Didactic Transposition of Absolute Value in Calculus Courses: Analyzing Curricula, Textbooks, and Classroom Instruction

Didactic Transposition of Absolute Value in Calculus Courses: Analyzing Curicula, Textbooks, and Classroom Instruction. Objective; This study aimed to analyze the knowledge to be taught in absolute value learning as part of the didactic transposition process. Method; A qualitative approach with a descriptive design was employed to examine curriculum documents and calculus textbooks as primary data sources. The research adopted a didactic transposition and praxeological framework to analyze the structure of absolute value instruction. The methodology included document selection based on inclusion criteria, content analysis of absolute value concepts in textbooks, comparison with theoretical praxeology models, and expert validation to ensure alignment with established mathematical and pedagogical principles. Triangulation was applied by analyzing multiple textbooks and curricula to enhance validity and reliability. Findings; The study results indicate that learning absolute value requires comprehensive material to bridge the transition of knowledge from school to university. Differential calculus textbooks introduce the absolute value concept with an initial definition as a non-negative value that geometrically represents distance, followed by a piecewise definition commonly found in high school textbooks. Content analysis reveals that task techniques related to absolute value material predominantly focus on perceptual, algebraic, and operational aspects, while graphical visualization is lacking, which hinders a thorough conceptual understanding. This highlights the contrast between the procedural approach in schools and the conceptual approach in universities, emphasizing the necessity of comprehensive materials to prevent learning obstacles. Conclusion; The findings emphasize the need for a more comprehensive presentation of absolute value in university calculus textbooks to support a smooth transition from school to higher education. The analysis revealed that while absolute value is introduced conceptually, the lack of graphical representation limits students' understanding. Additionally, inconsistencies between curriculum documents and learning materials indicate the necessity of aligning instructional resources. To prevent learning obstacles, it is recommended that absolute value content in differential calculus textbooks be presented in a complete and structured manner, integrating both procedural and conceptual approaches.

Keywords: knowledge to be taught, absolute value, didactic transposition.