Analysis the proportional reasoning abilities of senior high school students in solving mathematical problems

Abstract

Penelitian ini bertujuan untuk menganalisis kemampuan penalaran proporsional siswa SMA dalam memecahkan masalah matematika. Subjek pada penelitian deskriptif kualitatif ini adalah 3 siswa kelas X SMA Negeri 2 Salatiga berkemampuan matematika tinggi. Instrumen utama adalah peneliti sendiri, didukung oleh instrumen tes dan pedoman wawancara. Data hasil tes dan wawancara dianalisis menggunakan langkah reduksi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan bahwa ketiga subjek memiliki kemampuan penalaran proporsional yang berbeda dalam memecahkan masalah matematika. Kemampuan penalaran proporsional subjek S cenderung berada pada level 1 dengan menunjukkan strategi menggunakan gambar dan membuat perbandingan kualitatif. Kemampuan penalaran proporsional subjek F cenderung berada pada level 2 dengan menunjukkan strategi menghubungkan model melalui perhitungan numerik, menggunakan unit komposit, dan menggunakan penalaran kuantitatif. Kemampuan penalaran proporsional subjek M cenderung berada pada level 3 dengan menunjukkan strategi menggunakan cara formal dan mengetahui hubungan invarian dan kovarian. Ketiga subjek menunjukkan kemampuan penalaran proporsional pada level 0 dalam memecahkan masalah yang memerlukan perbandingan aditif dan multiplikatif dengan hanya menggambarkan situasi perubahan dalam pandangan aditif.

Student Proportional Reasoning on Missing Value Problems Based on Multiplicative Concepts

“…When solving a missing value problem, students fail to remember to apply the concept of proportion because the concept is not well embedded in the students' memory. Therefore, considering the importance of the concept of proportion for students, teachers need to pay serious attention to building their proportional reasoning (Permatasari et al, 2017;Sari & Mampouw, 2019). Instead of presenting them simultaneously, the majority of mathematics teachers present the types of proportion problems separately while ideally in helping students solve proportion problems, teachers should explain proportions using a multiplication strategy that involves a situation of proportions.…”

“…If students' thinking processes can be identified, the mistakes made by students can also be identified. The teacher also plays an important role in supporting the development of students' mathematical thinking (Sapti et al, 2019;Sari & Mampouw, 2019). It is important for the teacher to improve teaching and class preparation by continuing to present students with the concepts of ratio and proportion that were learned at previous meetings.…”

“…Students who lack mastery in proportional reasoning tend to start back to additive reasoning when presented with proportion problems. Students still have difficulty in distinguishing proportional and non-proportional problem statements (Sari & Mampouw, 2019). The level of students' proportional reasoning skills is still low before being taught problem-solving strategies (Şen & Güler, 2017).…”