PENALARAN PROPORSIONAL DALAM MENYELESAIKAN MASALAH MULTIPLIKATIF TIPE PRODUCT OF MEASUREMENT

Abstract

This study aims to explore students’ proportional reasoning in solving multiplicative problems on products of measurement type. Three 8 grade students of Public Junior High School 21 Malang were being purposively studied. The sampling technique is also called as the judgement sampling. Data then was being analyzed in three steps: data reduction, data presentation, and conclusion drawing/verification. The data were studied and analyzed based on Bexter’s and Junker’s Constructions of Proportional Reasoning theory consisting 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. Result shows that students with low capability (S1) solved problems by registering the number of first measurement then pair it with second measurement by summing the two measurements identified as early attempts at quantifying phase. It is also found that students with moderate capability (S2) solved the problem by registering all existing possibilities and then summing them all, concluding them qualified as being in recognition of multiplicative relationships phase. Moreover, students with high capability (S3) solved the problem by listing the number of the first measurement then multiplying it with the second measurement, qualifying them as being in the accommodating covariance and invariance phase in proportional reasoning.