Examination of the Abstraction Process of Complex Number Knowledge

The aim of this study was to examine the abstraction process of tenth grade students' complex number knowledge. A semi-structured interview was held with two students who were successful at mathematics and who voluntarily participated in the study. In this interview, the students faced three different research problems prepared by the researcher in order to reveal the students' knowledge formation processes. The students studied these research problems together. In the meantime, their cognitive processes related to recognizing, building-with, and constructing of discourses was analysed. The analyses indicated that both of the students recognized and built-with the preliminary knowledge necessary for them to construct the knowledge of complex numbers. Moreover, it was understood that one of these students recognized and build-with their previous knowledge of linear functions, coordinate systems, and parallel displacement. In conclusion, it could be said that this student constructed the knowledge of complex plane.