Reinventing the area of a circle through Kue Lontar : an iceberg learning trajectory

Purpose Mathematics instruction on the area of a circle often emphasizes formula application rather than conceptual understanding. This study aims to examine how Kue Lontar, a culturally meaningful Papuan artefact, supports pre-service mathematics teachers in developing the area formula through an iceberg learning trajectory (ILT). Design/methodology/approach Grounded in realistic mathematics education, emergent modelling, embodied cognition and ethnomathematics, this study used design research with 28 pre-service mathematics teachers at a university in Papua, Indonesia. Data comprised student worksheets, classroom observations, video and audio recordings, semi-structured interviews and reflective field notes across a teaching experiment and subsequent retrospective analysis. Findings Retrospective analysis produced six interconnected ILT levels: situational engagement, area conservation, sector partitioning and rearrangement, rectangular approximation, mathematization of geometric relationships and formalization. Participants reconstructed A=πr2 by relating the radius to the rectangle’s width and half the circumference to its length. Misconceptions and temporary regressions prompted instructional refinements during the design cycles. Originality/value This study extends ethnomathematical research by conceptualizing Kue Lontar as an epistemic mediator connecting cultural experience, embodied activity, mathematical representation and formal reasoning. The ILT specifies how a culturally meaningful artefact can support the transition from situated experience to formal mathematical knowledge.