From misconceptions to machine models: A decade review of conceptual and technological advances in probability and combinatorics learning

Abstract

Abstract concept in probability and combinatorics often conflict with students’ intuitive reasoning, creating persistent challenges in teaching and learning. To investigate these challenges a systematic literature review (SLR) following the PRISMA framework was conducted of 50 peer-reviewed articles published between 2015 and 2025. The articles were retrieved through WATASE UAKE, an academic literature discovery platform that provide access to a curated collection of open access educational research published in Scopus Indexed journals across quartile Q1-Q4. This study identified three key findings. First, probability dominates 84% ​​of the literature, yet instruction remains largely mechanistic, with modern approaches such as Bayesian reasoning underutilized especially in primary education. In addition, human-centered strategies such as multiple representations, contextual modeling, and game-based learning have proven effective in addressing misconceptions but are rarely systematized in curricula. Second, while 26% of studies involved technology (CAI, GeoGebra, AI), only 10% used modern AI, and none developed systems that diagnostically adapt to student misconceptions such as equiprobability bias. Third, because curricula treat probability's classical, frequentist, and subjective perspectives as disconnected, future research should pursue cross-cultural, design-based studies that adapt effective pedagogical strategies to local curricula, alongside teacher education programs that build diagnostic competence rather than content mastery alone. This reveals a critical gap: the absence of AI-based learning materials that address the cognitive structures behind errors. This review contributes to mathematics education research by mapping the disconnect between cognitive-pedagogical strategies and AI-based innovation, an integration that remains largely absent from existing research frameworks. It also proposes a cognition-aware AI model as a novel direction for future instructional design. The study calls for curricula that integrate classical, frequentist, and subjective perspectives, and teacher education programs that strengthen epistemological understanding of uncertainty.