Analyzing students’ abstraction in learning common tangent lines of two circles based on cognitive styles
Authors: Sumekar Wirani , Nurhasanah Farida , Sutopo Sutopo 
Published: March 2020

[English]: This study was aimed to describe the abstraction process of students with different cognitive styles in learning common tangent lines of two circles using recognizing, building-with, and construction (RBC) model. This qualitative research collected data through questionnaires, written tests, and task-based interviews. Eight students with field-dependent and field-independent were involved as the subjects. The interview transcripts were analyzed and grouped into cognitive actions of the RBC model. Findings showed that to reach the stage of construction activities, field-dependent students tend to need guidance and more time in recognizing and constructing the concept of a common tangent of two circles using their prior knowledge. Meanwhile, field-independent students tend to directly recognize and construct the concept using their prior knowledge so that they successfully constructed the concept of common tangent lines of two circles. This study shows that (1) field-dependent students use their prior knowledge that relates to the concept of common tangent lines of two circles less than field-independent students who tend to be able to use most of their prior knowledge relevant to the concept of common tangent lines of two circles, and (2) students who has similar cognitive style may not show the same success in abstraction process.

Keywords: Abstraction, Circles, Common tangent line, Cognitive style, RBC Model

[Bahasa]: Penelitian kualitatif ini bertujuan untuk mendeskripsikan abstraksi siswa SMP dengan gaya kognitif berbeda dalam mempelajari garis singgung pada dua lingkaran yang dianalisis menggunakan model RBC (Recognizing, Building-with, Construction). Data penelitian dikumpulkan melalui angket, tes tertulis, dan wawancara berbasis tugas. Delapan siswa dengan gaya kognitif field-dependent dan field-independent dipilih sebagai subjek penelitian. Data penelitian dianalisis berdasarkan rekaman wawancara yang sudah ditranskrip dan dikelompokkan berdasarkan tindakan kognitif model RBC. Hasil penelitian menunjukkan bahwa siswa field-dependent cenderung memerlukan petunjuk dan waktu lebih lama untuk mengenali dan membangun konsep garis singgung pada dua lingkaran melalui pengetahuan terdahulu hingga sampai pada aktivitas konstruksi. Sementara siswa field-independent cenderung langsung mengenali dan membangun konsep garis singgung pada dua lingkaran melalui pengetahuan terdahulu sehingga berhasil mengkonstruksi konsep garis singgung pada dua lingkaran. Penelitian ini menunjukkan bahwa (1) siswa field-dependent lebih sedikit menggunakan pengetahuan terdahulu yang berkaitan dengan konsep garis singgung dua lingkaran daripada siswa field-independent yang cenderung dapat melihat sebagian besar pengetahuan lama yang relevan dengan konsep garis singgung dua lingkaran, (2) siswa dengan gaya kognitif yang sama belum tentu menunjukkan keberhasilan yang sama pada proses abstraksi.

Kata kunci: Abstraksi, Dua lingkaran, Garis singgung, Gaya kognitif, Model RBC