Analyzing teachers’ scripts from teachers’ reflections after they tried to encourage students’ flexible mathematical thinking

Teachers play a key role in promoting flexible mathematical thinking in society. There is a growing need to develop better methods for both pre- and in-service teacher training, but not enough is so far understood about what knowledge and skills teachers use in practical teaching situations. The means for investigating this are few. A new analytic framework was developed using abductive content analysis to investigate signs of script restructuring and construction as they appear in teachers' written reflections reporting their experiences in applying novel methods in their classrooms. Scripts are mental knowledge structures combining formal professional knowledge and the knowledge teachers use in practical situations with representations, assessments, and predictions of different classroom events. Scripts enable teachers to make (rapid) snap decisions to structure their teaching and manage classrooms to facilitate students' attention towards objectives, activities, and information that support learning. In this multiple case qualitative study, six teachers enrolled on the “Flexible and Adaptive Arithmetic Skills in Primary School” course, part of the JoMa (Towards Flexible Mathematics) in-service training program, teaching assignment and end-of-course reflections were investigated in depth. The goal was to advance the application of script theory to the study of teachers' actions and thinking as they engage in teaching intended to promote flexible mathematical thinking. The results suggest that signs of script restructuring and construction can be investigated post-hoc from textual accounts, scripts may have a considerable influence on teachers’ actions and thinking, and by engaging in teaching practice in real-life settings and reflecting on these accumulating experiences, processes leading to script development may be initiated. The results suggest that the analytic framework developed is functional and robust, paving the way for future investigations with larger samples. This study provided a more profound understanding of how online in-service education can support teachers to develop scripts supporting their competences to teach mathematical flexibility.