and to engage in hard thinking than she possessed. Further, the mathematics methods course did not require the student teacher to reconsider her knowledge base, to confront the contradictions between her knowledge base and at least some of her beliefs, or to reassess her beliefs about how she would learn to teach. These findings suggest that mathematics teacher education programs should reconsider how they provide subject matter knowledge and opportunities to teach it, and whether and how they challenge student teachers' existing beliefs.