ANALYSIS OF STUDENTS' ABILITY TO UNDERSTAND MATHEMATICAL CONCEPTS IN PROBABILITY MATERIAL
Abstract
The concept of chance has an important role in everyday life, especially for vocational students who are able to master analytical and decision-making skills in the world of work, but students' low understanding of the concept of chance is a challenge that requires more attention in learning mathematics. This study aims to analyze students' understanding of mathematical concepts in opportunity material at the Vocational High School (SMK) level. The method used is descriptive qualitative, with data collection through written tests, interviews, and documentation. The research sample consisted of 28 students of class XI SMK using random sampling technique. The results showed that students' understanding of the concept of chance was still low, with an average mastery of only 20% of the total indicators tested. The indicators of restating concepts (4%) and classifying objects based on concepts (0%) have the lowest percentage, indicating that students still have difficulty in understanding the concept of chance in depth. The indicator of applying concepts in algorithms and mathematical representations (54%) had the best results, although there were still errors in choosing the right formula. Meanwhile, the indicator of connecting the concept of chance with other fields (21%) shows that students are not familiar with the application of chance outside of mathematics. The main factor causing this low understanding is the lack of understanding of the basic theory of probability and the tendency of students to memorize the formula.
Konsep peluang sangat penting dalam kehidupan sehari-hari, khususnya bagi siswa SMK yang perlu menguasai keterampilan analitis dan pengambilan keputusan. Namun, pemahaman siswa terhadap konsep ini masih rendah, yang menjadi tantangan dalam pembelajaran matematika. Penelitian ini bertujuan untuk menganalisis pemahaman konsep matematis siswa dalam materi peluang di tingkat Sekolah Menengah Kejuruan (SMK). Metode yang digunakan adalah deskriptif kualitatif, dengan pengumpulan data melalui tes tertulis, wawancara, dan dokumentasi. Sampel penelitian terdiri dari 28 siswa kelas XI SMK dengan teknik random sampling. Hasil penelitian menunjukkan bahwa pemahaman konsep peluang siswa rata-rata hanya 20% dari indikator yang diuji. Indikator seperti menyatakan ulang konsep (4%) dan mengklasifikasikan objek (0%) memiliki persentase terendah, menunjukkan kesulitan siswa dalam memahami konsep secara mendalam. Meskipun indikator menerapkan konsep dalam algoritma dan representasi matematis (54%) menunjukkan hasil terbaik, masih terdapat kesalahan dalam pemilihan rumus. Indikator yang menghubungkan konsep peluang dengan bidang lain (21%) juga menunjukkan bahwa siswa belum terbiasa dengan penerapan peluang di luar matematika. Faktor utama penyebab rendahnya pemahaman ini adalah kurangnya pemahaman teori dasar peluang dan kecenderungan siswa untuk menghafal rumus tanpa memahami penerapannya. Oleh karena itu, diperlukan strategi pembelajaran yang lebih efektif, seperti pendekatan berbasis pemecahan masalah dan pembelajaran kontekstual, untuk meningkatkan pemahaman siswa dalam materi peluang.
References
Agustina, Syaifudin, and Supriadi, A. (2019). Analysis of Students' Ability to Understand Word Problems in Linear Programming in Class XI. GAUSS: Journal of Mathematics Education 2(1): 1-12 doi: http://dx.doi.org/10.30656/gauss.v2i1.1082
Ananda, R. P., Sanapiah, and Yulianti, S. (2018). Analysis of Errors Made by Grade VII Students at SMPN 7 Mataram in Solving Line and Angle Problems for the 2018/2019 School Year. Media Pendidikan Matematika 6(2): 79-87. doi: https://doi.org/10.33394/mpm.v6i2.1838
Andini, U. (2017). Analysis of Students' Conceptual Understanding in Solving Mathematics Problems on Absolute Value Inequalities. FKIP.UM-Palembang 2(1):522–30.
Arnidha, Y. (2017). Analysis of Elementary School Students' Understanding of Mathematical Concepts in Solving Plane Figures Problems. Jurnal Pendidikan Guru Madrasyah Ibtidaiah. doi: 10.54892/jpgmi.v3i1.22.
Astuti, N. F., Yusmin, E., and Suratman, D. (2015). Analysis of Conceptual Understanding Difficulties in Solving Probability Problems at MAN Sanggau. Jurnal Pendidikan Dan Pembelajaran Khatulistiwa 4(10):1–10. doi: https://doi.org/10.26418/jppk.v4i10.11971.
Ate, M. B., Irianti, N.P., and Setiawan, R. (2022). Analysis of Students' Conceptual Understanding in Probability Material. Prismatika: Journal of Mathematics Education and Research 5(1):75–84. doi: Https://doi.org/10.33503/prismatika.v5i1.2016.
Damayana, R., Andinasari., and Lusiana. (2019). Improving Understanding of Probability Concepts Through the Discovery Learning Model. Lentera Pendidikan: Journal of Education and Teaching Science 22(2):223. doi: https://doi.org/10.24252/lp.2019v22n2i4.
Handayani, Y., and Aini, I. A. (2019). Analysis of Students' Mathematical Conceptual Understanding in Class IX SMP on Translation Material. National Seminar on Mathematics and Mathematics Education Proceedings 575–81.
Heppinia, M, and Tiya, K. (2015). Analysis of Errors Made by Grade VII Students at SMP Negeri 1 Wawotobi in Solving Fraction Problems. Mathematics Education Research Journal 3(3):27–40. doi: https://doi.org/10.36709/jppm.v3i3.3018.
Hutagalung, R. (2017). Improving Students' Mathematical Conceptual Understanding Through Guided Discovery Learning Based on Toba Culture at SMP Negeri 1 Tukka. Journal of Mathematics Education and Science 2:70. doi: https://doi.org/10.30743/MES.V2I2.133.
Laman, E. G. (2019). Analysis of Students' Errors in Solving Higher Order Thinking Skills Mathematics Problems Based on Hadar's Criteria, in Terms of the Initial Ability of Class XII Students at SMAN 5 Makassar. State University of Makassar.
Lestari, K. E., and Yudhanegara, R. (2018). Penelitian Pendidikan Matematika. Bandung: PT. Refika Aditama.
Lumbantoruan, J. H., and Male, H. (2020). Analysis of Misconceptions in Word Problems on Probability Theory in the Mathematics Education Program. Jurnal EduMatSains 4(2):153–68.
Manurung, A., and Manurung, N. (2024). Conceptual Understanding Procedures Learning Model for Improving Students' Mathematical Conceptual Understanding. Journal of Mathematics Education 15(2):173–81. doi: https://doi.org/10.36709/jpm.v15i2.192.
Nailopo, F., Fitriani, and Simarmata, J. E. (2022). Analysis of Students' Conceptual Understanding on Probability Material from the Apos Theory for Grade VIII Students at SMP. Jurnal Eduscience 9(1):168–81. doi: https://doi.org/10.36987/jes.v9i1.2587.
Nurhangesti, M., and Seruni. (2024). Factors Affecting Mathematical ConceptualUnderstanding: A Literature Review. 2(12). doi: https://doi.org/10.62281/v2i12.1381.
Putridayani, I. B., and Chotimah, S. (2020). Analysis of Students' Learning Difficulties in Mathematics on Probability Material. MAJU: Scientific Journal of Mathematics Education 7(1):57–62.
Radiusman. (2020). Literacy Study: Students' Conceptual Understanding in Mathematics Learning. FIBONACCI: Journal of Mathematics Education and Mathematics 6(1):1. doi: https://doi.org/10.24853/fbc.6.1.1-8.
Rahmi, F., Iltavia, and Zarista, R. H. (2021). Effectiveness of Realistic Mathematics Learning to Build Relational Understanding on Probability Material. Cendekia Journal: Journal of Mathematics Education 5(3):2869–77. doi: https://doi.org/10.31004/cendekia.v5i3.673.
Ramdan, and Anwar. (2019). Analysis of Errors Made by Grade X Students at SMA Negeri Baubau in Solving Trigonometry Problems. Academic Journal of Mathematics Education FKIP Unidayana 5(1):24–33.
Rismawati, M. (2016). Structure of Mathematical Connections in Grade X Students on Linear Equation System Material. State University of Malang.
Rismawati, M., and Hutagaol, A. S. R. (2018). Analysis of Mathematical Conceptual Understanding Ability of PGSD Students at STKIP Persada Khatulistiwa Sintang. PerKhasa Journal of Basic Education 4(1):91–102. doi: https://doi.org/10.31932/jpdp.v4i1.17.
Setiani, N., Roza, Y., and Maimumah. (2022). Analysis of Students' Mathematical Conceptual Understanding in Probability Material for SMP Students. Cendekia Journal: Journal of Mathematics Education 06(02):2286–97. doi: https://doi.org/10.31004/cendekia.v6i2.1476.
Ummah, S. N. (2023). Mathematical Conceptual Understanding of Students in the Probability Sub-element of the Merdeka Curriculum in Class X at SMA Negeri Jenggawah. Kiai Haji Achmad Siddiq Islamic State University of Jember. http://digilib.uinkhas.ac.id/id/eprint/26067
Yanti, A. W., Kusumawardani, A. D. P., Rohmah, F. M., and Kulsum, U. (2022). Students' Conceptual Understanding in Solving Mathematical Problems on Quadratic Function Material According to Kilpatrick's Theory. MUST: Journal of Mathematics Education, Science and Technology 7(1):30–49. doi: http://dx.doi.org/10.30651/must.v7i1.10938.
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