How Do Indonesian Students Learn Function Concepts? A Praxeological Analysis of Textbook

The conception of functions, defined as the relationship between magnitudes or sets of ordered pairs, varies among students depending on the contextualization of the concept within the curriculum, notably in school textbooks. This investigation endeavors to scrutinize the approach taken by Indonesian textbooks in introducing the function concept at the lower secondary school level. An eighth-grade mathematics textbook was scrutinized utilizing praxeology, the fundamental construct of the Anthropological Theory of the Didactic. The analytical process unfolded in three main phases: examination of the praxis block, analysis of the logos block, and evaluation of the textbook's praxeological structure in collaboration with experts and educators. The examination revealed that the Indonesian textbook organizes functions into three distinct local praxeological frameworks: functions as sets, bijective functions, and functions as relationships between magnitudes. The praxis primarily emphasizes tasks and techniques for functions formulated by sets, shaping the landscape of function learning in Indonesia. Consequently, a notable epistemological gap within logos stems from the disparity between two conceptions of functions: functions as sets and analytical expressions. These findings underscore the necessity for an alternative praxeological arrangement of functions, mainly to bridge the divide between the set-theoretical definition and the analytical expression of a function.