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Research, from all around the world, has shown that teachers' actions are informed by a variety of factors, including long-held and frequently unarticulated traditions about teaching and learning, systemic expectations of the processes of schooling, available textbooks, traditions of teacher education, school cultures, assessment traditions and personal beliefs and values. In the fourth article of this series, the authors describe what mathematics teachers actually teach in four European countries. These countries include Flanders, England, Hungary and Spain. The authors conclude that the teachers of each country were acting in accordance with the customs and practices of their country. (Contains 4 tables and 1 note.) [For part 3, see EJ768785.]

In this article, the authors compare texts, times, technologies, and trails in mathematics lessons in five European countries (Flanders, England, Finland, Hungary and Spain). They start by discussing the provision and use of textbooks. After this they discuss lesson lengths and their impact on learners. They consider the extent of technology integration in project classrooms and close with a brief look at the ways in which teachers trail the content of their lessons. (Contains 2 tables and 2 notes.)

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.)

This paper addresses four questions concerning the influence of culture on mathematics teachers' professional practice. Firstly, drawing on categorical data yielded by the application of low inference coding schedule to video recordings of sequences of lessons taught by case study teachers on four common topics in England, Flanders, Hungary and Spain, we undertook an exploratory factor analysis to examine the ways in which such coded variables interact. This process yielded five factors, each of which was interpretable against the literature and highlighted the extent to which dichotomisations of mathematics teaching as reform or traditional are not necessarily helpful, not least because all project teachers exhibited characteristics of both. Secondly, factors scores were analysed by nationality to reveal culturally located practices resonant with the available literature. Thirdly, cluster analyses yielded four well-defined cross-cultural clusters of episodes, each indicative of particular didactical perspectives that appeared to challenge the exclusivity of these culturally located practices. Finally, the key methodological finding was that the manner in which data are analysed influences greatly the outcomes of comparative mathematics research. [ABSTRACT FROM AUTHOR]