Study of asymptotes in upper secondary mathematics education: A praxeological analysis of textbooks in Croatia

The notion of the asymptote is part of the upper secondary and university mathematics curriculum. Acknowledging the existing literature on student issues with asymptotes and the influential role of textbooks in mathematics education, we examined the knowledge of asymptotes provided in upper secondary mathematics textbooks in Croatia. Within the framework of the Anthropological Theory of the Didactic, we constructed a reference model for the study of asymptotes and conducted a systematic and detailed textbook analysis, focusing on praxeological organisation, ostensive manifestations, and the process of study. The analysis revealed that textbooks fail to connect knowledge and representations of asymptotes across different contexts, to organise the process of study in a mathematically and pedagogically coherent manner, and to address recognised student issues related to asymptotes. This study contributes to the research on asymptotes and textbook analysis, and proposes a reference model based on exploration using different representations, analogous work, and the construction of a generalised discourse.