Researching cognitive extensions of mathematical subjects in high school students and presenting them with statistical methods

Today's societies consist of individuals who live in the information age. The most important feature of the information age is that the increase in information is extremely fast. In order for societies to follow this speed, information must be coded permanently and quickly. The most important thing that provides this is the correct perception specific to the person. Students must first achieve this in mathematics classes. In this respect, mathematics has become an indispensable part of education. Although some sources summarize the most basic goals of mathematics education at the secondary school level as "perceiving the concept of proof", "being able to comprehend the difference between proven scientific results and dogmas", "perceiving the necessity of actions based on geometric concepts and models", "forming abstract concepts and abstract thought structure", the truth of the matter always lies in the details. The purpose of this study is to try to examine the cognitive extensions left in the student by the mathematics course taught in secondary education. The main idea of our study is that "If the same or similar cognitive extension of the teacher who teaches mathematics in a subject is formed in the student, the student's learning skills in this subject can become more active." However, the answers given to some questions directed to the person can be used as a measurement to some extent. For this reason, we decided that the most appropriate method to be used in the study would be a clinical interview. After obtaining the necessary permissions for the study, a total of 36 students were interviewed. During the interview, questions were asked of the students about their opinions and perception patterns on five basic subjects, namely geometric concepts, numbers, arithmetic operations, function structures and trigonometry, and the students' statements were recorded. In addition, in order to facilitate measurement in the simulation, 16 two-choice questions were asked and they were asked to emphasize the option that was closest to them and why. As a result of the study, kappa statistics were examined and a comparison was made.