Thinking through actions with things : a systemic perspective on analytic problem solving and mental arithmetic

In solving everyday problems or making sense of situations, people interact with local resources, both material and cultural (Kirsh, 2009a). Through these interactions with the world, thinking emerges from within and beyond the boundaries of the mind. Traditional frameworks specify that problem solving proceeds from initial state to goal state through the transformation of a mental representation of the problem by the retrieval and manipulation of symbols and rules previously stored in memory. Information garnered through bodily actions or from transactions with the world is considered to be a passive input. As a result, classical models of cognitive psychology frequently overlook the impact of the interaction between an individual and the environment on cognition. The experiments reported here were designed to inform a different model of problem solving that included the ubiquitous nature of interactivity in daily life by examining problem solving using artefacts. This research programme began with two experiments using an analytical problem, namely the river-corssing task. These experiments offered a platform to investigate the role of interactivity in shaping and transforming the problem presented. However, the problem space in the river-crossing task is relatively narrow and the research programme proceeded to three further experiments, this time using mental arithmetic tasks where participants were invited to complete long sums. These problems afford a much larger problem space, and a better opportunity to monitor how participants' action shape the physical presentation of the problem. Different task ecologies were used in the five experiments to contrast different levels of interactivity. In a low interactivity condition, solvers relied predominantly on internal mental resource; in a high interactivity condition participants were invited to use artefacts that corresponded to key features of the problen in producing a solution. Results from all experiments confirmed that increasing interactivity improved performance. The outcomes from the river-crossing experiments informed accounts of transferm as it was revealed that attempting the problem initially in a low interactivity condition followed by the high interactivity condition resulted in the most efficient learning experience. The conjecture being that learning of a more deliberative nature was experienced in the low interactivity version of the problem when followed by the opportunity to showcase this learning through the enactment of moves quickly in a second attempt that fostered as high level of interactivity. The mental arithmetic experiments revealed that a high level of interactivity not only produced greater accuarcy and efficiency, but participants were also able to enact different arithmetic knowledge as they reconfigured the problem. In addition, the findings indicated that: maths anxiety for long additions could be mitigatd through increased interaction with artefacts; trajectories for problem solving and the final solutions varied across differing interactive contexts; and the opportunity to manipulate artefacts appeared to diminish individual differences in mathematical skills. The varied task ecologies for the problems in these experiments altered performance and shaped differing trajectories to solution. These results imply, that in order to establish a more complete understanding of cognition in action, problem solving theories should reflect the situated, dynamic interaction between agent and environment and hence, the unfolding nature of problems and their emerging solutions. The findings and methods reported here suggest that a methodology blending traditional quantitative techniques with a more qualitative ideographic cognitive science would make a substantial contribution to problem solving research and theory.