From mistakes, we learn? Mathematics teachers' epistemological and positional framing of mistakes

This interpretive cross-case study investigates complexity in the ways teachers frame mistakes and the reasons behind their framing, challenging the assumption in the literature that productive beliefs about errors generate productive error-handling practices, while unproductive beliefs result in unproductive practices. The study draws on interviews and classroom observations with three secondary mathematics teachers who were selected using purposive sampling. Analysis examines how the teachers framed mistakes in their classroom practice and the instructional moves that enacted each frame. We paid particular attention to epistemological frames, which concern the value of mistakes in the construction of mathematical knowledge, and positional frames, which concern the roles that students are authorized or obligated to take to address errors, researching how teachers' epistemological and positional framing of errors were related. The results suggest that teachers invoked four primary frames related to errors: a epistemological frame of errors-as-resources, a positional frame of students-as-capable, an epistemological frame of errors-as-deficiencies, and an positional frame of students-as-incapable. We discuss barriers to using mistakes as resources for learning and implications for mathematics teacher education.