Supporting the use of external representation in problem solving: the need for flexible learning environments

Abstract

External representations (ERs) are effective in reasoning due to their cognitive and semantic properties. We investigated subjects’ use of ERs in their solutions to analytical reasoning problems. Two sources of data were analysed. The first consisted of a large corpus of ERs (‘workscratchings’) used by students in their solutions to problems administered via paper and pencil tests. The second source of data was collected using switchER, a computer-based system that administered the problems, provided a range of ER construction environments for the subject to choose between and which dynamically logged user–system interactions. SwitchER was developed in order to study the process and time-course of ER use and to investigate the mechanisms (such as ER switching) by which subjects resolve impasses in reasoning. The results showed great diversity of ER use across subjects, allowing the utility of various ERs under differing task conditions to be studied. The range of ERs used by subjects included plan diagrams, various tabular representations, directed graphs, set diagrams, logic, lists, and natural language. Subjects’ prior knowledge of ER formalisms was shown to be an important determiner of effective ER use. A review of research on individual differences in problem solving with ERs is also provided. The conclusions indicate the importance of a number of issues relevant to support both for analytical reasoning and for problem solving in general. These results are currently being used to inform the design of the coaching component of switchER II — an interactive learning environment that offers limited learner support in the use of ERs and which is intended to facilitate learning via ER switching.