The Teaching of Initial Multiplication Concepts and Skills in Croatian Textbooks

The goal of this paper is to describe the teaching of initial multiplication concepts and skills, up to the multiplication table, in the Croatian educational system. As Stiegler and Hiebert (1999) concluded, teaching is a complex system rooted in a cultural script of a given society. To describe it without ignoring certain features of it that appear to be self-evident to an insider, it is necessary to step out of this cultural frame. For that reason, we study the teaching of initial multiplication in Croatia by comparing Croatian mathematical textbooks with textbooks from Singapore, Japan, and England. For the textbook analysis, we adapt the framework of Charalambous, Delaney, Hsu, and Mesa that examines a textbook as an environment for the construction of knowledge of a single mathematical concept. The analysis provides evidence that practice and automation are at the centre of the initial learning of multiplication in Croatia. The meaning of multiplication usually is not clear, and pupils are not provided additional tools for developing understanding, nor they are encouraged to use different calculation strategies in a flexible manner. The study also indicates that Croatian textbooks present mathematics as a practice that is closed and pre-given, restricted to the one and the only right way through it.