The challenges of formal definitions of continuity real -valued fonctions in Tunisian secondary education

Abstract

This study analyzes the challenges of teaching the formal (ε-δ) definition of continuity for real-valued functions in Tunisian secondary education. It examines curricular instability (teaching continuity before limits), the marginalization of ε-δ formalism in textbooks in favor of an intuitive approach, and gaps in teacher knowledge using the (MKT-AC model), particularly in SCK (Specialized Content Knowledge) and MMK (Meta-Mathematical Knowledge). The analysis reveals a tension between formal rigor and students' cognitive needs, evidenced by the majority preference among teachers for graphical strategies and the low operational use of the ε-δ definition. The study advocates for targeted training addressing epistemological and didactic dimensions to bridge intuition and formalism.