FOLIA 345 Annales Universitatis Paedagogicae Cracoviensis Studia ad Didacticam Mathematicae Pertinentia 13(2021) ISSN 2080-9751 DOI 10.24917/20809751.13.5 Veronika Hubeňáková, Ute Sproesser, Ingrid Semanišinová Comparing German and Slovak teachers’ knowledge of content and students related to functions * Abstract. A crucial aspect of learning about (linear) functions is the abil- ity to change between graph representation and equation and vice versa. Traditionally, German, and Slovak students are being exposed to different procedures for these representational changes. Within a sample of 49 Ger- man and 56 Slovak teachers, we analyzed if these different procedures can also be observed in the teachers’ corresponding knowledge of content and students, i.e., if the teachers expected different student strategies and errors. The results confirm this assumption and emphasize the importance of con- sidering this teacher’s knowledge in a country-specific way and to be careful when comparing such knowledge of teachers from different countries. 1. Introduction The purpose of this study is to investigate potential diferences in particular components of teachers’ professional knowledge between Germany and Slovakia. This should provide new insights about teachers’ knowledge that will help to im- prove pre- and in-service teachers’ education practices. The idea of this study arose as the authors exchanged ideas about what kind of procedures for repre- sentational changes between function graph and equation are helpful to support students’ learning and to what extent they are common in teacher education and practice in these two countries. In order to frame this study in more detail, we will outline the theoretical background related to functions and teachers’ professional knowledge. * 2020 Mathematics Subject Classification: Primary: 97B50 ; Secondary: 97D70 Keywords and phrases: linear function, learning difficulties, country-specific teachers’ knowledge