Exploring students' proportional reasoning in mathematical literacy problem solving: recognition of multiplicative relationship strategies

Abstract

Introduction. A multiplicative relationship represents the association between two or more variables in the form of multiplication. For example, when one variable increases, the other variable also escalates proportionally. Accordingly, it is important for students to have the ability to identify the pattern of multiplicative relationships, describe them in the form of equations or comparisons, and apply them in different situations. This study describes the strategies used by students in recognizing multiplicative relationships, particularly in solving mathematical literacy problems containing proportional situations. Study participants and methods. The research was conducted in three junior high schools located in Malang, Indonesia, involving 191 ninth-grade students. They were asked to work on a mathematical literacy question, and then their answer sheets were corrected and grouped based on the developmental stage of proportional reasoning, particularly in recognizing multiplicative relationships. Furthermore, the subjects were interviewed in-depth concerning their experience in solving literacy problems in proportional situations. This study used a qualitative approach with a phenomenological research type. the subject's experience was investigated holistically, along with the appearing phenomenon. The garnered data were interpreted through continuous reflection and analysis for a deeper understanding. The results were then summarized. Results. In this study, two variations of strategies have been identified being used by students at the stage of recognizing multiplicative relationships in solving mathematical literacy problems, namely the multiple strategies and the pattern strategy. This finding serves as a valuable contribution to understanding students' strategies and behaviors in recognizing multiplicative relationships, which has not been revealed in previous studies. The main difference between these two strategy variations lies in the approach used in solving the problem. The multiples strategy emphasizes the conceptual linking of quantity values between objects, relying on the conceptual shifts that transpire as students navigate through their additive reasoning steps within the framework of multiplication. In this case, students need to comprehend various number concepts and number relationships, with frequent focus on multiplication as a form of repeated addition. On the other hand, pattern strategies rely on students' ability to match patterns, use the arrangement of numbers constituting the pattern, and relate them to other patterns in solving problems. Practical significance. The results of this study serve as a crucial reference for more effective and efficient mathematics learning formulation for improving students' proportional reasoning.