The Thinking Process of Students in Proving Ceva's Theorem in Basic Geometry Course

Abstract

. The thinking process is crucial in identifying students' challenges in formulating logical arguments, particularly when proving geometric concepts such as Ceva's Theorem. This study investigates the cognitive processes of students with high and medium mathematical ability to solve proof problems related to Ceva's Theorem. Adopting a qualitative approach, the research employed a case study design, utilising data collection techniques including tests, interviews, observations, documentation, and triangulation. The research subjects comprised two undergraduate students of Mathematics Education, representing a medium and high mathematical ability category. The research findings revealed that students with high mathematical ability progressed through assimilation, accommodation, and equilibrium stages in proving Ceva's Theorem. In contrast, students with moderate mathematical ability experienced the disequilibrium phase first before advancing to assimilation, accommodation, and equilibrium. The fundamental difference between these two groups lies in their ability to identify the question posed in the problem and correctly identify the theorem to be proved. This research provides valuable insights into the cognitive processes involved in mathematical proof, offering an in-depth understanding of how students approach the proof of Ceva's Theorem.