Integrating Popular Digital Contexts into Realistic Mathematics Education: Designing a Hypothetical Learning Trajectory for Arithmetic Sequences and Series

The integration of popular culture and digital platforms into mathematics learning remains underexplored, limiting the development of meaningful and context-based instructional designs. This study develops a Hypothetical Learning Trajectory (HLT) for arithmetic sequences and series by integrating TikTok into a digital mathematics classroom. The study was conducted within the preliminary design phase of design research using qualitative methods, including literature review, classroom observations, teacher interviews, and expert validation through focus group discussions. The resulting HLT consists of two iceberg models grounded in the principles of Realistic Mathematics Education (RME). Each model contains six sequential activities comprising one contextual situation and five guided mathematical problems. The first model employs viewer-growth data from the TikTok account @raimlaode94 to support students in constructing the arithmetic sequence formula (Un) through repeated addition and ratio tables. The second model uses engagement data from the TikTok account @jeromepolin98 to guide students in deriving the arithmetic series formula (Sn) using structured tables, ratio columns, and visual folding strategies. Both trajectories are collaboratively implemented using Canva to maximize the pedagogical use of digital devices. This study provides a theoretically grounded and scalable framework that connects students’ informal digital experiences with formal mathematical reasoning in technology-enhanced classrooms.