Enhancing vocational students’ mathematical problem-solving through contextual teaching factory learning

Authors

  • Muhtarom Muhtarom Universitas PGRI Semarang
  • Hary Nurprio Utomo Universitas PGRI Semarang
  • Ida Dwijayanti Universitas PGRI Semarang

DOI:

https://doi.org/10.29408/jel.v12i2.31809

Keywords:

mathematics instruction, quasi-experimental design, vocational education

Abstract

The discrepancy between classroom mathematics and the demands of the Business and Industrial World often results in less-than-ideal problem-solving ability for vocational high school students. To meet this challenge, learning methods that link mathematics to real-world work contexts are needed. The purpose of this study is to investigate the effectiveness of integrating the Teaching Factory (TeFa) model with a contextual learning approach in teaching relations and functions. A quantitative quasi-experimental method with the pre-test–post-test control group design was employed. The sample was 46 eleventh-grade pharmacy students at Muhammadiyah Al Manaar Vocational High School, Pemalang, selected through purposive sampling and divided equally into experimental and control groups. Data were collected using a validated mathematical problem-solving instrument and analysed using an independent samples t-test. Post-test performances differed significantly between the two groups (p < 0.05). The experimental group gained a moderate improvement with an N-gain score of 0.42. Moreover, the Cohen’s d value of 0.81 indicated a large effect of the TeFa model compared with conventional instruction.  These findings indicate that the integration of TeFa and contextual learning is effective to improve students’ mathematical problem-solving abilities while reinforcing the relevance of mathematics learning to real industrial workplace contexts in vocational education.

References

Amiyani, R., & Widjajanti, J. B. (2018). The Excellence of guided discovery learning on mathematical knowledge-based, skill-based, and attitude. Journal of Physics: Conference Series, 1097(1), 1–7. https://doi.org/10.1088/1742-6596/1097/1/012145

Ansel, H. C. (2010). Pharmaceutical calculations 13th edition. Wolters Kluwers Health.

Arifin, S., & Aprisal, A. (2020). Penerapan model pembelajaran kooperatif tipe pair checks Terhadap kemampuan pemecahan masalah matematika [The Application of the pair checks cooperative learning model on mathematical problem-solving ability]. Jurnal Pendidikan Matematika, 11(1), 89–98. https://doi.org/10.36709/jpm.v11i1.9974

Arsanti, M., Zulaeha, I., Subiyantoro, S., & Haryati, N. (2021). Tuntutan kompetensi 4C abad 21 dalam pendidikan di perguruan tinggi untuk menghadapi era society 5.0 [The 21st Century 4C competency demands in higher education to face the society 5.0 era]. Prosiding Seminar Nasional Pascasarjana Universitas Negeri Semarang, 319–324. http://pps.unnes.ac.id/prodi/prosiding-pascasarjana-unnes/

Bakker, A. (2014). Characterising and developing vocational mathematical knowledge. Educational Studies in Mathematics, 86(2), 151–156. https://doi.org/10.1007/s10649-014-9560-4

Bergamin, Werlen, Ziska, & Siegenthaler. (2012). The Relationship between flexible and self-regulated learning in open and distance universities. The International Review of Research in Open and Distance Learning, 101–122.

Boone, W., Staver, J., & Yale, M. (2014). Rasch analysis in the Human Sciences. https://doi.org/10.1007/978-94-007-6857-4

Chandra Wardana, L., Dwi Suryana, I., & Nandi, M. (2024). Integrating real world applications into mathematics education: Approaches and outcomes. International Journal of Mathematics and Science Education, 1(Mei), 19–25. https://doi.org/10.62951/ijmse.v1i2.88

Collins, A., Brown, J. S., & Newman, S. E. (2018). Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In Knowing, Learning, and Instruction (pp. 453–494). Routledge. https://doi.org/10.4324/9781315044408-14

Dalby, D., & Noyes, A. (2015). Connecting mathematics teaching with vocational learning. Adults Learning Mathematics: An International Journal, 10(1), 40–49.

Darmawan, M., Budiyono, B., & Pratiwi, H. (2019). Mathematics learning achievement of vocational high school students’ viewed by adversity quotient. Journal of Physics: Conference Series, 1157(4), 1–8. https://doi.org/10.1088/1742-6596/1157/4/042121

Duignan, gerard, Casley, S., Fraser, C., Haggerty, C., Hannam, S., Hitchcock, J., Rodrigues, A., Ross, K., Leno, L., Stewart, D., Taylor, B., & Webster, A. (2018). Teaching strategies that build employability skills of vocational education graduates.

Fantinelli, S., Cortini, M., Di Fiore, T., Iervese, S., & Galanti, T. (2024). Bridging the gap between theoretical learning and practical application: A Qualitative study in the italian educational context. Education Sciences, 14(2), 1–20. https://doi.org/10.3390/educsci14020198

Fraihat, M. A. K., Khasawneh, A. A., & Al-Barakat, A. A. (2022). The effect of situated learning environment in enhancing mathematical reasoning and proof among tenth grade students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), 1–10. https://doi.org/10.29333/ejmste/12088

Frejd, P., & Arleback, J. (2024). Mathematical modelling in vocational mathematics education: A literature review focusing on vertical and horizontal mathematising. In Springer. Springer. https://doi.org/10.1007/978-3-031-53322-8_9

Gallagher, M. A., Parsons, S. A., & Vaughn, M. (2022). Adaptive teaching in mathematics: a review of the literature. In Educational Review, 74(2), 298–320. Routledge. https://doi.org/10.1080/00131911.2020.1722065

Geist, M., Anthony, H., & Majors, T. (2018). Authentic helath-care scenarios make athematics meaningful. The National Council of Teachers of Mathematics, 111(7), 497–502.

Gupta, U., & Zheng, R. Z. (2020). Cognitive load in solving mathematics problems: Validating the role of motivation and the interaction among prior knowledge, worked examples, and task difficulty. European Journal of STEM Education, 5(1), 1–14. https://doi.org/10.20897/ejsteme/9252

Hadam, Rahayu, & Ariyadi. (2017). Strategi implementasi revitalisasi SMK 10 langkah revitalisasi SMK) [Revitalization strategy for vocational high schools 10 steps to revitalizing vocational high schools). Direktorat Jenderal Pendidikan Dasar Dan Menengah, Kementerian Pendidikan dan Kebudayaan.

Hall, G. (2014). Integrating real-world numeracy applications and modelling into vocational courses. Adults Learning Mathematics: An International Journal, 9(1), 53–67.

Hanh, N. T. (2020). Silence is gold?: A study on students’ silence in EFL classrooms. International Journal of Higher Education, 9(4), 153–160. https://doi.org/10.5430/ijhe.v9n4p153

Hasnida, N., & Ghazali, M. (2016). A reliability and validity of an instrument to evaluate the school-based assessment system: A pilot study. International Journal of Evaluation and Research in Education (IJERE), 5(2), 148–157. https://doi.org/10.11591/ijere.v5i2.4533

Hidayati, R. M., & Wagiran, W. (2020). Implementation of problem-based learning to improve problem-solving skills in vocational high school. Jurnal Pendidikan Vokasi, 10(2), 177–187. https://doi.org/10.21831/jpv.v10i2.31210

Jatisunda, M. G., Suryadi, D., & Prabawanto, S. (2024). Enhancing mathematical problem-solving ability through project-based learning: A study of vocational high school student. Jurnal Elemen, 10(3), 711–727. https://doi.org/10.29408/jel.v10i3.26244

Kaya, D., & Kesan, C. (2023). The Connection of mathematics with real-life situations: Preservice elementary mathematics teachers’ perceptions of creating and evaluating story problems. International Online Journal of Primary Education, 12(2), 118–135. https://doi.org/10.55020/iojpe.1135191

Langenfeld, T., Thomas, J., Zhu, R., & Morris, C. A. (2020). Integrating multiple sources of validity evidence for an assessment-based cognitive model. Journal of Educational Measurement, 57(2), 159–184. https://doi.org/10.1111/jedm.12245

Li, Y., Leong, W. Y., & Zhang, H. (2025). Innovative teaching practice in vocational education using smart technology: A case study of cement production course. Eurasia Journal of Mathematics, Science and Technology Education, 21(12). https://doi.org/10.29333/ejmste/17491

Linacre, J. M. . (2019). A user’s guide to WINSTEPS ministep : rasch-model computer programs. Winsteps.com. https://www.researchgate.net/publication/238169941_A_User’’s_Guide_to_Winsteps_Rasch-Model_Computer_Program

Mahmuti, A., Hamzić, D. K., & Thaqi, X. (2025). The impact of contextual teaching and learning on improving student achievement in economic mathematics. International Electronic Journal of Mathematics Education, 20(3). https://doi.org/10.29333/iejme/16233

Mar, J., Regis, M., & Gomez, R. S. (2023). Contextualized Teaching in Mathematics, Perceptions and Attitudes towards Problem-Solving. United International Journal for Research & Technology, 4(5), 154–164.

Muhayyang, M., Nasta, M., & Sakkir, G. (2023). Students’ Affective Silence in English Classroom Interaction. 7(2), 290–304.

Muhtarom, M. (2024). Developing an instruments to measure prospective teacher beliefs about mathematical problem-solving using the Rasch model. Jurnal Elemen, 10(2), 274–288. https://doi.org/10.29408/jel.v10i2.25040

Norainna, P. H. S. (2018). Situated learning theory: The key to effective classroom teaching ? HONAI: International Journal for Educational, Social, Political & Cultural Studies, 1(1), 49–60. https://www.journals.mindamas.com/index.php/honai/article/view/1022

Nurhayati, & Bernard, M. (2019). Analisis kesulitan siswa dalam pemecahan masalah matematik siswa kelas x SMK Bina Bangsa pada materi persamaan dan pertidaksamaan [Analysis of student difficulties in solving mathematical problems for 10th grade students at SMK Bina Insan Bangsa on the topic of equations and inequalities]. Journal on Education, 1, 497–502.

Obiano, J. A., & Parangat, K. B. (2023). Assesing the effect of polya’s theory in improving problem solving ability of grade 11 students in san marcelino district. American Journal of Humanities and Social Sciences Research, 7(8), 110–119.

OECD. (2020). OECD Economic Outlook. OECD Publishing. https://doi.org/10.1787/39a88ab1-en

Ouanhlee, T. (2023). Learning human resources and applying it to real-life situations. International Business Research, 16(2), 13–26. https://doi.org/10.5539/ibr.v16n2p13

Peng, F., Wang, S., & Yan, T. (2023). enhancing vocational education through innovative skills competitions: Challenges and solutions. Journal of Contemporary Educational Research, 7(7).

Perdana, N. S. (2018). Evaluasi pelaksanaan pembelajaran model teaching factory dalam upaya peningkatan mutu lulusan [Evaluation of the implementation of the teaching factory learning model in efforts to improve graduate quality]. Jurnal Serunai Administrasi Pendidikan, 7(1).

Prianto, A., Firman, F., Mayasari, D., & Widoyoningrum, S. (2025). Teaching factory-based learning and its impact on students’ employability skills. International Journal of Learning, Teaching and Educational Research, 24(12), 215–240. https://doi.org/10.26803/ijlter.24.12.10

Rahman, M. M. (2019). 21st Century skill “problem solving”: defining the concept. Asian Journal of Interdisciplinary Research, 64–74. https://doi.org/10.34256/ajir1917

Rusiyah, Eraku, S. S., & Supadmi. (2020). Analisis soal ujian akhir semester mata pelajaran geografi dengan menggunakan permodelan rasch [Analysis of end-of-semester exam questions for geography using rasch modeling]. Jurnal Swarnabhumi: Jurnal Geografi dan Pembelajaran Geografi, 5, 11–18. https://doi.org/10.31851/swarnabhumi.v5i1.4136

Samo, D. D., Darhim, D., & Kartasasmita, B. (2017). developing contextual mathematical thinking learning model to enhance higher-order thinking ability for middle school students. International Education Studies, 10(12), 17–29. https://doi.org/10.5539/ies.v10n12p17

Sari, D. R., Sekarwana, N., Hinduan, Z. R., & Sumintono, B. (2016). Analisis tingkat kepuasan masyarakat terhadap dimensi kualitas pelayanan tenaga pelaksana eliminasi menggunakan pemodelan rasch [Analysis of community satisfaction levels with the service quality dimensions of elimination implementation personnel using rasch modeling]. Jurnal Sistem Kesehatan, 2(1), 47–55. https://doi.org/10.24198/jsk.v2i1.10419

Sepriyanti, N., Trinova, Z., & Susanto, A. (2020). The Application of the polya’s steps reviewed from problem-solving ability in two-variable linear equation system (SPLDV). Tarbiyah : Jurnal Ilmiah Kependidikan, 9(1), 51–65. https://doi.org/10.18592/tarbiyah.v9i1.3543

Sinaga, B., Sitorus, J., & Situmeang, T. (2023). The influence of students’ problem-solving understanding and results of students’ mathematics learning. Frontiers in Education, 8, 1–9. https://doi.org/10.3389/feduc.2023.1088556

Siswanto, E. (2024). Kemampuan pemecahan masalah pada pembelajaran matematika: systematic literature review [Problem-solving ability in mathematics learning: systematic literature review]. Jurnal Riset Pembelajaran Matematika Sekolah, 8.

Suarsana, I. M., Lestari, I. A. P. D., & Mertasari, N. M. S. (2019). The effect of online problem posing on students’ problem-solving abilitiy in mathematics. International Journal of Instruction, 12(1), 809–820. https://doi.org/10.29333/iji.2019.12152a

Sumantri, D., Subijanto, Siswantari, Sudiyono, & Warsana. (2017). Pengelolaan pendidikan kejuruan - pengembangan sekolah menengah kejuruan (SMK) 4 Tahun [vocational education management - development of 4-year vocational high schools (SMK)].

Sumintono, B. (2018). Rasch model measurements as tools in assessment for learning. AtlantisPress, 173, 38. https://doi.org/10.2991/icei-17.2018.11

Triyono, D., Gorky Sembiring, M., & Dwi Susandi, A. (2025). Sinergi pembelajaran berbasis masalah dan motivasi berprestasi: membentuk kompetensi pemecahan masalah matematis siswa sekolah menengah kejuruan [The synergy of problem-based learning and achievement motivation: shaping vocational high school students’ mathematical problem-solving competence]. International Journal of Progressive Mathematics Education, 5(2), 350–378. https://doi.org/10.22236/ijopme.v5i2.21210

Tusi Fatimah, A., & Yuniawan Isyanto, A. (2022). Integrator kontekstual untuk pembelajaran matematika di sekolah menengah kejuruan program agribisnis perikanan [Contextual integrator for mathematics learning in vocational high schools, fisheries agribusiness program]. Seminar Nasional Penelitian LPPM UMJ, 1–9.

Utomo, H., Muhtarom, & Dwijayanti, I. (2024). Eksplorasi media interaktif googles site dengan alur merdeka berbasis design thinking [Analysis of students’ difficulties in mathematical problem solving]. 4(1), 42–58.

Wahjusaputri, S., & Bunyamin, B. (2022). Development of teaching factory competency-based for vocational secondary education in Central Java, Indonesia. International Journal of Evaluation and Research in Education, 11(1), 353–360. https://doi.org/10.11591/ijere.v11i1.21709

Zega, O., Telaumbanua, Y. N., & Zega, Y. (2024). Implementation of realistic mathematics education learning model to improve students’ mathematics learning outcomes.

Downloads

Published

30-04-2026

How to Cite

Muhtarom, M., Utomo, H. N., & Dwijayanti, I. (2026). Enhancing vocational students’ mathematical problem-solving through contextual teaching factory learning. Jurnal Elemen, 12(2), 392–408. https://doi.org/10.29408/jel.v12i2.31809

Issue

Section

Articles

Similar Articles

<< < 9 10 11 12 13 14 15 16 17 18 > >> 

You may also start an advanced similarity search for this article.