Observations are widely used in research and evaluation to characterize teaching and learning activities. Because conducting observations is typically resource intensive, it is important that inferences from observation data are made confidently. While attention focuses on interrater reliability, the reliability of a single-class measure over the course of a semester receives less attention. We examined the use and limitations of observation for evaluating teaching practices, and how many observations are needed during a typical course to make confident inferences about teaching practices. We conducted two studies based on generalizability theory to calculate reliabilities given class-to-class variation in teaching over a semester. Eleven observations of class periods over the length of a semester were needed to achieve a reliable measure, many more than the one to four class periods typically observed in the literature. Findings suggest practitioners may need to devote more resources than anticipated to achieve reliable measures and comparisons.
This chapter aims to link the known research results on the teaching and learning of linear algebra to research on teaching practices. The same person, as a teacher and as a researcher, plans and implements a teaching sequence, constructs multimodal narratives (MNs) for some classes, and reflects on his own practice, based on the emerging categories from content analysis of the MNs. Regarding the methodology and focusing on the role of MNs in this research, it is worth highlighting the value attributed to MNs because they function as an instrument that embodies the practices of the teacher and aid him in reflecting on his own practice.
Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-Art and Looking Ahead