PROSES TRANSPOSISI DIDAKTIK MAHASISWA CALON GURU MATEMATIKA MELALUI DIDACTICAL DESIGN RESEARCH PADA MATERI HIMPUNAN - Jamilah, - (2021)
ABSTRAK Penelitian ini secara umum bertujuan untuk menghasilkan desain pembelajaran untuk membantu mahasiswa calon guru matematika melakukan proses transposisi didaktik pada materi himpunan. Metode penelitian yang digunakan adalah penelitian kualitatif dengan pendekatan fenomenologi hermeneutik. Desain penelitian yang digunakan adalah didactical design research (DDR) yang memuat tiga tahapan analisis, yaitu analisis prospektif, analisis metapedadidaktik, dan analisis retrospektif. Partisipan dalam penelitian ini terdiri dari 28 orang siswa kelas VII SMP, seorang guru bidang studi matematika kelas VII SMP, 3 orang mahasiswa semester VII dan 2 orang mahasiswa semester I, serta seorang dosen pengampu mata kuliah teori himpunan dan fungsi. Hasil penelitian ini memaparkan temuan pada masing-masing tahapan analisis. Pada tahap analisis prospektif ditemukan: (1) hasil analisis transposisi didaktik menunjukkan adanya kesenjangan concept image (CI) siswa dengan formal concept definition pada scholarly knowledge, bahkan dengan taught knowledge dan knowledge to be taught pada materi himpunan. Kesenjangan CI ini disebabkan karena adanya hambatan didaktik, hambatan ontogenik, dan hambatan epistemologi yang disebabkan oleh ketidaktepatan sajian materi maupun situasi didaktik yang dihadirkan; (2) susunan hypothetical learning trajectory (HLT) mahasiswa; dan (3) desain pembelajaran hipotetik yang memuat situasi didaktik, prediksi respon, dan antisipasi didaktik pedagogik (ADP). Pada tahap metapedadidaktik ditemukan: (1) adanya hubungan antara hubungan didaktik, hubungan pedagogik, dan ADP selama implementasi desain pembelajaran yang menunjukkan kesatuan, fleksibilitas, dan koherensi; dan (2) terbentuknya pengetahuan sebagai hasil dari proses transposisi didaktik mahasiswa berupa pengetahuan ilmiah (scholarly knowledge) sebagai pengetahuan dasar transposisi, susunan HLT siswa sebagai representasi knowledge to be taught-nya, outline desain pembelajaran dan desain pembelajaran hipotetik yang memuat pengetahuan yang diajarkan (taught knowledge). Pada tahap retrospektif ditemukan: (1) hasil refleksi dan evaluasi desain pembelajaran menunjukkan adanya tambahan situasi didaktik yang dihadirkan selama implementasi desain pembelajaran awal yang berdampak pada penambahan learning trajectory yang dilalui mahasiswa; (2) susunan HLT perbaikan; dan (3) susunan desain pembelajaran empirik. ABSTRACT This study generally aims to produce learning designs that can help pre-service mathematics teacher carry out the didactic transposition process on set material. The research method used is qualitative research with a hermeneutic phenomenological approach. The research design used was Didactical Design Research (DDR) which contained three stages of analysis, namely prospective analysis, metapedadidactic analysis, and retrospective analysis. Participants in this study consisted of 28 seventh grade students of junior high school, a mathematics teacher of seventh grade of junior high school, 4 students of 7th semester and 2 students of 1st semester, and a lecturer who taught the theory of set and function course. The results of this study describe the findings at each stage of the analysis. At the prospective analysis stage, it was found: (1) the results of the didactic transposition analysis showed that there is zone of concept image differences (ZCID) between students' concept image with formal concept definition in scholarly knowledge, even with taught knowledge dan knowledge to be taught on set material. ZCID was caused by learning obstacles, such as didactical obstacle, ontogenic obstacles, and epistemological obstacle, which caused by inaccuracies of the material presentation and the didactic situation that was presented; (2) students' hypothetical learning trajectory (HLT) structure; and (3) a hypothetical learning design that contains didactic situation, responses prediction, and anticipation of didactic pedagogic (ADP). In the metapedadidactic stage, it was found that: (1) there was a relationship between relation of pedagogy, relation of didactic, and ADP during the implementation of the learning design which showed unity, flexibility and coherence; and (2) the formation of student transposition knowledge after going through the didactic transposition process, in the form of scholarly knowledge as a basic knowledge of transposition, the arrangement of students' HLT as a representation of their knowledge to be taught, and a hypothetical learning design that contains taught knowledge. At the retrospective stage, it was found: (1) the results of reflection and evaluation of the learning design showed that there is additional didactic situation that was presented during the implementation of the initial learning design which had an impact on the addition of the learning trajectory that the students went through; (2) new HLT structure; and (3) composition of empirical learning designs. Keywords: Didactic Transposition, Didactical Design Research, Set Material