TRANSPOSISI DIDAKTIK BERPIKIR ALJABAR AWAL - Septiani Yugni Maudy, - (2023)
Dalam pembelajaran aljabar, pengetahuan selalu berupa makna dan pemaknaannya terdapat di dalam proses transposisi sehingga bersifat situasional dan berupa abstraksi dari konteks penggunaannya. Penelitian ini bertujuan untuk mengkonstruksi makna di balik pengalaman belajar siswa terhadap munculnya pemikiran aljabar awal sebagai implementasi desain didaktik yang merupakan perwujudan dari knowledge to be taught yang dirancang peneliti setelah melalui proses transposisi didaktik. Metode penelitian yang digunakan adalah penelitian kualitatif dengan pendekatan fenomenologi hermeneutik. Objek matematis dikonstruksi dalam bentuk formal melalui proses re-depersonalisasi dan re-dekontekstualisasi, maka terbentuklah konstruksi scholarly knowledge mengenai aljabar esensial yang akan berkaitan dengan berpikir aljabar awal. Scholarly knowledge bersifat sebagai pengetahuan a priori sehingga perlu dilakukan transposisi menjadi materi kurikulum (knowledge to be taught). Transposisi diawali dengan repersonalisasi dan rekontekstualisasi sehingga menjadi pengetahuan yang bersifat a posteriori. Dalam proses transposisinya, peneliti juga melakukan analisis terhadap kurikulum serta buku ajar yang digunakan di sekolah dasar yang diteliti dengan menggunakan praxiologi. Peneliti membentuk pengetahuan esensial untuk diajarkan dan panduan knowledge to be taught di sekolah dasar yang dapat mengakomodasi berpikir aljabar awal sebagai pengalaman belajar siswa. Peneliti mengerucutkan permasalahan berpikir aljabar awal menjadi konsep spesifik proporsionalitas sebagai salah satu contoh dari pemikiran aljabar awal. Kurikulum matematika sekolah dasar ditransposisikan menjadi objek pengajaran di kelas dalam kerangka proses belajar mengajar (taught knowledge). Dalam proses transposisi untuk menyusun objek pengajaran, peneliti juga melakukan analisis terhadap proses pembelajaran matematika di sekolah dasar untuk mengidentifikasi beragam masalah yang terjadi, dan melakukan analisis learning obstacle konsep proporsionalitas di sekolah menengah. Peneliti menyusun objek pengajaran dalam bentuk desain didaktik yang terdiri dari dua komponen, yaitu praxis (type of task dan teknik) serta logos (teknologi dan teori). Dari implementasi desain didaktik, peneliti menganalisis pemikiran aljabar awal siswa yang terbentuk (learnt knowledge) dalam permasalahan proporsionalitas di sekolah dasar, antara lain melalui pendekatan tabel rasio dengan penalaran aditif dan multiplikatif, pendekatan rasio satuan, pendekatan faktor perubahan, pendekatan pecahan dan rasio yang ekuivalen, serta koneksi pendekatan rasio satuan dan faktor perubahan ke dalam algoritma standar. Sehingga terbentuk penalaran proporsional yang sebenarnya membangun berpikir aljabar awal mengenai konsep invarian dan kovarian, kelas ekuivalensi, dan fungsi linier. In learning algebra, knowledge is always in the form of meaning and its meaning is contained in the transposition process so that it is situational and in the form of an abstraction from the context of its use. This study aims to construct the meaning behind the students' learning experience towards the emergence of early algebraic thinking as the implementation of a didactic design which is an embodiment of knowledge to be taught that was designed by researchers after going through a didactic transposition process. The research method used is qualitative research with a hermeneutic phenomenological approach. Mathematical objects are constructed in a formal form through the process of re-depersonalization and re-decontextualization, so that the construction of scholarly knowledge regarding essential algebra is formed which will be related to initial algebraic thinking. Scholarly knowledge is a priori knowledge so it is necessary to transpose it into curriculum material (knowledge to be taught). Transposition begins with repersonalization and recontextualization so that it becomes a posteriori knowledge. In the transposition process, the researcher also conducted an analysis of the curriculum and textbooks used in the elementary schools studied using praxiology. Researchers form essential knowledge to be taught and guide knowledge to be taught in elementary schools that can accommodate early algebraic thinking as a student learning experience. The researcher narrows the problem of early algebraic thinking into a specific concept of proportionality as an example of early algebraic thinking. The elementary school mathematics curriculum is transposed into teaching objects in class within the framework of the teaching and learning process (taught knowledge). In the process of transposition to arrange teaching objects, the researcher also conducted an analysis of the process of learning mathematics in elementary schools to identify various problems that occur, and conducted an analysis of learning obstacles to the concept of proportionality in secondary schools. The researcher arranges the teaching object in the form of a didactic design which consists of two components, namely praxis (type of task and technique) and logos (technology and theory). From the implementation of the didactic design, the researcher analyzed the students' initial algebraic thinking that was formed (learnt knowledge) in proportionality problems in elementary schools, including through the ratio table approach with additive and multiplicative reasoning, unit ratio approach, change factor approach, fractional approach and equivalent ratios, as well as the connection of unit ratio approaches and factor of change into standard algorithms. So that proportional reasoning is formed which actually builds initial algebraic thinking about the concepts of invariant and covariance, equivalence classes, and linear functions.