Mathematical knowledge is more abstract than other school subjects (Duval, 2006), and the mathematical language is particularly challenging for multilingual students. Researchers highlight how various teaching strategies, such as multimodality (Takeuchi, 2015) or the use of different representations (Duval, 2006), promote students’ learning in mathematics. Representations can be equated with modes of expression mentioned in the curriculum for mathematics grades 4–6, namely that students should develop their [...] ability to use mathematical forms of expression to discuss and explain questions, calculations, and conclusions (From the Swedish curriculum “Läroplan för grundskolan, förskoleklass, och fritidshemmet [Lgr22], 2024”, translated to English). 

The aim of the present thesis has been to investigate how mathematics teachers in a Swedish school context use different representations during whole-class teaching in grades 4–7, based on two areas of the core content: (1) geometry and (2) number sense and the use of numbers (Lgr22, 2024). 

The study is based on a systematic investigation. The method for data collection was structured observation using an observation protocol, which made it possible to describe teachers’ use of different forms of representation. 

The results show that within the area of geometry, a higher degree of conversions occur, often combined with several different representations. In contrast, within number sense and the use of numbers, conversions are used to a lesser extent. The results thus indicate that there is greater variation in how mathematical content is communicated in the area of geometry compared to number sense and the use of numbers. Based on Duval’s (2006) theoretical framework, all mathematics teaching should be characterized by a greater variety of representations, where conversions are consistently implemented in teaching to strengthen students’ learning in mathematics.