Meaningful context in mathematical problem solving: a case study

Problem solving is highly recognised as a basic component of mathematical activity. In addition, recent studies have pointed out the significance of perceptuo-motor activities in mathematics learning, which become more or less active depending on the context. Some years ago in cognitive science the theory of embodied cognition began to stress the fact that abstract and formal mathematics is rooted in concrete sensory-motor experiences. Furthermore, the role of the context in which mathematical concepts are learnt or taught comes to be essential. Assuming such a viewpoint, Arzarello has introduced a new construct, the so-called APC space (Action, Production and Communication Space), suitable for analysing the cognitive dynamics that occur during mathematical lessons. In this report, we consider the case of a classroom activity which requires mathematical modelling. The problem is based on a popular legend, the Penelope story from Homer’s Odyssey. The choice of a legend enriches the issues discussed above with a new component (the narrative style), which plays a crucial role in stimulating students’ interest in solving the problem. The classroom activity was carried out with students attending the fifth grade of primary school. Research findings are discussed.