Representations and problem solving

Problem solving is an important practice in education, since it allows students to give meaning to concepts by contextualizing them. The literature reports evidence that developing problem solving abilities strongly depends on developing problem representation abilities. This, in turn, appears to be connected with students' ability to understand not only the problem's explicit information, but also the implicit one, and to connect both to their previous knowledge. Different roles in problem solving appear to be played by representations which are given with the text of problems and representations which the solvers build by themselves to support their activity during problem solution. Representations play a crucial role in problem solving in particular when abstract concepts are handled, as it is the case with mathematical problems. Here, particular attention should be paid at didactical level, since students easily assimilate abstract concepts with their representations, hence finding even more difficult than in other disciplines the use of multiple representations of a same concept. Finally, several authors address, in different ways, the issue to help problem solvers to improve their representational abilities. Despite the diversity of approaches, most of these studies highlight the need to make the students acquire critical knowledge and critical awareness of the nature and affordances of representations.