STUDENTS’ ERRORS IN SOLVING CALCULUS PROBLEMS ON INCREASING, DECREASING, AND CONCAVITY OF FUNCTIONS
Abstract
Calculus is a fundamental course in mathematics education; however, many students experience difficulties that lead to errors in problem solving. This study aimed to identify and analyze students’ errors in solving calculus problems involving increasing functions, decreasing functions, and function concavity. A qualitative descriptive case study approach was employed involving 22 fifth-semester mathematics education students at UIN Sheikh Ali Hasan Ahmad Addary Padangsidimpuan during the 2024/2025 academic year. Data were collected through four essay-test items and semi-structured interviews with six purposively selected students representing different error categories. The data were analyzed using the interactive model of Miles, Huberman, and Saldaña, including data condensation, data display, and conclusion drawing. The findings revealed three categories of errors: conceptual, operational, and factual errors. Operational errors were the most dominant, particularly in derivative calculations, algebraic manipulations, and interval determination. Conceptual errors occurred when students misinterpreted the meaning of first and second derivatives in determining function behavior, whereas factual errors were related to the incorrect use of mathematical symbols and notation. The errors were mainly influenced by insufficient conceptual understanding, lack of carefulness, and ineffective problem-solving practices. These findings provide important implications for calculus instruction by highlighting the need to strengthen conceptual understanding alongside procedural fluency. The study contributes to the literature on calculus error analysis by providing an in-depth examination of students’ difficulties in applying derivative concepts to analyze increasing functions, decreasing functions, and function concavity.
Kalkulus merupakan salah satu mata kuliah dasar dalam pendidikan matematika. Namun, banyak mahasiswa mengalami kesulitan yang menyebabkan terjadinya kesalahan dalam menyelesaikan masalah matematika. Penelitian ini bertujuan untuk mengidentifikasi dan menganalisis kesalahan mahasiswa dalam menyelesaikan soal kalkulus yang berkaitan dengan fungsi naik, fungsi turun, dan kecekungan fungsi. Penelitian ini menggunakan pendekatan kualitatif dengan desain studi kasus deskriptif yang melibatkan 22 mahasiswa semester V Program Studi Pendidikan Matematika di UIN Syekh Ali Hasan Ahmad Addary Padangsidimpuan pada tahun akademik 2024/2025. Data dikumpulkan melalui empat butir soal uraian dan wawancara semi-terstruktur terhadap enam mahasiswa yang dipilih secara purposive untuk mewakili kategori kesalahan yang berbeda. Data dianalisis menggunakan model analisis interaktif Miles, Huberman, dan Saldaña yang meliputi kondensasi data, penyajian data, dan penarikan kesimpulan. Hasil penelitian menunjukkan adanya tiga kategori kesalahan, yaitu kesalahan konseptual, kesalahan operasional, dan kesalahan faktual. Kesalahan operasional merupakan jenis kesalahan yang paling dominan, terutama dalam perhitungan turunan, manipulasi aljabar, dan penentuan interval. Kesalahan konseptual terjadi ketika mahasiswa salah menafsirkan makna turunan pertama dan turunan kedua dalam menentukan perilaku fungsi, sedangkan kesalahan faktual berkaitan dengan penggunaan simbol dan notasi matematika yang tidak tepat. Kesalahan-kesalahan tersebut terutama dipengaruhi oleh kurangnya pemahaman konseptual, rendahnya ketelitian, serta praktik pemecahan masalah yang kurang efektif. Temuan penelitian ini memberikan implikasi penting bagi pembelajaran kalkulus dengan menekankan perlunya penguatan pemahaman konseptual yang seimbang dengan kelancaran prosedural. Penelitian ini berkontribusi pada kajian analisis kesalahan dalam kalkulus melalui penyajian analisis mendalam mengenai kesulitan mahasiswa dalam menerapkan konsep turunan untuk menganalisis fungsi naik, fungsi turun, dan kecekungan fungsi.
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