Analysis of The Occurrence of Reversible Reasoning for Inverse Cases: A Case Study on The Subject Adjie
Abstract
Background. Student reasoning in learning mathematics contributes significantly to the achievement of student mathematics learning outcomes. The main objective of this study is to investigate the process of reversible reasoning in students for inverse problems, in the case of Adjie (Ad). The research method used to reveal the reversible reasoning in Adjie's case using descriptive qualitative research methods. Sampling was carried out using purposive sampling technique where the research sample was selected based on reversible reasoning criteria. Retrieval research data uses the results of students' mathematical work, think aloud, interviews, and the components that cause reversible reasoning. The results of our study found that the process begins with an obstacle that causes Ad to be unable to continue the resolution process, resulting in a metacognition process by analyzing the problem again analytically and developing other heuristic strategies. Ad shows a change in perspective where he initially interpreted inverse as the act of swapping independent and dependent variables and switched to interpreting inverse as the opposite of a function process involving analogy and image representation. The contribution of this research provides knowledge that reversible reasoning can occur in understanding and solving mathematical problems in inverse material.
Latar belakang. Penalaran siswa dalam pembelajaran matematika memberikan kontribusi yang signifikan terhadap pencapaian hasil belajar matematika siswa. Tujuan utama dari penelitian ini adalah untuk menyelidiki proses penalaran reversibel pada siswa untuk masalah invers, dalam kasus Adjie (Ad). Metode penelitian yang digunakan untuk mengungkap alasan reversibel pada kasus Adjie menggunakan metode penelitian deskriptif kualitatif. Pengambilan sampel dilakukan dengan menggunakan teknik purposive sampling dimana sampel penelitian dipilih berdasarkan kriteria penalaran yang dapat dibalik. Pengambilan data penelitian menggunakan hasil kerja matematis siswa, think aloud, wawancara, dan komponen penyebab reversible Reasoning. Hasil penelitian kami menemukan bahwa proses tersebut diawali dengan adanya kendala yang menyebabkan Ad tidak dapat melanjutkan proses penyelesaiannya sehingga terjadi proses metakognisi dengan menganalisis kembali permasalahan tersebut secara analitis dan mengembangkan strategi heuristik lainnya. Iklan menunjukkan perubahan cara pandang dimana awalnya ia mengartikan invers sebagai tindakan menukar variabel independen dan dependen dan beralih mengartikan invers sebagai kebalikan dari proses fungsi yang melibatkan analogi dan representasi gambar. Kontribusi penelitian ini memberikan pengetahuan bahwa penalaran reversibel dapat terjadi dalam pemahaman dan penyelesaian masalah matematika pada materi invers.
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