Rethinking How We Teach Derivatives Representation: The Framework of Hypothetical Learning Trajectory
DOI:
https://doi.org/10.31980/plusminus.v5i2.2816Keywords:
Hypothetical Learning Trajectory, Derivative Concept, Representation, Konsep Turunan, RepresentasiAbstract
Konsep turunan merupakan prinsip dasar dalam Kalkulus untuk pengajaran matematika di tingkat sekolah dan universitas. Namun demikian, definisi yang mencakup beberapa representasi terkadang membuat konsep turunan sangat sulit dipahami. Tujuan penelitian ini adalah untuk mengkaji representasi konsep turunan yang dipahami oleh partisipan. Penelitian ini menggunakan metodologi kualitatif untuk menyelidiki fenomena tertentu. Data penelitian dikumpulkan melalui wawancara klinis yang dilakukan terhadap mahasiswa (N=5) dari salah satu universitas di Provinsi Jawa Barat. Teknik analisis data menggunakan triangulasi meliputi reduksi data, analisis data, dan penarikan kesimpulan. Temuan penelitian ini menunjukkan bahwa representasi konsep turunan bagi banyak partisipan masih terbatas pada konteks simbolis untuk memecahkan masalah prosedural. Representasi yang terbatas dapat menimbulkan hambatan epistemologis dalam menyelesaikan masalah konseptual. Temuan ini menjadi dasar untuk mengembangkan Hypothetical Learning Trajectory (HLT) yang mencakup tujuan, prakiraan proses pembelajaran, dan aktivitas untuk mendorong terciptanya pemahaman melalui representasi konsep yang beragam.
The concept of a derivative is a fundamental principle in calculus that is essential for teaching mathematics at both the school and university levels. Nevertheless, definitions encompassing several representations sometimes render the concept of derivatives exceedingly challenging to comprehend. The objective of this research is to examine the representation of the derived notion as seen by the participants. The study employs qualitative methodologies through a case study framework to investigate certain phenomena. Research data collected via clinical interviews conducted with students (N=5) from a university in West Java Province. The data analysis technique using triangulation includes several stages, namely data reduction, data analysis, and drawing conclusions. The findings of this study suggest that the representation of derived concepts for many of participants remains confined to a symbolic context for solving procedural difficulties. The restricted representation can create epistemological obstacles in resolving conceptual issues. These findings serve as the foundation for developing a Hypothetical Learning Trajectory (HLT) design that encompasses objectives, forecasts of the learning process, and activities to promote the creation of understanding through diverse representations of concepts.
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