The process of mathematics students’ reflective abstraction in solving continuous random variable problems in the probability course

Abstract

Reflective abstraction is a mental mechanism in mental constructs in which all the structures of mathematical logic are developed in the mind of the individual. The mental mechanisms in question are interiorization, coordination, reversal, encapsulation, and generalization. This research is classified as exploratory research with a qualitative descriptive approach. This research data was taken from three fifth-semester mathematics students. The instruments used in this study were researchers as key instruments, essay tests, and interview guidelines. Data analysis included: 1) preparing the data for analysis, 2) reading the entire data, 3) encoding the data, 4) describing the data and presenting it in the narrative, and 5) interpreting the data and testing the validity of the data using data triangulation. The research found that (1) The first participant went through four components of reflective abstraction: interiorization – coordination – encapsulation – generalization. (2) The second participant went through five components of reflective abstraction thinking namely interiorization – coordination – reversal – encapsulation – generalization. (3) The third participant failed to solve the problem because the thought process in his mental mechanism had not yet manifested coordination, encapsulation, and generalization. Researchers found that the mental construction that the first participant had gone through could illustrate that the minimum mental construction that must be passed in solving the problem of continuous random variables required components- interiorization, coordination, encapsulation, and generalization.