Interview Prompts to Uncover Mathematical Knowledge for Teaching: Focus on Providing Written Feedback

One area of study that has been gathering enthusiastic attention and interest is mathematical knowledge for teaching (MKT). How to research MKT, however, is still unsettled despite the plethora of unexamined areas of practice. As one of ways to unearth and measure MKT, this study uses interview prompts designed to providing written feedback, as a target area of practice. This study specifies in what ways the interview prompts are used in order to provide a comprehensive method to researching MKT. From interviews across professional communities with different kinds of mathematical expertise, the author develops a conceptual model based on the tasks of teaching, elements of pedagogical context, and domains of MKT. This model provides the fluent character of proficient MKT decision making in teaching practice and explains key features of the design of prompts for investigating and measuring MKT. From the analysis, two claims emerged: bidirectional approaches to investigating MKT and continuous and spontaneous aspects of MKT.