An investigation of 8th grade students' knowledge construction process for the surface area of a right circular cone according to RBC+C model

Objective: This research was conducted to examine the knowledge construction processes of 8th grade students for the surface area of a right circular cone using the RBC+C model. Material and Methods: Case study, one of the qualitative research methods, was used in the study. The research was carried out with three 8th grade students with a high level of success in mathematics, studying at a public school in the Köşk district of Aydın province. An interview form with three questions prepared by the researcher was used as a data collection tool in the individual interviews with the students. Three different data collection methods were used in the study, namely clinical interview, observation and document analysis. Content analysis of the obtained data was performed by according to the RBC+C model. Results: The findings show that all students recognize the cone, net of the cone, and the geometric shapes that make up the cone. In addition, each student consolidated this formula by constructing a general formula for the surface area of the cone. The students constructed a new mathematical structure by recognizing and building with the knowledge that the arc of the circle segment forming the lateral surface and the circumference of the base are equal in length. However, only one student constructed a second general formula giving the surface area of the cone by building with this mathematical structure and consolidated this formula. Conclusion: It was seen that the students easily performed the process of recognizing and building the surface area of the cone while constructing the knowledge of the surface area, and they constructed the surface area formula of the cone by abstracting.