This study analyses an online scenario-based instrument in which secondary mathematics teachers from across the United States were presented with episodes of mathematics instruction and then asked to make a decision at a critical juncture. The theory of practical rationality suggests that the decisions of mathematics teachers can be understood as…

A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as "the" way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional…

Using mixed-effects regression, we analyzed teachers' responses to a multimedia survey of instructional practices in posing proof problems in geometry. Teachers described and rated for appropriateness three different ways of involving students in deciding what to prove, including one in which the teacher chooses the givens and the conclusion to…

We describe how multimedia scenarios delivered online can be used in instruments for the study of professional knowledge. Based on our work in the study of the knowledge and rationality involved in mathematics teaching, we describe how the study of professional knowledge writ large can benefit from the capacity to represent know-how using…

Video recordings of instruction have been a mainstay for supporting conversations about teaching by representing particularities of instruction and by presenting the viewer with a multitude of details for interpretation. In this essay, we contrast non-fictional videotapes of actual classroom interaction with fictional animations of classroom…

We describe the development of measures of teachers' recognition of an instructional norm--that proof problems in high school geometry are presented in a diagrammatic register. A first instrument required participants to openly respond to depictions of classroom scenarios in which the norm was breached. A second instrument was a survey that…

Background/Context: For decades, teacher educators and professional developers have been using video recordings of actual classroom practice to help teachers reflect on their teaching (e.g., van Es & Sherin, 2002, 2008) and to help preservice teachers come into contact with practice (Lampert & Ball, 1998). However, the use of video records of…