How Are Students' Prior Knowledge Differentiate Analytical Thinking Process in Identifying the Convergence of Real Number Sequences?

Abstract

Analytical thinking is needed in solving complex problems, including mathematics. One of them is identifying the convergence of real number sequences. The analytical thinking process includes three cognitive processes, namely differentiating, organizing, and attributing. It will allow a student to build knowledge by connecting experience with prior knowledge. Until now there has been no study that examines the analytical thinking process in terms of students' prior knowledge. This present study aims to describe students’ analytical thinking process in identifying the convergence of real number sequences in terms of students' prior knowledge. This descriptive study with a qualitative approach involved twenty-one students as subjects consisting of students with low, medium, and high prior knowledge. Data were collected using tests and interviews. The triangulation method was carried out as a data validation process. Data analysis used the constant comparative method. The results showed that the higher the students' prior knowledge, the more detailed the differentiating process was. The organizing and attributing processes are carried out depending on the results obtained in the differentiating process. This is important to understand to be able to facilitate the development of analytical thinking skills by paying attention to students' prior knowledge.