In order to develop conceptual understanding students need to work with mathematical problems, i.e. tasks that are somewhat new to them, intellectual challenges that they can’t solve by merely imitating memorized procedures (Schoenfeld, 1985). Instead of solving tasks imitatively, students need to engage in productive struggles, creating (at least parts of) their own methods (Hiebert & Grouws, 2007) Studies have shown that students who are engaged in constructing their solving strategies learn more than students using procedures. The former student group outperforms the latter on posttests (Jonsson, Norqvist, Liljekvist, & Lithner, 2014). But, since procedures are constructed and taught in order to avoid mistakes it is likely that students who create their solving methods make more errors than students who are given a procedure to follow. However, even when students fail during training studies have shown that they score higher on post-tests (Kapur, 2011). These findings are described as productive failure and is in line with the idea of productive struggle (Ibid.).   

However, even if research has shown that creative strategies is preferable to imitative strategies, it seems like teaching, and using, procedures still dominate classroom activities. Teachers prefer to help students to avoid mistakes and to prevent them from struggling with errors, engaged in what could appear as unproductive rather than productive struggles.

These circumstances bring us to the aim of this study:
To bring some further insights into students’ struggling activities when they are dealing with mistakes during problem solving. How may these activities be described and to what extent could these activities be defined as productive as well as unproductive struggles.

The research questions guiding this study:

- What mistakes do students do when it comes to using prior knowledge as well as constructing their own solving methods? 

- What activities, described as struggle do students engage in when they are handling their mistakes

- To what extent could their struggle be described as productive?

- How far have they managed to solve the given problem in relation to the characteristics of their struggle?

Theoretical framework used to frame the study as well as analyzing the data emanates from Hiebert & Grouws’ (2007) framework of productive struggle. Struggle in that sense that students are engaged in making sense of mathematics, i.e. to figure something out that is not directly obvious to them. “If understanding is defined as the mental connections between mathematical facts, ideas and procedures, then struggling is viewed as a process that reconfigures these things” (Hiebert & Grouws, 2007, p. 388). A successful, productive struggle will result in a restructuring of the mental connections, in more powerful ways, in that the problem at hand will make sense and new information, ideas and facts, will become assimilated. These concepts constitutes the basis for analyzing the data (se method for more details).

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