Data will be used for three analytic purposes: first, to characterize the instructional representations used (or planned) by teachers with respect to their narrative and/or paradigmatic organization (more on this later), ways of describing theories and using data, and types of questions asked of students, etc. Second, the data will be used to trace the factors affecting the origins of instructional representations such as subject matter background, available resources and reasoning about students. Finally, the data will be used to develop detailed descriptions and specific practice-based examples of more and less successful instructional representations. This study will allow me to both articulate more clearly the relationship between instructional representations and the subject matter knowledge of teachers as well as inform the development of the second strand of my proposal: the development and testing of a subject matter assessment.

Building on the insights gained from my investigation of teaching practice, the second line of inquiry will be to iteratively develop open-ended assessment items to investigate the subject matter knowledge for teaching two topics in physical science: density and condensation/evaporation. These are topics relevant to both middle and high school teachers and they are sufficiently complex as to allow me rich conceptual territory to explore teachers' ways of knowing and subject matter knowledge. I aim to engage, and learn more about, the methodological and conceptual issues involved with instrument design for examining the relationships between instructional representations and subject matter knowledge for teaching science.

The third line of inquiry is conceptual and involves the articulation of the relationship between instructional representations and science subject matter knowledge for teaching. The framework I'm developing to examine the structure of scientific understanding and instructional representations is based on distinctions between narrative and paradigmatic ways of knowing. The development and further articulation of this framework will be informed by both the study of instructional representations and the testing and development of assessment instruments for subject matter knowledge for teaching science.

By studying a range of teachers, from pre-service through exemplary, this proposal engages both conceptual and pragmatic issues central to teaching -- and learning to teach -- science. Products will include journal articles, observation and interview protocols, subject matter assessment instruments and validated scoring rubrics. The breadth of products is intentional, for the research is designed to create products for research audiences (conceptual analyses, research instruments, and the like), as well as useful products for teacher educators (e.g., exemplars of instructional representations, assessments that teacher educators might use to track the learning of prospective teachers, and observation protocols to assess progress in student teaching). Ultimately, the trajectory begun here holds promise to positively impact and inform policy and practice in science teacher education and in the learning of school science.