Investigating number sense development in a mathematics content course for prospective elementary teachers

Includes bibliographical references (p. 428-436)In order to support children's learning of elementary mathematics meaningfully, elementary teachers need to understand that mathematics deeply and flexibly (Ball, 1990; Ma, 1999). In other words, they need good number sense (Reys & Yang, 1998). However, researchers have found that prospective elementary teachers tend to reason inflexibly, relying heavily on standard algorithms (e.g., Ma, 1999; Newton, 2008; Yang, 2007). Previous research has provided single snapshots or comparisons of pre/post snapshots of number sense. In this study, I analyzed prospective elementary teachers' number sense development. In earlier work, Nickerson and I created a local instruction theory (Gravemeijer, 1999) for the development of number sense (Nickerson & Whitacre, 2010). In a previous classroom teaching experiment, we found that prospective elementary teachers enrolled in a mathematics content course informed by the local instruction theory developed improved number sense (Whitacre & Nickerson, 2006). They moved from being reliant on the mental analogues of the standard algorithms to reasoning more flexibly in mental computation. In the present study, I duplicated analyses from the previous study and found similar results. I also moved beyond the previous study by investigating number sense development as a microgenetic, sociogenetic, and ontogenetic process (Saxe & Esmonde, 2005). I asked the following research questions: As prospective elementary teachers participate in a mathematics content course designed to support their development of number sense, 1. How does the number sense of individuals evolve? 2. What ideas come to function as if shared? What classroom mathematical practices emerge and become established? I approached this study from a situated perspective (Cobb & Bowers, 1999). The emergent perspective informed my approach to the research in terms of taking both social and individual lenses to the analysis of number sense development (Cobb & Yackel, 1996). I made innovations in the analysis of number sense. I documented collective activity in the class in terms of progressions through classroom mathematical practices. I also analyzed two case studies of individuals' number sense development. These analyses provide insights into the phenomenon of prospective elementary teachers' number sense development, which will inform revisions and elaboration to the local instruction theory