Fragmentation of thinking structure and its impact to students’ algebraic concept construction and problem solving

Abstract

The term “fragmentation” is adopted from the term of data storage which is used inefficiently in a computer. The analogy of fragmentation in thinking process is inefficient phenomenon of information storage within the brain which obstructs the process of reconstructing and solving mathematical problems. This descriptive qualitative research aims to describe the fragmentation of thinking structure and its impact on concept construction and algebraic problem solving in Junior Highs School Students. The subjects consisted of 8th grade students of junior high school in Surakarta, Indonesia. Data of this research were collected using a task-based in-depth interview method. This research shows that the students have the following fragmentation of thinking structure: (1) pseudo construction, which occurs when the students’ answers seem right even though the reasoning are wrong, (2) hole construction, which occurs when students do not thoroughly understand the concepts of addition, multiplication, algebraic power forms, and mathematical problems-modelling, (3) mis-analogical thinking, which occurs when students consider an algebraic form to be the same as another algebraic form.