Leveraging the design heuristics of realistic mathematics education and culturally responsive pedagogy to create a richer flipped classroom calculus curriculum

While the number of studies of flipped classrooms has increased, they have primarily addressed the efficacy of using such an approach on student outcomes, often failing to account for the classroom activities and learning theories used to design the curriculum. This study begins to fill this gap in the literature by uniting the at-home video and in-class curricular components of the flipped classroom via design heuristics that empower students to critically think about mathematical problems individually before engaging with the task in a collective environment. To that end, we illustrate how elements of the instructional design theory of Realistic Mathematics Education and Culturally Responsive Pedagogy influenced the written and hidden curriculum and how those considerations were then experienced by the students as part of the enacted components of the curriculum. The context of the study is a 2-week classroom teaching experiment covering topics in trigonometry and vectors for 27 calculus students at a Norwegian university.