Didactic Transposition from Scholarly Mathematics to School Mathematics: The Case of Function Concept

Riki Andriatna; Imam Sujadi

doi:10.31980/mosharafa.v13i1.1988

Authors

Riki Andriatna Universitas Sebelas Maret
Imam Sujadi Universitas Sebelas Maret

DOI:

https://doi.org/10.31980/mosharafa.v13i1.1988

Keywords:

Fenomenologi, Scholarly Mathematics, School Mathematics, Transposisi Didaktis, Didactic Transposition, Phenomenology

Abstract

Konsep fungsi menjadi jembatan beberapa konsep lain dalam matematika sehingga memberikan pandangan berbeda terhadap suatu permasalahan dalam matematika. Dengan demikian, proses transposisi pengetahuan menjadi sangat penting untuk diperhatikan. Penelitian ini bertujuan melihat transposisi konsep fungsi dari scholarly mathematics terhadap school mathematics. Penelitian menggunakan pendekatan fenomenologi dengan sumber data yaitu buku teks matematika universitas yaitu analisis real, struktur aljabar, dan kalkulus, serta buku teks sekolah yaitu matematika kelas X dan XI dari Kemendibudristek. Teknik analisis data yaitu deskriptif kualitatif. Hasil analisis menunjukkan transposisi terjadi pada konteks serta struktur dan bentuk. Pada konteks, konsep fungsi dapat dilihat pada bagaimana konsep fungsi tersebut dikonstruksi, dimana pada scholarly mathematics, konsep fungsi dibentuk dari konsep abstrak, sedangkan di school mathematics konsep fungsi didasarkan pada konsep konkret yang kemudian mengarah pada konsep abstrak. Pada aspek struktur dan bentuk, transposisi didaktis dapat dilihat dari penyajian konsep fungsi, dimana pada scholarly knowledge konsep fungsi disajikan dalam notasi abstrak, sedangkan pada school mathematics disajikan dalam beragam bentuk seperti diagram.

The concept of function becomes a bridge for several other concepts in mathematics so as to provide a different view of a problem in mathematics. Thus, the process of knowledge transposition is very important to be considered. This study aims to look at the transposition of the concept of function from scholarly mathematics to school mathematics. This research used phenomenological approach. The data sources in this study are mathematics textbooks at the university level, namely real analysis textbooks, algebraic structures, and calculus, while at the school level, namely mathematics textbooks for grades X and XI published by the Ministry of Education, Culture, Research and Technology. The data analysis technique used is qualitative descriptive analysis. The results of the analysis show that transposition occurs in context and structure and form. In the context, the function concept can be seen in how the function concept is constructed, where in scholarly mathematics, the function concept is formed from abstract concepts, while in school mathematics the function concept is based on concrete concepts which then lead to abstract concepts. In the aspect of structure and form, didactic transposition can be seen from the presentation of the function concept, where in scholarly knowledge the function concept is presented in abstract notation, while in school mathematics it is presented in a variety forms such as diagrams.

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