ANALISIS KESALAHAN SISWA SMP DALAM MENYELESAIAKAN SOAL MATERI RELASI DAN FUNGSI

Abstract

This study was prompted by the low level of understanding among eighth-grade students at SMPK St. Yoseph Naikoten Kupang regarding relations and functions, particularly in distinguishing relations from functions, determining the domain, codomain, and range, as well as calculating functional values. This study aimed to describe the types of errors committed by students when solving relations and functions problems and to identify the factors underlying these errors. A qualitative descriptive approach was employed, involving three students from Class VIII C who were selected purposively based on the variation and highest frequency of errors from a total of 32 students. Data were collected through an expert-validated written test consisting of three essay items, semi-structured interviews, and documentation. Data analysis proceeded through the stages of data reduction, data display, and conclusion drawing, using triangulation techniques to ensure data trustworthiness. The results indicated that students' errors were predominantly conceptual errors at 83.3%, followed by procedural errors at 68.7%, and operational calculation errors at 13.5%. Conceptual errors were manifested in students' inability to understand the condition of mapping exactly one element and inaccuracies in defining the "factor of" relation. Procedural errors were evident in the absence of systematic algebraic substitution steps, whereas operational calculation errors stemmed from basic arithmetic inaccuracies. The underlying causes of these errors originated from internal factors, namely weak mastery of prerequisite set concepts, the absence of a habit of rechecking completed work, and low student precision and interest in learning mathematics. Overall, it is concluded that students' primary difficulty is rooted in incomplete conceptual understanding of functions, which in turn triggers a chain of errors in subsequent procedural stages.

ABSTRAK

Penelitian ini dilatarbelakangi oleh rendahnya pemahaman siswa kelas VIII SMPK St. Yoseph Naikoten Kupang pada materi relasi dan fungsi, khususnya dalam membedakan relasi dan fungsi, menentukan daerah asal (domain), daerah kawan (kodomain), daerah hasil (range), serta menghitung nilai fungsi. Penelitian ini bertujuan untuk mendeskripsikan jenis-jenis kesalahan yang dilakukan siswa dalam menyelesaikan soal relasi dan fungsi serta mengidentifikasi faktor-faktor penyebab kesalahan tersebut. Pendekatan yang digunakan adalah deskriptif kualitatif dengan subjek penelitian sebanyak tiga siswa kelas VIII C yang dipilih secara purposive berdasarkan variasi dan jumlah kesalahan terbanyak dari total 32 siswa. Pengumpulan data dilakukan melalui tes tertulis berupa tiga butir soal uraian yang telah divalidasi ahli, wawancara semiterstruktur, dan dokumentasi. Analisis data berlangsung melalui tahapan reduksi data, penyajian data, serta penarikan kesimpulan dengan teknik triangulasi untuk menguji keabsahan data. Hasil penelitian menunjukkan bahwa kesalahan siswa didominasi oleh kesalahan konsep sebesar 83,3%, diikuti kesalahan prosedur sebesar 68,7%, dan kesalahan operasi hitung sebesar 13,5%. Kesalahan konsep tampak pada ketidakmampuan siswa memahami syarat pemetaan tepat satu pasangan dan kekeliruan mendefinisikan relasi faktor dari. Kesalahan prosedur terlihat dari ketiadaan langkah substitusi aljabar yang sistematis, sedangkan kesalahan operasi hitung terjadi akibat kekeliruan perhitungan aritmetika dasar. Faktor penyebab kesalahan bersumber dari faktor internal, yaitu lemahnya penguasaan konsep prasyarat himpunan, ketiadaan kebiasaan memeriksa kembali hasil pekerjaan, serta rendahnya ketelitian dan minat belajar matematika siswa. Secara umum disimpulkan bahwa kesulitan utama siswa berakar pada pemahaman konsep fungsi yang belum tuntas sehingga memicu kesalahan berantai pada tahapan prosedural berikutnya.