Implementation of APOS theory to encourage reflective abstraction on Riemann Sum

Abstract

The purpose of this study is to explore the implementation of APOS (Action-Process-Object-Schema) in first-year students at higher education as a basis of instructional learning in Riemann Sum to emerge the reflective abstraction. This is qualitative research, and data were taken by tests, interviews, and observation. To construct the Riemann Sum understanding, students came through the Action by estimating the area under the curve with various shapes, looking for the area under the curve through several partitions, and make repetitions. The Process was built by interiorizing the previous action on n partitions. The Object was constructed through the encapsulation mechanism by determining the existence and value of the limit for the Riemann Sum. Schemes occurred through thematization by applying Riemann Sum to contextual situations involving functions of distance and time. The results showed that the success of APOS implementation was determined by genetic decomposition, assistance, reinforcement of preconditions and reinforcement of concepts by lecturers. Some effective scaffoldings to help the construction of reflective abstractions in Riemann Sum are worksheets and guided question from educator.