Kalkulus Diferensial: Analisis Kesulitan Mahasiswa Dalam Menyelesaikan Soal Turunan

Abstract

Abstrak: Penelitian ini dilakukan dengan tujuan untuk (1) mengidentifikasi kesulitan-kesulitan mahasiswa dalam menyelesaikan soal ujian akhir mata kuliah Kalkulus Diferensial dan (2) mengidentifikasi faktor penyebab kesulitan-kesulitan mahasiswa di setiap penyelesaian soal. Penelitian ini menggunakan pendekatan penelitian kualitatif dengan subjek penelitian dengan mengambil 5 orang mahasiswa. Pengumpulan data dalam penelitian ini menggunakan metode tes dan wawancara. Hasil penelitian ini antara lain: (1) kesulitan–kesulitan yang dialami mahasiswa antara lain; (a) kesulitan memahami konsep, (b) kesulitan menerapkan konsep dalam menyelesaikan soal, (c) kesulitan dalam operasi perhitungan, (d) kesulitan memahami konsep prasyarat, dan (e) kesulitan dalam menyederhanakan bentuk Aljabar. (2) Penyebab kesulitan-kesulitan yang dialami mahasiswa antara lain: (a) pada soal nomor 1, mahasiswa kurang teliti dalam membaca pertanyaan soal, bingung menentukan notasi turunan serta mahasiswa masih kurang memahami konsep turunan persamaan implisit, (b) pada soal nomor 2, mahasiswa tidak memeriksa kembali jawaban yang sudah dituliskan dan mahasiswa kurang paham menentukan turunan trigonometri. (c) pada soal nomor 3, mahasiswa kurang memahami aturan rantai pada turunan dan konsep operasi pada bilangan berpangkat. (d) pada soal nomor 4, mahasiswa masih kurang paham konsep turunan eksponen.

Abstract: This research was conducted with the aim of (1) identifying student difficulties in solving the final exam questions for the Differential Calculus course and (2) identifying the factors causing student difficulties in solving each problem. This study uses a qualitative research approach with research subjects took five students. Data collection in this study used the test and interview methods. The results of this study include: (1) difficulties experienced by students, among others; (a) difficulties in understanding concepts, (b) difficulties in applying concepts in solving problems, (c) difficulties in calculating operations, (d) difficulties in understanding prerequisite concepts, and (e) difficulties in simplifying algebraic forms. (2) The causes of the difficulties experienced by students include: (a) in question number 1, students are not careful in reading questions, are confused in determining derivative notation and students still do not understand the concept of implicit equation derivatives, (b) in question number 2, students do not re-check the answers that have been written and students do not understand how to determine trigonometric derivatives. (c) in question number 3, students do not understand the chain rule on derivatives and the concept of operations on numbers to exponents. (d) in question number 4, students still do not understand the concept of exponential derivative.