Exploring Students’ Conceptual Understanding of Mathematical Modeling through Inquiry-Based Learning Experiences

Abstract

This phenomenological study explores secondary school students’ lived experiences of conceptual understanding in mathematical modeling through inquiry-based learning (IBL) in an Indonesian public senior high school. The research aims to uncover the interpretive processes, challenges, and meaning-making dynamics that occur when students engage in authentic modeling tasks within an IBL framework. Data were collected via semi-structured interviews with 15 students and 3 mathematics teachers, participatory observation of 10 IBL sessions, and analysis of modeling artifacts and reflective journals. Thematic analysis following Miles and Huberman’s interactive model revealed three interconnected themes: conceptual integration through iterative exploration, challenges in contextual translation, and enhanced meaning-making via collaborative inquiry. Findings indicate that iterative cycles and peer collaboration transform initial procedural approaches into coherent conceptual networks, while culturally relevant tasks help bridge experiential disparities between rural and urban students. The study contributes a phenomenological depth to existing constructivist and sociocultural literature, highlighting the critical role of cultural congruence and relational processes in fostering deep, adaptive understanding of mathematical modeling. Theoretically, it enriches Vygotskian and Deweyan frameworks by foregrounding lived experience and iterative mediation. Practically, the results advocate for culturally responsive curriculum design and teacher training in scaffolded collaborative inquiry. Future research should examine longitudinal retention and cross-cultural transferability of these conceptual gains