Middle School Students’ Proportional Reasoning Ability in Solving Proportional and Non-proportional Problem

Abstract

The objective of this descriptive qualitative study is to describe students' proportional reasoning ability in solving each type of proportional problem, namely missing-value problem, numerical comparison problem, and qualitative comparison problem. A non-proportional problem was also included in this study to assess students' ability in one of the indicators used to measure proportional reasoning ability. The instrument used in this study consists of mathematical word problems on the proportion concept. The participants involved nine eighth-grade students, who were chosen from a total of 49 eighth-grade students at a school in Bandung City. These students were selected using a technique known as purposive sampling, by looking at the answers of students who best represent the answers of other students. The gathered data were analyzed using content analysis and narrative analysis techniques. According to the results, students appeared to have difficulty solving proportional problems of all types using proportional reasoning. Students are still struggling with distinguishing between proportional and non-proportional situations, as well as direct and inverse proportions. Furthermore, students often encounter difficulties when attempting to solve numerical comparison and qualitative comparison problems. This might be a consequence of students' lack of experience in solving these types of problems. Another tendency is the use of the cross-multiplication algorithm in solving missing-value problems without knowing the purpose of using the algorithm.