Prospective Secondary Teachers’ Emergent Knowledge and Beliefs: Inquiry-Oriented Differential Equations Contributing to Teacher Preparation

Abstract

This article reports on the evolution of prospective secondary teachers’ knowledge (meanings for frac{dy}{dt}) and beliefs (about teaching and learning mathematics) in a semester-long inquiry-oriented differential equations class. Students entered the course with limited, primarily procedural, meanings for frac{dy}{dt}. Throughout the semester, they engaged in collaborative mathematical inquiry using a research-based curriculum. As viewed through the emergent perspective, students’ meanings for frac{dy}{dt} and their beliefs about teaching and learning mathematics co-evolved with community norms and practices through the classroom discourse. Students’ end-of-term portfolios and portfolio presentations were analyzed for evidence of meanings for frac{dy}{dt} and beliefs about students’ roles, instructors’ roles, and the general nature of learning mathematics. In these, students expressed rich, multifaceted meanings for frac{dy}{dt} and beliefs about learning as an active process of meaning-making. While many prospective teachers do not see the relevance of advanced mathematics coursework to their career, these students reflected on their experiences in the course and volunteered ways in which their emerging knowledge and beliefs would influence their future practice. We emphasize that the classroom norms supported students in pursuing connections themselves, and conjecture that similar norms would support the development of reflective practitioners in other contexts.