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Flipped classroom (FC) pedagogical frameworks have recently gained considerable popularity, especially at secondary school levels. However, there are rich opportunities to explore FC at tertiary levels, but progress on the area requires instructors' attention to well-designed tasks for students' collaborative learning. Realistic Mathematics Education (RME) provides a foundation for the development of such tasks. This article advances research on the role of task design in a FC context by considering how RME heuristics may be developed to include the out-of-class phase, where students prepare for in-class work with videos. This adaption, named flipped RME classroom design, is explored through two realizations of such a design with a group of computer engineering students during their first year of studying compulsory mathematics. Thematic analysis of the classroom observations shows that students' modelling activity in-class is supported by the design of an out-of-class component in combination with teacher guidance of students' modelling activity.

This study explores contradictions that emerge when utilising a flipped classroom approach to university mathematics education. The work uses Activity Theory and its principle of dialectical contradiction as a theoretical framework to identify and analyse contradictions that arise in flipped mathematics classrooms for engineering students. Data was collected mainly by means of video recording of classroom activities and interviews with two cohorts of first-year engineering students in a Norwegian university over two years. An inductive approach to data analysis based on the interaction between the theoretical framework and the empirical data is used to provide evidence about the contradictions. The results show that contradictions manifest themselves as tensions in flipped mathematics classrooms. They emerge at different activity levels and affect student learning of mathematics. The aim of the study is to address the lack of research on tensions and contradictions in flipped mathematics classrooms at the university level.

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