Students' learning obstacles in solving equivalent ratio problems: a developmental perspective on proportional reasoning

Abstract

This study aims to analyze students’ learning difficulties in equivalent ratio problems from the perspectives of conceptual and procedural understanding, as well as to identify the factors contributing to these difficulties. The study employed a qualitative approach with a descriptive research design. Data were collected through diagnostic tests and in-depth interviews involving seventh-grade students at a junior high school in Tasikmalaya City. The data were analyzed through data reduction, data presentation, and conclusion drawing. The findings revealed that students continued to experience both conceptual and procedural difficulties in solving equivalent ratio problems. Conceptual difficulties were indicated by students’ inability to understand proportional relationships and their tendency to employ additive reasoning in situations requiring multiplicative reasoning. Meanwhile, procedural difficulties involved errors in determining scale factors, the use of inappropriate solution procedures, and unsystematic problem-solving steps. These difficulties were influenced by weak conceptual understanding and learning practices that remained predominantly procedure-oriented. The findings highlight the importance of implementing equivalent ratio instruction that is more conceptual, contextual, and oriented toward developing students’ Proportional reasoning. 

Penelitian ini bertujuan untuk menganalisis kesulitan belajar siswa dalam menyelesaikan masalah rasio ekuivalen berdasarkan pemahaman konseptual dan prosedural serta mengidentifikasi faktor-faktor penyebabnya. Penelitian menggunakan pendekatan kualitatif dengan desain deskriptif. Data dikumpulkan melalui tes diagnostik dan wawancara mendalam terhadap siswa kelas VII di salah satu SMP di Kota Tasikmalaya, kemudian dianalisis melalui reduksi, penyajian, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa siswa masih mengalami kesulitan konseptual dan prosedural. Kesulitan konseptual ditandai oleh ketidakmampuan memahami hubungan proporsional serta kecenderungan menggunakan additive reasoning pada situasi yang memerlukan multiplicative reasoning. Kesulitan prosedural meliputi kesalahan menentukan faktor pengali, penggunaan prosedur yang tidak tepat, dan penyelesaian yang tidak sistematis. Kesulitan tersebut dipengaruhi oleh lemahnya pemahaman konsep dan pembelajaran yang berorientasi pada prosedur. Temuan ini menegaskan pentingnya pembelajaran rasio ekuivalen yang lebih konseptual, kontekstual, dan berorientasi pada pengembangan proportional reasoning siswa.