We describe and analyze three episodes from mathematics classrooms. In each case, the teacher was confronted by a "contingent" situation that they had not anticipated or planned for yet that offered interesting and fruitful learning possibilities if pursued. In two cases, we analyze the teacher's response; in the third, we speculate how they might…

There is considerable research on teachers' beliefs and teachers' knowledge, but little empirical evidence exists as to the interplay between them. This article reports a study of 356 Norwegian teachers who answered a questionnaire and a multiple-choice test. Based on this study, the connections between two knowledge constructs and two beliefs…

The purpose of this study was to explore and identify the experiences that informed the development of three veteran (15+ years of teaching experience) 9th grade physics teachers' specialized knowledge, or PCK, for using representations to teach the topics of energy transformation and transfer. Through the lens of phenomenography, the study…