Instructional decisions in a mathematics course for elementary education majors

Thesis (D.Ed.)--Boston UniversityAlthough it recommended that pre-service elementary teachers be provided with opportunities to develop mathematical understanding through engagement in experiences where they reason, explain, justify and generalize about mathematics, much still remains to be learned about how a mathematics teacher educator can support pre-service teachers in developing understanding during these experiences. This study investigated the instructional decisions of an experienced instructor in an undergraduate mathematics course for pre-service elementary teachers as he supported developing understanding around geometric measurement topics. Two lessons on the geometric measurement topic of area formulas were considered by the researcher. Multiple interviews were conducted with the instructor including a pre-interview session, four video-stimulated recall sessions, and one post-interview. All observed lessons and interviews were recorded and transcribed. Lastly, participants completed a Pre-test and Post-test on area formula. Analysis of the instructor's descriptions of his teaching enabled the researcher to construct a description of the intended implementation of the two area formula lessons. Video-stimulated recall sessions along with the classroom observations and interviews were used to analyze the instructor's decisions during teaching. The instructor's actions, decisions, and strategies during whole-class discussion were mapped to the Math-Talk Learning Community Framework (Hufferd-Ackles, Fuson & Sherin, 2004) in order to provide a description of how the instructor actually supported the development of participants' mathematical understanding. Three levels of instructional decisions emerged. High-level decisions included the instructor's choice of curriculum and his use of discussion as the primary instructional methodology. Mid-level decisions included the instructor's decisions around the social and academic norms created in the classroom. For instance, the instructor provided few explicit mathematical statements so that participants were the source of mathematical ideas. Additionally, the instructor would not accept partial mathematical justifications from participants. Also, to engage the class in discussion, the instructor reminded participants of their roles as future teachers and their responsibility to ask questions of each other. Micro-level decisions included the instructor's choice of when and how to use talk moves (Chapin, O'Connor & Anderson, 2013) and his selection of discussion participants. There was evidence that participants' understanding improved as shown by significant change in achievement on the Area Formula Pre- and Post-test. Overall the instructor's intended instructional decisions and enacted instructional decisions were aligned