Exploring the cognitive process of prospective mathematics teachers in constructing a graph
Authors: Afriyani Dona , Yuberta Kurnia Rahmi 
Published: July 2019

[English]: This article aims to analyze the strategies and cognitive process of prospective mathematics teachers (PMTs) in constructing graphs of composition function. Forty-four PMTs participated in graph construction tasks (GCT) of composition function. Four of them were purposively selected as the subjects. Data were collected through subjects' works on GCT and interviews based on their works. Data analysis started with organizing subjects' construction of the graph and transcribing the results of the interview. We then explored and coded the subjects' constructed graphs, followed by describing the subjects' strategies and structure of the cognitive process of graph construction and establishing themes, representing and reporting the findings with tables, schemes and narratives, interpreting the findings, and validating the accuracy of the findings by triangulation of the data sources. We found (1) two strategies used by the subjects in constructing graph namely with-translation and without-translation; and (2) the translation process in constructing the graphs begins by unpacking the source representation, preliminary coordination, constructing the target representation and end with determining the equivalence between the source representation and the target representation. The findings indicate that there are transfer variations in conceptual content from micro-concepts of source representation to micro-concepts of target representation. The variations are caused by the differences in the types of mapping carried out at the initial coordination stage.
Keywords: Cognitive process, Graph construction, Prospective mathematics teacher, Composition function
[Bahasa]: Artikel ini bertujuan menganalisis strategi dan proses kognitif mahasiswa calon guru matematika dalam mengonstruksi grafik fungsi komposisi. Empat puluh empat calon guru menyelesaikan tugas konstruksi grafik (GCT) fungsi komposisi kemudian empat orang dipilih sebagai subjek. Data penelitian dikumpulkan melalui hasil kerja subjek pada GCT dan wawancara berdasarkan hasil kerja. Analisis data dimulai dengan mengelompokkan hasil konstruksi grafik oleh subjek dan membuat transkrip wawancara. Peneliti kemudian mengeksplorasi dan membuat kode hasil konstruksi grafik, menjelaskan strategi dan struktur proses kognitif subjek dalam mengonstruksi grafik, membuat tema berdasarkan strategi dan proses kognitif. Selanjutnya, peneliti menggunakan tabel, skema dan narasi untuk menampilkan dan melaporkan temuan penelitian, menafsirkan temuan penelitian dan melakukan validasi hasil penelitian dengan triangulasi sumber data. Kami menemukan (1) dua strategi yang digunakan oleh subjek dalam membangun grafik yaitu dengan-translasi dan tanpa-translasi; dan (2) proses translasi dalam mengonstruksi grafik dimulai dengan membongkarrepresentasi sumber, koordinasi awal, membangun representasi target dan diakhiri dengan menentukan kesetaraan antara representasi sumber dan representasi target. Temuan menunjukkan bahwaada variasi transfer dalam konten konseptual dari mikro konsep representasi sumber ke mikro konsep representasi target. Variasi disebabkan oleh perbedaan dalam jenis pemetaan yang dilakukan pada tahap koordinasi awal.
Kata kunci: Proses kognitif, Konstruksi grafik, Calon guru matematika, Fungsi komposisi