Development of Sahabat Aktuaria: Website-Based Actuarial Mathematics Learning Using a Learning Trajectory Approach

Ani Nuraini; Lailatul Maziyah Wildan Mufaridho; Wahyu Joko Saputro

doi:10.33394/j-ps.v14i4.22314

Authors

Ani Nuraini Universitas Darunnajah
Lailatul Maziyah Wildan Mufaridho Universitas Darunnajah
Wahyu Joko Saputro Universitas Darunnajah

DOI:

https://doi.org/10.33394/j-ps.v14i4.22314

Keywords:

Learning trajectory, Students’ conceptual understanding, Website based learning, Actuarial mathematics, Learning media

Abstract

The digital transformation of higher education has encouraged the use of technology-based, student-centered learning. However, digital technology remains underutilized in university mathematics education, particularly in actuarial mathematics, which involves complex and hierarchical concepts. This study developed and evaluated Sahabat Aktuaria, a website-based learning medium designed with a learning trajectory approach that integrates mastery-based adaptive progression and Universal Design for Learning principles specific to actuarial mathematics, as a developmental (pilot) implementation. Following the ADDIE model (Analysis, Design, Development, Implementation, and Evaluation), the medium was validated by experts and implemented with ten (N = 10) fourth-semester students of the Actuarial Science Study Program at Universitas Darunnajah who had completed the Actuarial Mathematics I course. Data were collected through expert validation sheets, lecturer and student response questionnaires, and learning outcome tests. The medium achieved an expert validation score of 0.764 (valid category), practicality ratings of 85.50% (lecturers) and 86% (students), and an N-Gain score of 0.57 (medium category). A paired-sample t-test showed a statistically significant increase from the pretest (M = 58.50) to the posttest (M = 82.10). These findings provide preliminary evidence that Sahabat Aktuaria is valid, practical, and potentially useful for improving students' conceptual understanding, and they warrant further evaluation in larger controlled studies.

References

Abuhassna, H., Alnawajha, S., Awae, F., Mohamed Adnan, M. A. Bin, & Edwards, B. I. (2024). Synthesizing technology integration within the ADDIE model for instructional design: A comprehensive systematic literature review. Journal of Autonomous Intelligence, 7(5), 1546. https://doi.org/10.32629/jai.v7i5.1546

Akın, A. (2022). The effectiveness of web-based mathematics instruction (WBMI) on K-16 students’ mathematics learning: A meta-analytic research. Education and Information Technologies, 27(6), 8015–8040. https://doi.org/10.1007/s10639-022-10931-x

Alqahtani, A. Y., & Rajkhan, A. A. (2020). E-learning critical success factors during the COVID-19 pandemic: A comprehensive analysis of e-learning managerial perspectives. Education Sciences, 10(9), 1–16. https://doi.org/10.3390/educsci10090216

Bloom, B. S. (1968). Learning for mastery. Evaluation Comment, 1(2), 1–12.

Branch, R. (2010). Instructional design: The ADDIE approach. https://doi.org/10.1007/978-0-387-09506-6

CAST. (2018). Universal design for learning guidelines version 2.2. Wakefield (MA): CAST. Available from: https://udlguidelines.cast.org

Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1

Coletta, V. P., & Steinert, J. J. (2020). Why normalized gain should continue to be used in analyzing preinstruction and postinstruction scores on concept inventories. Physical Review Physics Education Research, 16(1). https://doi.org/10.1103/PhysRevPhysEducRes.16.010108

De Vreugd L, van Leeuwen A, J. R., & van der Schaaf M. (2024). Learning analytics dashboard design and evaluation to support student self-regulation of study behavior. Journal Learn Anal, 11(3), 249–262. https://files.eric.ed.gov/fulltext/EJ1455909.pdf

Elmabaredy, A., Elkholy, E., & Tolba, A. A. (2020). Web-based adaptive presentation techniques to enhance learning outcomes in higher education. Research and Practice in Technology Enhanced Learning, 15(1). https://doi.org/10.1186/s41039-020-00140-

Gall, M., Borg, W., & Gall, J. (2003). Educational research: An introduction. https://doi.org/10.2307/3121583

Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74. https://doi.org/10.1119/1.18809

Hasani, L. M., Sensuse, D. I., Kautsarina, & Suryono, R. R. (2020). User-centered design of e-learning user interfaces: A survey of the practices. In 2020 3rd International Conference on Computer and Informatics Engineering (IC2IE) (pp. 1–7). https://doi.org/10.1109/IC2IE50715.2020.9274623

Jamilah, J., Sandie, S., & Muchtadi, M. (2023). Learning trajectory pengembangan kompetensi pedagogik calon guru matematika. Jurnal Pendidikan Informatika dan Sains, 12, 197–210. https://doi.org/10.31571/saintek.v12i1.5044

Kusuma Dewi, U., & Subekti, E. (2024). Efektivitas media papan pintar terhadap hasil belajar siswa kelas II sekolah dasar. Ainara Journal (Jurnal Penelitian dan PKM Bidang Ilmu Pendidikan), 5(4), 519–525. https://doi.org/10.54371/ainj.v5i4.652

Matcha, W., Uzir, N. A., Gašević, D., & Pardo, A. (2020). A systematic review of empirical studies on learning analytics dashboards: A self-regulated learning perspective. IEEE Transactions on Learning Technologies, 13(2), 226–245. https://doi.org/10.1109/TLT.2019.2916802

Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of Cardiac Anaesthesia, 22(1), 67–72. https://doi.org/10.4103/aca.ACA_157_18

Nielsen, J. (2000). Why you only need to test with 5 users. Nielsen Norman Group. https://www.nngroup.com/articles/why-you-only-need-to-test-with-5-users/

Nieveen, N., & Folmer, E. (2013). Formative evaluation in educational design research. In T. Plomp & N. Nieveen (Eds.), Educational design research – Part A: An introduction (pp. 152–169). SLO.

Nikou, S., & Economides, A. (2023). User-centered design and usability evaluation of learning technologies. Interact Learn Environ, 31(2), 431–445.

Pettersson, F. (2021). Understanding digitalization and educational change in school by means of activity theory and the levels of learning concept. Education and Information Technologies, 26(1), 187–204. https://doi.org/10.1007/s10639-020-10239-8

Prior, S., Campbell, S., Greenwood, M., Shearer, T., Walker, K., & Young, S. (2020). Purposive sampling: complex or simple? Research case examples. Journal of Research in Nursing, 25. https://doi.org/10.1177/1744987120927206

Sailer, M., Maier, R., Berger, S., Kastorff, T., & Stegmann, K. (2024). Learning activities in technology-enhanced learning: A systematic review of meta-analyses and second-order meta-analysis in higher education. Learning and Individual Differences, 112. https://doi.org/10.1016/j.lindif.2024.102446

Samo, D. D., Ekowati, C. K., Soko, I. P., & Ngawas, K. R. (2023). Pengaruh penggunaan media pembelajaran matematika berbasis website terhadap peningkatan hasil belajar siswa: Meta-analisis. Jurnal Riset Pendidikan Matematika, 10(1), 89–101. https://doi.org/10.21831/jrpm.v10i1.49357

Sanusi, D., & Uhomoibhi, J. (2025). Transforming actuarial education and practice in emerging markets through AI-enhanced learning systems.

Sari, F. F., Sudatha, I. G. W., Santoso, M. H., & Suartama, I. K. (2025). Mengurangi beban kognitif dalam pembelajaran matematika: Tinjauan sistematis strategi dan intervensi pembelajaran. Jurnal Pendidikan Dan Pembelajaran Indonesia (JPPI), 5(3), 1630–1644. https://doi.org/10.53299/jppi.v5i3.2190

Shoffa, S., Subroto, D. E., Nasution, F. S., Astuti, W., Rommadi, U., Azhari, D. S., … Gusmirawati. (2023). Media pembelajaran. Yani, Eds.) (1st ed.). CV. Afasa Pustaka.

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205

Sofroniou, A., Patel, M. H., Premnath, B., & Wall, J. (2025). Advancing conceptual understanding: A meta-analysis on the impact of digital technologies in higher education mathematics. Education Sciences. https://doi.org/10.3390/educsci15111544

Sugiyono. (2017). Metode penelitian dan pengembangan (Research and Development/R&D). Alfabeta.

Sukadari. (2019). Professional competency instrument validity of assessment on teacher work performance. Utopía y Praxis Latinoamericana, 6(24), 188–189. https://dialnet.unirioja.es/descarga/articulo/7406865.pdf

Syifaurrahmadania, S., Kamid, K., & Sainuddin, S. (2025). Mapping research trends on learning trajectory in mathematics education: A systematic literature review and bibliometric analysis. Journal of General Education and Humanities, 4(4), 1877–1892. https://doi.org/10.58421/gehu.v4i4.771

Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147–156. https://doi.org/10.3102/0013189X12442801

Taber, K. S. (2018). The use of Cronbach’s alpha when developing and reporting research instruments in science education. Research in Science Education, 48(6), 1273–1296. https://doi.org/10.1007/s11165-016-9602-2

Tambunan, E. H., Simbolon, I., & Rantung, J. (2024). Exploring the essence of web-based interactive learning to enhance higher order thinking skills in nursing students: A focus group study. Nutrix Journal, 8(2), 282–296. https://doi.org/10.1186/s41239-025-00421

Tessmer, M. (1993). Planning and conducting formative evaluations: Improving the quality of education and training. Kogan Page.

Thabane, L., Ma, J., Chu, R., Cheng, J., Ismaila, A., Rios, L. P., Robson, R., Thabane, M., Giangregorio, L., & Goldsmith, C. H. (2010). A tutorial on pilot studies: The what, why and how. BMC Medical Research Methodology, 10(1), 1–10. https://doi.org/10.1186/1471-2288-10-1

Turmuzi, M., & Lu’luilmaknun, U. (2023). The impact of online learning on the mathematics learning process in Indonesia: A meta-analysis. Journal of Technology and Science Education, 13(3), 694–717. https://doi.org/10.3926/JOTSE.2138

van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Educational design research (1st ed.). Routledge.

Van Teijlingen, E., & Hundley, V. (2001). The importance of pilot studies. Social Research Update, 35, 1–4.

Ventura, M., Moadebi, S., & Damian, D. (2021). Impact of motivational interviewing training on emergency department nurses’ skills: A one-group pretest–posttest pilot study. International Emergency Nursing, 56, 100980. https://doi.org/10.1016/j.ienj.2021.100980

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.

Weigand, H. G., Trgalova, J., & Tabach, M. (2024). Mathematics teaching, learning, and assessment in the digital age. ZDM - Mathematics Education, 56(4), 525–541. https://doi.org/10.1007/s11858-024-01612-9

Wulandari, M., Salsabila, N. H., & Ah Ramadhani, A. ’. (2025). Analisis efektivitas penggunaan teknologi digital dalam pembelajaran matematika. Jurnal Media Akademik (JMA), 3(1), 3031–5220. https://doi.org/10.62281

Zakariyah, M. F., Yulianingsih, W., Hidayah, L. N., & Anisa, A. (2024). Implementation of universal design for learning (UDL) in digital learning media: A systematic review. JPPM (Jurnal Pendidikan dan Pemberdayaan Masyarakat), 11(2), 175–188. https://doi.org/10.21831/jppm.v11i2.83253