Interpretation and Application of the Van Hiele Model from the Perspective of Meaningful Learning in the Characterization of Qualitative Variables

Abstract

This article aimed to analyze the interpretation and application of Van Hiele's reasoning model, based on Ausubel's theory of meaningful learning, for the characterization of qualitative variables in secondary school students. The methodological strategies employed were based on an interpretive qualitative paradigm and a pedagogical action research (PAR) design, with a total of 60 key subjects comprised of students from the sixth cycle of the Marcos García Carrillo Educational Institution (Colombia). Methodological triangulation was used, utilizing a diagnostic questionnaire, pre-post tests, semi-structured interviews, classroom observation, and field notes. The results showed that the analysis revealed a significant progression in students' reasoning levels. While 66% of students initially struggled to identify and classify variables, 79% were able to differentiate them, organize them into frequency tables, and interpret their graphical representations after the intervention. Five learning descriptors emerged: contextual recognition, classification by attributes, tabular construction, graphical interpretation, and statistical argumentation. Finally, concluded that the theoretical framework connecting Van Hiele's theory to meaningful learning provides an appropriate didactic scaffolding that facilitates the transition from visual-descriptive reasoning to analytical and argumentative levels in school statistics. Furthermore, its application is recommended for teacher training and curriculum development.