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All Journal MUSTEK ANIM HA Journal of Honai Math JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Varian Jurnal Magister Pendidikan Matematika (JUMADIKA)
Ruslau, Maria Fransina Veronica
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Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Social Sciences Other

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Journal : Jurnal Varian

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A Bayesian Ordinal Analysis of Students’ Progression Across Van Hiele Levels Ruslau, Maria Fransina Veronica; Pratama, Rian Ade; Meirista, Etriana
Jurnal Varian Vol. 9 No. 1 (2026)
Publisher : Universitas Bumigora

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30812/varian.v9i1.6079

Abstract

Understanding students’ progression across hierarchical levels of geometric reasoning requires analytical approaches that respect ordinal structure and quantify uncertainty. The purpose of this study is to model students’ progression across Van Hiele levels probabilistically and to estimate level-specific transition probabilities under uncertainty using paired pretest–posttest data from Grade 8 and Grade 9 students. The method used in this study is Bayesian ordinal regression with a cumulative logit specification estimated via MCMC sampling. Van Hiele levels were modeled as ordered categorical outcomes, and posterior summaries, transition matrices, and posterior predictive checks were used to characterize progression and assess model adequacy. The results indicate that progression is predominantly upward in both grades, with negligible posterior support for regression. Grade-dependent differences are evident: Grade 8 shows broader, more heterogeneous transitions from a uniformly low baseline, whereas Grade 9 exhibits more constrained, incremental progression from a higher, more dispersed initial distribution. Posterior predictive checks confirm that the model adequately reproduces the observed posttest patterns, supporting the validity of the Bayesian ordinal specification. Pedagogically, these findings imply that students at lower baseline levels tend to undergo broader conceptual shifts, whereas those at higher levels require sustained, targeted instructional support to advance further. These findings indicate that baseline ordinal structure shapes progression dynamics and that Bayesian ordinal modeling offers a coherent alternative to significance-based approaches for analyzing hierarchical learning outcomes. Educationally, this underscores the need to align instruction with students’ initial Van Hiele levels to support optimal conceptual advancement.
Co-Authors Datu, Rianto Pali' Ernawati, Lusia Greitha Meirista, Etriana Mutmainnah, Linda Za’farani Nur?aini, Khumaeroh Dwi Nurlianti Oswaldus Dadi Palobo, Markus Pratama, Rian Ade Suryani, Dessy Rizki Suryani, Dessy Rizky