The effect of open-ended approach on enhancing mathematical understanding in vocational high school students
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Abstract
This study aims to evaluate the extent to which the open-ended approach affects the achievement of students' mathematical understanding ability in vocational high schools (SMK). The method used was a quasi-experiment with a pretest-posttest control group design, in which two groups of students (experimental group and control group) were compared based on test results before and after treatment. The research sample consisted of 72 students who were selected by intact group (based on the class that had been formed) to minimize disruption to teaching and learning activities at school. This sampling was done by considering the real conditions in the field so as not to disrupt the existing learning schedule and class structure. The research data was obtained through a description test consisting of three questions, with a maximum score of 12 for each question. Data analysis was conducted in two stages: first, a normality test to check data distribution, and second, a mean difference test using the Mann-Whitney U test because the data were not normally distributed. The results showed that the group of students taught with the open-ended approach had better mathematical understanding achievement than the group that received direct learning. This finding indicates that the open-ended approach is effective in promoting mathematical conceptual understanding through independent exploration.
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Rifai, R., Turmudi, Jarnawi Afgani Dahlan, & Suhendra. (2025). The effect of open-ended approach on enhancing mathematical understanding in vocational high school students. Kalamatika: Jurnal Pendidikan Matematika, 10(2), 58-72. https://doi.org/10.22236/KALAMATIKA.vol10no2.2025pp58-72
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Boaler, J. (2016). Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching. Jossey-Bass.
BSNP. (2023). Laporan Hasil Ujian Nasional SMK 2023. Jakarta: Kemdikbud.
Hadi, S., Retnawati, H., Munadi, S., & Apino, E. (2021). The Challenges of Learning Mathematics for Vocational High School Students. Journal of Research and Advances in Mathematics Education, 6(1), 1-12.
Hattie, J. (2017). Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning. Corwin.
Kemdikbud. (2022). Kurikulum SMK: Fokus pada Kompetensi Kejuruan. Jakarta: Kemdikbud.
Kemdikbud. (2018). Peraturan Menteri Pendidikan dan Kebudayaan Nomor 34 Tahun 2018 tentang Standar Nasional Pendidikan Sekolah Menengah Kejuruan/Madrasah Aliyah Kejuruan. Jakarta: Kemdikbud.
Khoriyani, Y., Sutrisno, S., & Murtiyasa, B. (2018). Analisis sistematis implementasi pendekatan open-ended dalam pembelajaran matematika: Fokus pada siswa SMK. Jurnal Pendidikan Matematika, 12(3), 45-60.
Kurniawan, A., & Pratama, L. D. (2022). Pengaruh Pendekatan Open-Ended terhadap Kemampuan Representasi Matematis Siswa SMK. Jurnal Pendidikan Matematika, 10(2), 45-60.
Mulyawan, S., Hidayat, W., & Nurlaelah, E. (2023). Efektivitas pendekatan open-ended dalam meningkatkan Higher Order Thinking Skills (HOTS) matematis siswa SMP. Journal of Mathematics Education Research, 10(3), 215-230.
NCTM. (2020). Catalyzing Change in High School Mathematics: Initiating Critical Conversations. National Council of Teachers of Mathematics.
Nurhasanah, F., Kusumah, Y. S., & Suryadi, D. (2021). Students’ negative perceptions of mathematics in vocational schools: A case study of Indonesian SMK students. Journal of Mathematics Education Research, 8(2), 45-60.
OECD. (2023). PISA 2022 Results: Indonesia’s Mathematical Literacy Performance.
Paris: OECD Publishing.
Schoenfeld, A. H. (2019). Mathematical practices, mathematics for teachers: Activities, models, and real-life examples. Cengage Learning.
Shimada, S. (1997). The Significance of an Open-Ended Approach in Mathematics Education. Tsukuba Journal of Educational Study in Mathematics, 16, 1-12.
Sugiyama, Y. (2021). Rethinking mathematics pedagogy for vocational education: Developing applied mathematical thinking. International Journal of STEM Education for Workforce Development, 3(2), 45-59.
Suharta, I. G. P., & Suharta, I. M. (2021). Open-Ended Approach dalam Pembelajaran Matematika: Tinjauan Sistematis. Jurnal Pendidikan Matematika, 15(1), 1-12.
Rosyidi, A. H., Junaedi, I., & Kusuma, W. (2022). Vocational students' mathematical literacy in technical calculations: A case study of Indonesian SMK. Journal of Vocational Education Studies, 5(1), 12-25.
Van De Walle, J. A. (2007). Elementary and Middle School Mathematics: Teaching Developmentally. Pearson Education.
Wulandari, S., & Jailani, J. (2022). Enhancing Problem-Solving Skills in Vocational Students through Open-Ended Mathematics Tasks. Journal of Technical Education and Training.
Widodo, S. & Putri, R. (2020). "Pembelajaran Matematika Kontekstual di SMK: Tantangan dan Peluang". Jurnal Pendidikan Vokasi, 10(2), 145-160.