Fragmentation of thinking structures and learning independence in solving differential equation problems

Abstract

This study aims to describe the characteristics of fragmentation of students' thinking structures in constructing exponential equation material in terms of learning independence. The form of research used in this study is a mix-method study, where quantitative data is supported by descriptive qualitative data. Quantitative data collection in this study used an independence questionnaire test. The magnitude of the influence of learning independence and fragmentation of thinking can be seen from the R square value which shows 0.857 or 85.7%. While 14.3% is influenced by other variables that were not studied. In addition, from 48 questionnaire items with a sample of 40 students, the average results of students in each category were obtained, including those with high learning independence of 32.5%, moderate learning independence of 55%, and 12.5% in the low category of learning independence. The study is supported by qualitative data with the think aloud method and interviews. The forms of fragmentation of thinking structures that may occur include: Hole construction, pseudo construction, random structure and separate structure. The subjects in this study were 40 students taken using the purposive sampling method. Subjects To ensure the validity of the data, this study used the triangulation method to determine the suitability between the data from the think aloud method and those reinforced by the data from the interview method. The results of this study indicate that subjects with students with independent learning experience a form of fragmentation of the thinking structure including: construction holes, pseudo-constructions, random structures and separate structures. The characteristics of students with an independent learning style who experience fragmentation are: 1) construction holes are seen when students do not have an understanding of the concept of homogeneous differential equations, 2) Pseudo-constructions are seen when students experience fuzzy memory events, where the subject seems to remember the concept that has been learned but it turns out that the concept is not quite right, 3) Random structures occur when students ignore the requirements that must be met to become a form of equation that must be transformed integrally from homogeneous differential problems and 4) Separate structures occur when students cannot connect the knowledge they have to solve problems that have never been exemplified by the lecturer. The impact of the form of fragmentation experienced by students causes students to have difficulty in solving mathematical problems because the knowledge they have is only limited to memory.