An information theory analysis of spatial decisions in cognitive development

Performance in a cognitive task can be considered as the outcome of a decision-making process operating across various knowledge domains or aspects of a single domain. Therefore, an analysis of these decisions in various tasks can shed light on the interplay and integration of these domains (or elements within a single domain) as they are associated with specific task characteristics. In this study, we applied an information theoretic approach to assess quantitatively the gain of knowledge across various elements of the cognitive domain of spatial, relational knowledge, as a function of development. Specifically, we examined changing spatial relational knowledge from ages 5 to 10 years. Our analyses consisted of a two-step process. First, we performed a hierarchical clustering analysis on the decisions made in 16 different tasks of spatial relational knowledge to determine which tasks were performed similarly at each age group as well as to discover how the tasks clustered together. We next used two measures of entropy to capture the gradual emergence of order in the development of relational knowledge. These measures of "cognitive entropy" were defined based on two independent aspects of chunking, namely (1) the number of clusters formed at each age group, and (2) the distribution of tasks across the clusters. We found that both measures of entropy decreased with age in a quadratic fashion and were positively and linearly correlated. The decrease in entropy and, therefore, gain of information during development was accompanied by improved performance. These results document, for the first time, the orderly and progressively structured "chunking" of decisions across the development of spatial relational reasoning and quantify this gain within a formal information-theoretic framework.