Utilizing Praxeology and the cKȼ Model to Developing Didactical Design in Derivatives: An Indonesian Mathematics Textbook Study

Analyses of mathematics textbooks have predominantly employed praxeological approaches to examine the organization of theory and institutional relations to knowledge. However, limited attention has been given to the epistemological foundations underlying the mathematical concepts presented. This study addresses this gap by employing the cKc model to connect textbook concepts with historical interpretations. We analyzed how the concept of ‘rate of change’ was institutionalized in Calculus: Early Transcendentals (CET) and Matematika Tingkat Lanjut (MTL) to inform didactical design for upper secondary students. The findings reveal that the concept of the derivative is transformed from an algebraic to a calculus perspective. Textbooks tend to present the rate of change and the slope of the tangent line as applications of the derivative rather than as epistemological foundations of the concept itself. Consequently, students often prioritize algebraic manipulation over a conceptual understanding of change and increment, which should serve as the central focus of calculus instruction.