UC Berkeley

Although educators and policymakers are becoming increasingly aware of the need for professional development that is content specific (Kennedy, 1999) and focuses on deepening and broadening teachers' knowledge of content for teaching (American Federation of Teachers, 2002; National Academy of Education, 2009), little attention has been given to supporting teachers' development of content knowledge as defined by Shulman (1986). Principle-Based Mathematics (PBM), a presentation of K-12 mathematics that adheres to the "fundamental principles of mathematics" (Wu, 2011a), has the potential to fill this void. This dissertation is an instrumental case study (Stake, 1995) that explores how teachers of 2 different grades (fourth and sixth) attempted to implement PBM in their classrooms and what the impact was on student learning. Results from analysis of teacher interviews, classroom artifacts, and student state test scores suggest: (1) The different approaches that the teachers used to teach the division interpretation of a fraction demonstrate the flexibility of PBM instruction to accommodate different curricular demands and teaching contexts; (2) The estimated average effect of PBM training on student achievement ranged between 0.25 and 0.34 standard deviations, but only 1 of the 4 teachers exhibited an increase in effect after PBM training. Estimated standardized effects on student achievement either decreased or remained nil for the other teachers after PBM training. The study's findings provide exploratory evidence to inform future evaluations of PBM training and instruction.