Toward a set of design principles for mathematics flipped classrooms: A synthesis of research in mathematics education

Abstract This paper analyzed the journal publications of mathematics flipped classroom studies in K-12 and higher education contexts. We focused specifically on a set of flipped classroom studies in which pre-class instructional videos were provided prior to face-to-face class meetings. We examined the following four major issues: (a) the types of out-of-class and in-class instructional activities used, (b) the effect of flipped learning on student achievement, (c) the participant perceptions of flipped classroom benefits, and (d) the main challenges of flipped classroom implementations. A meta-analysis of 21 comparison studies showed an overall significant effect in favor of the flipped classroom over the traditional classroom for mathematics education (Hedges' g = 0.298, 95% CI [0.16, 0.44]), with no evidence of publication bias. A broader research synthesis of 61 studies revealed that the flipped classroom approach benefited student learning in three main aspects: increasing in-class time for task/practice, integrating new knowledge with existing beliefs, and real-time feedback. The two most frequently reported flipped classroom challenges were students' unfamiliarity with flipped learning and significant start-up effort on the part of instructors. We hence propose a set of design principles to help foster the transition to the flipped classroom and improve the out-of-class and in-class learning designs. This set of design principles can also provide a more focused agenda for future research to examine the effect of the flipped classroom approach on student learning and motivation.