Secondary Practising Teachers’ Professional Noticing of Students’ Thinking About Pattern Generalisation

Abstract

In this article we describe secondary school practising teachers’ professional noticing expertise, which includes (a) attending to the details of students' written or verbal responses, (b) interpreting students' mathematical understandings, and (c) deciding how to respond to students based on their understandings, with a focus on algebraic-pattern generalisation. Quantitative results indicated that the majority of teachers in our study provided evidence that they could attend to the mathematical details of students' thinking.  However, the practising secondary school teachers provided less evidence of interpreting students' understandings, and even less of deciding how to respond to students based on those understandings.  We present qualitative trends to help mathematics professional developers prepare for the teachers they will support and discuss how these trends might influence work with secondary school practising teachers on noticing student thinking in pattern-generalisation tasks.