Penalaran Proporsional Siswa Kelas IV Sekolah Dasar dalam Menyelesaikan Masalah Missing Value Perkalian dan Pembagian

Abstract

This study aims to describe the proportional reasoning of fourth-grade students in solving missing value problems in multiplication and division contexts. A descriptive qualitative approach was employed involving 26 fourth-grade students at SDN Lowokwaru 5 Malang City. Data were collected through written tests, observations, interviews, and documentation. Data analysis was conducted using the Miles and Huberman model, including data reduction, data display, and conclusion drawing. The analysis focused on students’ problem-solving strategies (scaling, unit rate, cross-multiplication, and additive strategies) and five stages of proportional reasoning, namely understanding the situation, forming representations, identifying multiplicative structures, applying solution strategies, and evaluating ratio equivalence. The results indicate that most students tend to use cross-multiplication procedurally without fully understanding the underlying concepts. In multiplication contexts, students generally demonstrate better performance by applying scaling strategies. However, in division contexts, students encounter significant difficulties, particularly in determining unit rates, and tend to rely on additive reasoning. These findings suggest that most students are still at the pre-proportional to early proportional reasoning stages. This study highlights the importance of strengthening conceptual understanding in mathematics learning at the elementary school level.