In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We used Epistemic Network Analysis to consider the teachers' knowledge organization and connections between knowledge resources as a way to make sense of his understanding. Then, we examined how his understanding was reflected…

The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient)…

There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education…

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

This study offers an analysis of the learning of practicing teachers as they acquire a deeper knowledge of mathematics. While some professional developers have shifted part of their focus to helping practicing teachers acquire a deeper knowledge of mathematics (e.g., Stein & Silver, 1996), the results from studies often describe what translates…