Teachers’ reflections on non standard students work

One of the tasks of teaching (Ball, Thames, & Phelps, 2008) concerns the work of interpreting student error and evaluating alternative algorithms used by students. Teachers’ abilities to understand nonstandard student work affects their instructional decisions, the explanations they provide in the classroom, the way they guide their students, and how they conduct mathematical discussions. However, their knowledge or their perceptions of the knowledge may not correspond to the actual level of knowledge that will support flexibility and fluency in a mathematics classroom. In this paper, we focus on Norwegian and Portuguese teachers’ reflections when trying to give sense to students’ use of nonstandard subtraction algorithms and of the mathematics imbedded in such. By discussing teachers’ mathematical knowledge associated with these situations and revealed in their reflections, we can perceive the difficulties teachers have in making sense of students’ solutions that differ from those most commonly reached.