A study of proportional reasoning: Tackling missing value and numerical comparison challenges

This study aims to examine students’ proportional reasoning in solving multiplicative problems. Three seven-grade students from SMPIT Al-Fahmi Palu were purposively selected using judgment sampling. Data analysis was conducted in three stages: data reduction, data presentation, and conclusion drawing/verification. The analysis was based on Bexter and Junker’s theory of proportional reasoning, which consists of five stages: (1) qualitative, (2) early attempts at quantifying, (3) recognition of multiplicative relationships, (4) accommodating covariance and invariance, and (5) functional and scalar relationships. The results show that students with low ability (R1) solved problems by recording the first measurement and pairing it with the second measurement through addition, indicating the early attempts at quantifying stage. Students with moderate ability (R2) solved the problems by listing all possible combinations and summing them, indicating recognition of multiplicative relationships. Meanwhile, high-ability students (R3) solved the problems by multiplying the first and second measurements, indicating they were in the accommodating covariance and invariance stage of proportional reasoning.