Analyzing mathematics textbooks through a constructive-empirical perspective on abstraction: The case of pythagoras' theorem

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic tool. The results show that Taiwanese textbooks intended to develop the object through the variation among the levels of generality as well as between more and less familiar connections. The procedural diagrams were less provided than the conceptual diagrams, and the diagrams required more processing were less provided than the diagrams required less processing. Nonetheless, there were differences among the three textbooks. On the basis of similarities and differences, we discuss issues related to the learning and teaching of mathematics.