A glimpse into the diagnostic competence of teachers during real-time modelling instruction

This study explores the diagnostic competence of five lower-secondary mathematics in-service teachers during real-time instruction, while implementing Mathematical Modelling (MM) tasks in their classrooms. Teachers’ diagnostic competence, defined as their ability to identify students’ challenges, has not been thoroughly explored in the context of real-time instruction, or within the modelling phases, pointing to an underexplored area in current research. A qualitative analysis of nine observed lessons was conducted to uncover what challenges that students encounter or may face in the MM process are identified by teachers, along with the diagnostic practices teachers apply to detect these challenges. The findings revealed two key factors exemplifying teachers' diagnostic competence: the frequency and diversity of challenges identified within each modelling phase. These factors were evident throughout all modelling phases, yet were most prominent in the mathematise phase, which exhibited the highest frequency and a full range of diversity of identified challenges. Teachers’ diagnostic competence was also significant in both the understand simplify and mathematical work phases, and least prominent in the interpret phase. Further in-depth analysis revealed five distinct diagnostic practices that teachers employ to detect modelling challenges within different phases of MM, each with various goals and timings for application during instruction. This study makes a theoretical contribution by expanding the definition of teachers’ diagnostic competence to include the frequency and diversity of challenges identified within the various modelling phases, as well as teachers’ diagnostic practices and the underlying intentions behind their application.