Using First- and Second-Order Models to Characterise In-Service Teachers’ Video-Aided Reflection on Teaching and Learning with 3D Pens

This study examines the processes through which video-aided reflections may guide teachers to become aware of, and develop, expertise in the use of a novel-to-them technology in mathematics classrooms. Four mathematics teachers participated in this study aimed at exploring teachers’ initial experience of using and planning lessons with the technology of “3D Pens”, which enables learners to construct 3D models instantly via moving their hands. We analyse the participants’ reflections and interpretations of students’ actions during semi-structured interview sessions while they were watching video episodes of a lesson integrating 3D Pen for mathematics teaching and learning. Adopting the constructs of first- and second-order models, we provide fine-grained characterisation of the teachers’ mathematical and pedagogical learning in the moment of their reflection. The results suggest that the teacher participants not only shifted from operating on their first-order models to constructing second-order models of students’ geometrical thinking as supported by 3D Pens, but they also reasoned pedagogically based on their second-order models. Hence, watching videos of authentic technology-rich lessons facilitated a productive noticing experience for mathematics teachers in terms of realising the educational potential for the technology of the 3D Pens.