Teaching and Learning Proofs of the Pythagorean Theorem during Distance Learning and in the Flipped

Abstract

This paper presents the findings of two design research cycles on learning and teaching different proofs of the Pythagorean theorem in German secondary schools during distance learning in the first research cycle and a flipped classroom in the second research cycle. The study explores students' difficulties when learning proofs in the different scenarios by analyzing students' proof schemes, occurring error patterns, the students' descriptions of their proof comprehension, and evaluations of the learning scenarios. The findings indicate that typical difficulties occur less in the flipped setting, especially for students with a low or average level of prior knowledge. Further analysis of the evaluation of the learning activities suggests that this can be attributed to the implemented adaptations of the learning scenario when changing it from a distance learning setting to a flipped learning setting, in particular, the opportunity to work collaboratively and direct support the teacher. These results have implications regarding the potential of the flipped classroom as a way for educators to integrate instructional approaches they developed during the COVID-19 pandemic into their in-person teaching in the future.