Investigation of Secondary School Students' Processes of Constructing Area and Volume Relations of Rectangular Prisms

The purpose of this study is to examine the knowledge construction processes of 5th grade students, who do not have any knowledge about the surface area and volume of the rectangular prism, within the framework of the observable epistemic actions of the RBC (Recognizing, Building-with, Constructing) abstraction model. This study was carried out according to the case study pattern, which is one of the qualitative research types. The study was carried out in the 2021-2022 academic year. For the research, six students were selected by the maximum diversity sampling method. Three homogeneous groups were formed and semi-structured interviews were conducted. An activity paper consisting of eight problems was used to obtain data. The obtained data were evaluated in the context of observable epistemic actions of RBC. Only a student with a low level of mathematics achievement couldn’t construct knowledge of the surface area of the prism. All students have found the number of unit cubes that can fit inside the rectangular prism. But three students with a high level of success were able to construct and use volume formulas. In the research, it has been seen that recognition and building-with actions are easier to perform than construction action. As the level of mathematics achievement decreased, the speed and success of abstraction decreased.