PROPORTIONAL REASONING: INSIGHTS FROM STUDENTS' EARLY ATTEMPTS AT QUANTIFYING IN SOLVING MATHEMATICAL LITERACY PROBLEMS

Abstract

This research aims to explore students' proportional reasoning at the early stage of quantifying, when students face proportional situations, especially in mathematical literacy problems. This research uses a qualitative research approach involving grade 9 junior high school. Data was collected by providing mathematical literacy problems containing proportional situations and conducting in-depth interviews with research subjects. The research results show that students in the early stages of quantifying begin to identify critical variables, recognize regularities, and develop plans to solve problems. Students apply inappropriate addition relationships in proportional situations, add or subtract numbers without understanding the concept of comparison, and have a sense of comparing sizes that are bigger and smaller. Still, students have limitations in understanding the concept of proportionality, especially in recognizing when comparison should be used. Students try to identify comparative patterns, but have difficulty connecting patterns to multiplicative forms. They can conclude, but the conclusions are wrong due to limitations in understanding the concept of proportionality, which results in inaccurate results. This study provides a novel contribution by explicitly focusing on the "early attempts at quantifying" stage, a crucial yet under-examined phase in proportional reasoning development. The findings fill a gap in understanding how students transition from additive to multiplicative reasoning when faced with real-world mathematical problems. The implication is that assistance is needed in the form of exercises that increase students' understanding and sensitivity to multiplicative situations and relationships between variables in solving mathematical literacy problems.