Exploring competence profiles of pre-service teachers' noticing of students' mathematical modelling processes: A type-building analysis

As mathematical modelling problems often allow for a variety of approaches and thus various difficulties can arise, it is particularly important that teachers spontaneously perceive and interpret students’ individual solutions and difficulties and come to a decision about their reaction. In this study, teacher noticing—namely perception, interpretation, and decision-making—is promoted in a modelling seminar. Pre-service teachers’ abilities to notice modelling processes are assessed before and after the seminar using a video-based instrument. The criteria breadth of perception, depth of interpretation and nature of decision-making are used to identify different types of competence profiles, which describe the differences and similarities in the ability to notice mathematical modelling processes. Furthermore, the individual development is evaluated. The analysis reveals tendencies to change in different facets of noticing regarding mathematical modelling processes: Instead of an overall improvement in noticing, the participants mostly develop regarding one facet of noticing (perception, interpretation or decision-making).