This study is a part of a bigger study of 23 fifth graders observed as they worked in heterogeneous groups on a sequence of 12 modelling tasks for eight months. This chapter focuses on nine students identified as having difficulties in mathematics. Our research goal was to identify the nature of the changes that occurred as they worked on these tasks and is exemplified by one case, that of Sami. The findings show how Sami's mathematical knowledge and modelling competencies developed and how, simultaneously, his group's attitude towards his contributions was affected. At the beginning of the process he did not understand the task situation, and even when he gave relevant realistic considerations his peers ignored him. Later he became more active not only in offering realistic considerations but also in suggesting mathematical ideas, and eventually Sami became dominant and effective in the group and was well aware of this change. Keywords Mathematical difficulties • Modelling competencies • Modelling tasks • Students with learning difficulties 12.1 Theoretical Background Researchers claim that teachers emphasize high thinking processes in good classrooms, while in classrooms of students with learning difficulties, they use methods of instruction that require only low order thinking (Shepard 1991; Raudenbush et al. 1993; Zohar et al. 2001). This tendency exists also when working in a heterogeneous class (Yair 1997).