Connecting Beliefs and Practices: A Fine-Grained Analysis of a College Mathematics Teacher's Collections of Beliefs and Their Relationship to His Instructional Practices

Findings about mathematics teachers' beliefs typically involve broad characterizations of those beliefs that are compared with general descriptions of practices. Teacher development research suggests that changes happen effectively from attention to specific practices. Few investigations of beliefs and practices are done at this level of detail. Thus, little is known about how beliefs shape practices at the very grain-size where development appears to happen most productively. This study focused on fine-grained details of beliefs, practices, and connections between them. Findings indicate that particular units of analysis ("collections of beliefs") are useful for investigating connections between beliefs and specific practices. Certain collections were also found to be especially influential, including beliefs about evidence of student understanding and about how learning happens.