Deep learning trajectories for statistical graphs in mathematics learning

This study develops and validates of a Learning Trajectory (LT) for statistical graph instruction by integrating a Deep Learning (DL) approach with the Structure of the Observed Learning Outcome (SOLO) taxonomy, ethnomathematics, and technology. Using an Educational Design Research (EDR) methodology, the study was conducted through pilot teaching, design experimentation, and retrospective analysis. A total of 190 final-year junior high school students from Binjai City, North Sumatra, Indonesia, participated. Data were collected through classroom observations and analyzed using the SOLO taxonomy to trace students’ conceptual development. The Hypothetical Learning Trajectory (HLT) was iteratively compared with the Actual Learning Trajectory (ALT) to produce a validated LT, which was further developed into a Local Instructional Theory (LIT). The results show that students’ understanding progressed from Unistructural to Extended Abstract levels, particularly in interpreting and generalizing graphs and mean values. The integration of ethnomathematics through the Berahoi tradition, combined with GeoGebra and AI, supported meaningful and culturally relevant learning. Importantly, the findings reveal that conceptual progression was not driven by contextual or technological elements alone, but by how these were systematically integrated within a learning trajectory supported by targeted scaffolding. Theoretically, this study contributes to EDR by providing an empirically grounded explanation of how learning trajectories mediate students’ progression across SOLO levels. Practically, it offers a framework for designing contextual, technology-enhanced, and culturally responsive mathematics instruction.

Deep learning · Ethnomathematics · Statistical analysis · Statistical Learning · Advanced Graph Neural Networks · Big Data and Digital Economy · Graph Theory and Algorithms