UC San Diego

The idea that learning generalizes beyond the conditions of initial learning serves as a basis for our educational system (National Research Council, 2000). That is, educators hope students will use the learning that is generated in the classroom to productively reason about situations they have yet to encounter. One body of research that has examined the generalization of learning is the research on transfer. Traditionally, transfer has been characterized as "how knowledge acquired from one task or situation can be applied to a different one" (Nokes, 2009, p. 2). Transfer has had a rich and varied history wherein researchers have detailed numerous conceptualizations of transfer as well as corresponding ideas about how to best support it. Surprisingly, an extensive search of the literature did not yield any studies aimed to uncover teachers' beliefs about transfer. Consequently, my research addresses the following question : What beliefs do teachers have about the generalization of students' learning and how to support it? To answer this two-part question, I asked eight practicing teachers to engage in two 2-hour clinical interviews (Ginsburg, 1997). Qualitative analysis of such data led to the identification of 5 categories (fitting into 3 supercategories) of teachers' beliefs regarding the generalization of learning and 13 categories of teachers' beliefs regarding how to support the generalization of learning. Analysis of data subsequently collected in teachers' classrooms resulted in the elaboration of beliefs identified via interview data and to the identification of beliefs not captured by interview data. The beliefs identified in this study highlight the importance of bringing teachers into the ongoing conversation about transfer. The mathematical topic of slope provided the content domain in which data on teachers' beliefs were collected. Analysis of the relationship between teachers' beliefs and their mathematical knowledge for teaching (MKT; Silverman & Thompson, 2008) revealed that with the exception of one teacher, there was alignment between the nature of the mathematical content teachers believe generalizes (i.e., a specific meaning for slope versus an association, procedure, or formula) and teachers' personal understanding of slope. To help explain these results, two other components of teachers' MKT were examined