Matematik Öğretmen Adaylarının Ckȼ Teorisi Bağlamındaki Fonksiyon Anlayışlarının Kanıt Şemaları ile İncelenmesi

Abstract

In this study, the aim is to analyze the knowing of prospective mathematics teachers regarding the concept of functions in the best possible way and to reveal their mathematical thinking using Balacheff's cK¢ (conception, knowing, concept) theory. The study examines all conceptions in the proof process and analyzes them with proof schemes expressed in the operators associated with these conceptions. A case study, one of the qualitative research methods, was used in this study. The study was conducted with eight students, two from each grade level, studying in the mathematics teaching program at a state university in Ankara during the 2022-2023 academic year. Two theorems related to functions were presented to the teacher candidates in written form online, and their responses were collected in writing. The written responses of the teacher candidates, video recordings of their discussions during the solution process, and the researcher’s observations were analyzed as the study's data. To understand the students' thinking styles and logical steps, control structures were attempted to be determined from their explanations, focusing on the incorrect operators they frequently used. The proof schemes used by the students throughout the entire proof process were identified. In the first theorem, it was observed that first, second, and third-year students predominantly had external conviction and experimental proof schemes. First and fourth-year students were found to have analytical (inferential-deductive) proof schemes. In the second theorem, it was observed that students had transformational and ritual proof schemes.