María Luz Callejo and Antoni Vila have written an article that was published in Educational Studies in Mathematics last week. The article is entitled Approach to mathematical problem solving and students’ belief systems: two case studies. Most studies that focus on the role of beliefs in relation to problem solving are to some degree based on the works of Alan Schoenfeld, Günther Törner, Liewen Verschaffel, Erkki Pehkonen and several others. So does this. The theoretical part of the paper gives a nice overview of some of the most important earlier studies within this field. Personally, I would have included reference to some more critical perspectives, like Jeppe Skott, and when discussing belief systems, I also think the work of Keith Leatham provides an important contribution to the field. In their discussion, they consider inconsistencies between beliefs and actions, and in this connection, I think a reference to Leatham’s work and his proposed framework of viewing beliefs as sensible systems would have been worthwhile.

Still, I think it is an interesting article to read if you are interested in problem solving or research on beliefs. Here is the article abstract:

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between specific beliefs and problem-solving activity (or vice versa).