The Swedish National Agency for Education emphasizes that students in grades 1-3 should be able to develop addition and multiplication strategies based on the properties of these operations before focusing on standard algorithms. This means that teachers need to understand student perceptions of these concepts in order to be able to develop instructions for promoting such strategies. According to Ball, Thames and Phelps (2008) teachers need mathematical knowledge to be able to meet such a demand. Other researchers recommend carrying out qualitative studies investigating a field experience of pre-service and in-service teachers. Since the in-service teachers’ knowledge depends on what they were taught in school themselves, we studied the teaching process in grade 3 in order to learn how they were initially introduced to addition and multiplication (Van Dooren, De Bock, & Verschaffel, 2010).

The teaching process and teachers’ understanding of problems with multiplication content was studied in 3rd grade mathematics classrooms. This study investigated challenges faced by teachers when they went from interpretation to formulation of the multiplication problems. Data is drawn from three main sources: observation, interviews, field notes and video recordings. The data was analysed in a qualitative way, using variation theory (Marton, 2015). The analysis reveals that the participating teachers were more successful in using addition strategies than multiplication ones in problem development. For example, most teachers identified multiplication as a repeated addition. Consequently, they often missed important multiplication structures and their link to division. The results explain some reasons for difficulties in elementary mathematics experienced by in-service teachers and the consequences they lead to in their teaching. Teachers' understanding of mathematical concepts is crucial for their interpretation and setting of the example problems.