Integral (antiderivative) learning with APOS perspective: A case study

Abstract

The objective of this study is to determine students’ learning barriers in understanding integral concepts through their thinking processes with the perspective of APOS theory (Action, Process, Object-Scheme). This research applied qualitative research with a case study method. The samples of this research were 19 civil engineering students who had contracted calculus courses and who had been given a written test. The results of the written test were divided into three different categories – they are comprehension ability is high (score ≥ 75), medium (60 ≤ Score <75) and low (score < 60). Deep interviews were conducted with three representative students who took the written test and met the criteria for each group. The results of the interviews showed that students in the high category still had conceptual ontogenic learning obstacle despite passing the APOS path. Students in the moderate category be able to reach the encapsulation stage but they had not been able to de-encapsulate it to the process. They had conceptual and epistemological ontogenical learning obstacles. Whereas the low category students had the tendency to only reach the action stage and had difficulty in doing initial de-encapsulation due to lack of learning experience in the prerequisite materials. The learning obstacles they experienced were psychological and conceptual-ontogenical learning obstacles. Aggregately, the students tended to experience conceptual ontogenic learning obstacle. The result of this study is expected to be used as a basis for designing a hypothetical learning trajectory in future research.