The Coherence of Group Scheme of the High Initial Ability Students Based on Cognitive Style

Abstract

Teaching and learning deductive proof is one of the most important goals in mathematics education. According to the APOS theory, learning a concept is facilitated when students have constructed an adequate APOS mental structure for the concep. There are characteristics differences between field-dependent and field-independent students in responding to tasks to construct proofs. The purpose of this study was to analyze the coherence of the group scheme constructed by students with the high initial ability based on cognitive style to construct \xa0proofs. This study was a qualitative. The research subjects were determined by the purposive sampling. Data collection using test and in-depth interviews. The credibility of data was carried out using triangulation. Data analysis used Miles and Huberman s model. The results showed that the FI and FN Subjects had thematized the group scheme and were coherent, while the FD Subject had thematized the group scheme but was not coherent. Pengajaran dan pembelajaran bukti deduktif dalam matematika merupakan salah satu tujuan terpenting dalam pendidikan matematika. Menurut teori APOS (Aksi, Proses, Objek, Skema), belajar suatu konsep terfasilitasi apabila siswa telah mengkonstruksi struktur mental APOS yang memadai untuk konsep tersebut. Ditinjau dari gaya kognitifnya, ada perbedaan karakteristik antara mahasiswa field-dependent dan field-independent dalam merespon tugas yang memerlukan kemampuan mengkonstruksi bukti. Tujuan penelitian ini adalah menganalisis koherensi Skema grup yang dikonstruksi mahasiswa dengan kemampuan awal mengkonstruksi bukti adalah tinggi dan gaya kognitif FI, FN, FD.\xa0 Penelitian ini dirancang sebagai penelitian kualitatif. Subjek penelitian ditentukan dengan teknik purposive sampling. Teknik pengumpulan data menggunakan teknik tes dan wawancara mendalam.\xa0 Derajat kepercayaan data dilakukan dengan teknik pemeriksaan triangulasi.\xa0 Analisis data selama di lapangan mengggunakan model Miles dan Huberman. Hasil penelitian menunjukkan Subjek FI dan FN sudah mentematisasi Skema grup dan sudah koheren, sedangkan Subjek FD sudah mentematisasi Skema grup namun belum koheren.