Table 2 Mental simulation component codes, inter-rater reliability (Cohen’s Kappa, % agreement), coding rules, and brief summaries of typical examples from dataset

Ambiguity

(κ = 0.70, 99%)

When either the coach or teacher identified a situation where there was uncertainty about what the teacher would do, including potential outcomes of a particular teaching move or decision relative to the lesson context or concerns about a common problem of practice the teacher is struggling with

Pre-conference: Coach asks teacher to consider how the specific choices in her lesson plan might be expected to advance student learning goals

Post-conference: Teacher expresses uncertainty about what alternative strategies she could have used to achieve better outcomes, while reflecting on what occurred during a previous lesson

Alternative

(κ = 0.68, 98%)

When a teacher or coach raised a possible alternative scenario that could have taken place, as the result of either a different teacher move or a different student contribution

In pre- or post-conference: Coach prompts the teacher to brainstorm different moves she might use to help students link ideas; or how she would respond if a student came up with an unanticipated solution strategy

Weighing

(κ = 0.66, 96%)

When the coach and teacher engaged in discussion of the affordances and/or constraints of potential alternative strategies relative to student learning goals, including at least some pedagogically relevant reasons to explain their choices (i.e., alternatives selected and/or evaluated without reasoning did not count as weighing)

In pre- or post-conference: Coach and teacher might discuss how the phrasing of a particular question shaped (or could shape) students’ thinking opportunities; or what aspects of the mathematics concept would be highlighted if the teacher selected particular student answers to share