Real numbers from past to present and their place in the mathematics curricula during the Republican Era in Turkey

This study examines the historical development of the concept of real numbers and its treatment in Turkish middle and high school mathematics curricula during the Republican era. It aims to uncover how the concept is represented, positioned within the conceptual structure, and transformed over time. Grounded in the Theory of Didactic Transposition and supported by multiple theoretical perspectives, the study classifies learning outcomes into intuitive, operational, and formal levels, analyzing their evolution across programs. Conceptual ecology-based diagrams and historical timelines were also used to reflect the concept's broader mathematical connections and temporal trajectory. Findings reveal that real numbers were long approached at an operational level, with limited yet periodic attention to intuitive and formal representations. Although recent curricula attempt to centralize the concept, it often remains instrumental. The 2024 curriculum, however, marks a critical shift, presenting real numbers as a core and multidimensional construct. The study thus provides a comprehensive lens on the pedagogical evolution of this foundational concept. Keywords: Real numbers, Mathematics Curricula, Ecological model, Theory of Didactic Transposition, Historical analysis.