The role of students’ affective resources and topic knowledge on performance in parallel geometry proof and calculation tasks—evidence from a cross-cultural study

Abstract Complex mathematical practices, such as proving and calculating in geometry, draw on a range of students’ individual resources and may pose substantial challenges for students. The development of these resources and the skills required to enact these practices are affected by the cultural context and the role of proof in the mathematics curriculum. Drawing on cultural and curricular differences regarding the role of proof between Taiwan, as an East Asian country, and Germany, as a Western country, we compare students’ cognitive and affective resources for geometry calculation and proof, as well as their effects on performance between the two contexts in an experimental study with 519 secondary school students. The results showed only a few significant differences between the two countries, which can be explained by their cultural characteristics. For example, country-related differences in geometry proof and calculation performance were particularly pronounced for students with above-average geometry topic knowledge. The different role of proof in the curricula in the two countries resonates with significant differences in performance between proof and calculation performance in Germany, but not in Taiwan.