Analyzing the written discourse in calculus textbooks over 42 years: the case of primary objects, concrete discursive objects, and a realization tree of the derivative at a point

Abstract

Mathematical objects are the outcomes of human discourse and come to life through the process of objectification. Primary and concrete discursive objects (d-objects) play an important role in this process, forming different realizations through the objectification process. In the present study, we analyze the written discourses about the derivative at a point in fourteen Year 11 and Year 12 Iranian calculus textbooks over 42 years (1979–2020) in terms of primary objects, concrete d-objects, and the realizations used in them, here based on Sfard’s commognitive theory. The research method is a qualitative content analysis in which the analysis units were texts, examples, activities, and exercises in the textbooks. The results show that out of the 14 textbooks, only five included primary and concrete d-objects. The other textbooks only used abstract objects in their written discourse about the derivative. The pictures (visual mediators) that were used as primary objects gradually changed from schematic to real colored photos, and locally developed technologies and cultural elements were included in the new textbook editions. Additionally, the number of concrete d-objects increased in the new editions. In terms of the realizations, the number of roots also increased over time; however, none of the textbooks had all fve main realizations (i.e., symbolic, graphical, verbal, numerical, and physical) for the derivative at a point. The realization tree developed as part of this study can be used as an analytical framework to analyze calculus textbooks in other contexts and can be used by teachers and lecturers to help students have explorative participation in discourse on the derivative.