Textbook analysis on the differentiation of implicit or parametric functions from the perspective of correspondence

Mathematics textbooks are considered essential teaching and learning materials that teachers rely on for conducting lessons and assessments. The content of these textbooks can significantly influence students' logical understanding of mathematical concepts. This study analyzes the descriptions related to the differentiation of functions represented by implicit functions or parameters in high school calculus textbooks. The findings are as follows: First, all eight textbooks indicated that it is possible to appropriately restrict the domain and codomain when describing implicit functions to define them as functions. Second, only one textbook expressed the relationship of y as a function of x when describing functions represented by parameters, while the other seven textbooks described the relationship between the two variables x and y. Third, seven textbooks presented y not a function of x as the differentiation tasks concerning functions represented by parameters. The descriptions in mathematics textbooks can be a source of misconceptions and may lead to logical issues regarding concepts.