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Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular. [ABSTRACT FROM AUTHOR]