A Didactical Design Research: Knowledge Acquisition of Mathematics Teacher Prospective Students on Multiple Integral Concepts

Abstract

This research aims to determine prospective mathematics teacher students' learning obstacles and knowledge acquisition process on the concept of fold integrals and their applications. In the acquisition process, students extract, structure, and organize knowledge both obtained from reading results and information received during the learning process in class; this is studied comprehensively. This research is Didactical Design Research. The research participants were 46 fourth-semester students in a study program producing prospective mathematics teachers. Research data comes from tests, observations, interviews, and documentation. The stages of data analysis are identification, clarification, reduction, and verification, which are then presented in a narrative descriptive manner. This research is essential because apart from identifying learning obstacles, various types of learning obstacles and the process of knowledge acquisition on related concepts and their multiple causes are also analyzed. The results obtained were (1) Students experienced ontogenic learning obstacles of psychological, instrumental, and conceptual types in the fold integral concept; apart from that, epistemological learning obstacles were also identified; (2) the process of acquiring knowledge related to the concept of double and triple integrals and their applications is not yet running perfectly, hampered by prerequisite knowledge, lack of technical ability, weak mastery of concepts, and limited understanding related to student habits. Further studies need to be carried out regarding the diffusion process by lecturers to facilitate the knowledge acquisition process so that students can construct the fold integral concept well.

Penelitian ini bertujuan mengetahui hambatan belajar dan proses akuisisi pengetahuan mahasiswa calon guru matematika pada konsep integral lipat beserta aplikasinya. Pada proses akuisisi, mahasiswa melakukan ekstraksi, strukturisasi, dan pengorganisasian pengetahuan baik yang diperoleh dari hasil baca maupun informasi yang diterima selama proses belajar di kelas, hal ini dikaji secara kpmprehensif. Penelitian ini merupakan penelitian Didactical Design Research. Partisipan penelitian sebanyak 46 mahasiswa semester empat pada program studi penghasil calon guru matematika. Data penelitian berasal dari tes, observasi, wawancara, dan dokumentasi. Tahapan analisis data yaitu identifikasi, klarifikasi, reduksi, dan verifikasi, yang kemudian disajikan secara deskriptif naratif. Penelitian ini penting dilakukan, karena selain diidentifikasi hambatan belajar, juga dianalisa berbagai tipe hambatan belajar beserta proses akuisisi pengetahuan pada konsep terkait beserta berbagai penyebanya. Hasil yang diperoleh adalah (1) Mahasiswa mengalami hambatan belajar ontogenik tipe psikologis, instrumental, dan konseptual pada konsep integral lipat, selain itu teridentifikasi juga hambatan belajar epistemologis; (2) proses akuisisi pengetahuan terkait konsep integral lipat dua dan lipat tiga beserta aplikasinya belum berjalan sempurna, terkendala oleh pengetahuan prasyarat, kurangnya kemampuan teknis, lemahnya penguasaan konsep, dan terbatasnya pemahaman terkait dengan kebiasaan mahasiswa. Perlu dilakukan kajian lebih lanjut terkait proses difusi yang dilakukan dosen untuk memfasilitasi proses akuisisi pengetahuan, sehingga mahasiswa dapat mengkonstruksi konsep integral lipat dengan baik.