Scaffolding through cognitive mapping based on diagnosing students difficulties in solving problem

Abstract

This study shows the diagnosis of difficulties faced by students when solving problems with a system of linear equations with three variables and efforts to overcome them by providing scaffolding interventions. The approach used in this study is qualitative. The sample selection using a purposive sampling technique was made by giving three math problems, the topic of a system of linear equations with two variables, then three students were selected to be the research subjects. The selection of students is determined based on the category of communication skills and low, medium, or high mathematical abilities. The research data were obtained from 3 sources: test sheets, semi-structured interviews, and the results of student work after scaffolding was given. Several research results show students' difficulties in solving three-variable linear equation systems problems based on Polya-based cognitive mapping: first, the difficulty in understanding the problem. This difficulty arises because of mental holes that students should not have at grade levels, such as knowledge of fractions, algebra, basic concepts of triangles, and others. Second: Difficulty compiling a solution. This can be seen when students cannot correctly model contextual problems into mathematical models. Third, the implementation of the complete plan can be identified through students' mistakes when performing arithmetical algebraic operations and applying appropriate mathematical rules/principles, the leading cause of which can occur due to inaccuracy and misconceptions about mathematical concepts. The researchers tried to overcome these problems by providing Level 2 scaffolding with the techniques proposed by Angirelli, including (explaining, reviewing, and restructuring).