Constructing coherency levels to understand connections among the noticing skills of pre-service mathematics teachers

This study aims to analyze possible connections among the noticing skills of pre-service mathematics teachers, and specifically the skills of attending to students' thinking, interpreting students' mathematical understanding, and proposing teaching alternatives. We characterized these connections in terms of coherency, i.e., the extent to which pre-service teachers take into account (a) an identified critical event-including its mathematics and context-when interpreting students' statements, (b) their own interpretation of students' statements when interpreting the teacher's response, and (c) their own interpretation of students' statements when proposing alternative teaching strategies. The construct of coherency evolved during our attempts to analyze pre-service teachers' interpretations of the critical events they identified while observing mathematics lessons as part of their preparation program. In this paper, we elucidate the construct of coherency and its different levels and demonstrate how this construct relies upon and expands existing ideas from the literature on noticing. We propose a framework for identifying different coherency levels and the different patterns identified when using the framework to noticing among the pre-service teachers. Some of these patterns are supported by previous research, while others were unanticipated. We explore possible explanations for the emergence of these unanticipated patterns.