In this study, genre is a central concept. With a theoretical basis in three pragmatical genre traditions, an analytical tool is formulated, making it possible through different criteria to identify varied expressions of the genre notion in the syllabus for Swedish with a focus on early compulsory school and three textbooks with explicit focus on the teaching of genres. The analysis mainly draws upon six writing discourses (Ivanič, 2004), which enables me to study the actual and potential expressions of genre in the curriculum and study materials.The analysis shows that the written genre expressed in the analysed text materials is heavily influenced by a sociosemiotic perspective of genre, emphasizing internal structure, and that it is, regardless of study material, situated within the genre discourse. The variation in how genres are expressed in the texts concern whether they are influenced by the process discourse or social practices discourse as well. Genre is also discussed from a sociorhetorical perspective, focusing on the social context, but is shown to have limited expression in the text materials within this study.The study concludes that the genre notion within the Swedish curriculum for the school subject Swedish in primary school and within the study materials have de-emphasised the social purpose of genres. It also concludes that genre is too varied and complex in its semantic and pragmatic variation in different discourses inside and outside of school practises to be recognized in actual teaching.