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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.]