An Approach to the Teacher Educator's Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education

This study endeavors to illustrate how research on the professional development of mathematics teachers can help to enhance and nurture the professional knowledge of mathematics teacher educators (MTEs), thus becoming a potential source of professional growth for MTEs. To achieve this, a professional task was administered to 38 prospective secondary teachers from two Spanish public universities to explore their level of development in professional noticing. Specifically, the study focused on their skill of attending to children's strategies in relation to transformations between semiotic representations as well as their awareness of the role of the semiotic register in task design. Drawing from the responses provided for the task, we offer a range of insights regarding expected or desirable Pedagogical Content Knowledge (MTEPCK) aimed at fostering the development of professional noticing, such as several challenges to be overcome by pre-service teachers or the identification of three potential levels of progression in their skill to attend to children's strategies.