Preservice Mathematics Teachers' Noticing in Action and in Reflection

The aim of this paper is to discuss preservice mathematics teachers' in-the-moment noticing of mathematical opportunities and how they reflected on those opportunities both orally and in writing. A faculty-school collaboration program was set up to enable preservice teachers to work with students in a school setting throughout a year. Ten preservice teachers participated in the study. Videotapes and written documents were major tools to collect data, and a coding framework was used to describe and pursue the pattern in preservice teachers' noticing skills. The results revealed that preservice teachers were able to notice mathematical opportunities occurring in class both in the moment of and after implementation of mathematical tasks. Although their responding actions during implementation were mostly in the form of orienting students to correct solutions, they attempted to enrich students' mathematical interpretations by providing justifications from the students' work in their oral and written reflections.