This article discusses a comparative study, funded by the European Union, of the teaching of mathematics in five European countries, (Flanders, England, Finland, Hungary and Spain) to students in the upper primary (ages 10-12) and lower secondary (12-14) years. These ages were chosen as they represent a time when many students' experiences of mathematics shift from concrete and inductive to abstract and deductive. The project team video-recorded a single sequence of lessons in each country on each of four key topics. After an initial school-based meeting, during which the project aims and aspirations were outlined, each teacher was filmed for four or five successive lessons, starting with the first on a particular topic. The topics, which were representative of the breadth of school mathematics, concerned the teaching of: (1) percentages (a topic of arithmetic applicability) at the upper primary level; (2) polygons (a routine geometrical topic) at the upper primary level; (3) polygons (an opportunity to examine curriculum continuity) at the lower secondary level; and (4) linear equations (an early topic of formal algebra) at the lower secondary level. In summary, the project data indicates that teachers behave differently in different countries and that their reasons for so doing may be a consequence of informed decision-making or an unacknowledged conformity to a particular tradition of mathematics teaching. (Contains 4 tables.)