UNDERSTANDING AND TEACHING RATIONAL NUMBERS: A CRITICAL CASE STUDY OF MIDDLE SCHOOL PROFESSIONAL DEVELOPMENT

Abstract

A lot of money is spent each year on teacher professional development, but researchers and policymakers are still trying to determine what that investment yields in terms of improvements in teacher knowledge and practice. This study focuses on the extent to which middle school mathematics teachers comprehended and made use of the core content, pedagogical content and pedagogical components of a well designed professional development model. At the time of data collection, the teachers were participating in a large, federally funded randomized field trial on professional development that focused on rational numbers. Compared with many other teachers participating in the randomized study, these three teachers were highly receptive to the intensive, content-focused model and thus represent a critical case study of professional development. Using interview and classroom observation data from the 2007-08 school year, the study indicates that teachers understood and implemented many of the pedagogical components emphasized in the model, but they had difficulty comprehending and articulating the core rational number content. Within the domain of rational numbers, the study shows that teachers had more difficulty understanding ratio and proportion concepts as compared with fraction and decimal concepts. The study also describes sources of variation in teachers' understanding of the professional development material and the extent to which they utilized the professional development material while teaching. Teachers' understanding of math content is a critical link in the theory of action driving current educational policies that call for increased rigor and coherence in K-12 mathematics. This case study illustrates that even well designed and well implemented professional development models may be incapable of improving teachers' content knowledge to levels that positively affect their instructional practices.