Analytical reasoning with multiple external representations
Cox, Richard Jeffrey
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This thesis presents work on analytical reasoning with external representations (ERs) using problems similar to those used in the US GRE college-entrance examination. The work investigates the factors associated with effective ER use in situations where subjects select, construct and reason with their own ERs. Practically all previous work has tended to focus solely upon performance rather than process. In this thesis the emphasis is upon cognitive processes during the entire time-course of reasoning with ERs, from problem comprehension through to answer selection. A background to the work is provided by 2 comprehensive reviews of: 1.) previous research on ERs and reasoning and 2.) the cognitive and semantic properties of ERs. Results from three empirical studies are reported. The first study examined a large corpus of 'workscratchings' produced by subjects as they solved paper and pencil-based analytical reasoning problems under test conditions. The workscratching ERs showed great diversity between and within subjects and across a range of problems. They included lists, various kinds of table, set diagrams, node and arc diagrams, first-order and propositioned logic, plans and natural language. It is shown that problem-solving performance is related to the type of ER used in the solution. The second study utilised a computer-based system (switchERI). The system administered analytical reasoning problems and provided a. range of ER construction environments for the subject to choose and switch between. User-system interactions were recorded dynamically during problem solving. This methodology permitted microanalyses of the cognitive events at each stage during the time-course of problem solving. A process account of analytical reasoning with ERs is developed in which five major stages are identified - problem comprehension, ER selection, ER construction, read-off from the ER and answer selection/responding. A range of common slips and misconceptions are identified at each stage. The results show, inter alia, that subjects whose responses are consistent with their ERs perform better than subjects whose responses are inconsistent with their ERs even if the ER is partially incorrect. The data from the workscratching analysis and switchERI study informed the design of' switchERII, a second system. SwitchERII incorporates a. representation of the semantics of Euler's Circles, dynamically parses the user's representation and provides feedback and advice. A third study was conducted with the switchERII system. Few, if any, studies to date have attempted to relate subjects' prior knowledge of ER formalisms to their reasoning performance. Subjects' prior knowledge of ER formalisms was assessed in both switchER studies. It was observed that subjects' performance on representation interpretation tasks does not necessarily predict their performance in conditions where they select and construct their own representations. The reasons for the decoupling are discussed. Data from all three studies show that subjects often utilise multiple representations in their solutions, either concurrently or serially via. ER switching. Two distinctly different types of switching were observed. One kind ('thrashing') is associated with poorer performance and reflects less comprehensive prior knowledge, inability to select au appropriate ER and hazy problem comprehension. Judicious switching, on the other hand, is associated with high levels of problem comprehension and skilled matching of the ERs' properties to changing task demands. It is claimed that effective reasoning with ERs involves complex interactions between at least three factors: (a.) within-subject variables such as the subject's representational repertoire (prior knowledge) and representational modality preferences (cognitive style); (b.) skill at overcoming a variety of barriers to comprehension and an ability to discern the salient attributes and characteristics of different problem types and (c.) an understanding of the semantic and cognitive properties of graphical and non-graphical ERs coupled with an ability to match those properties to the problem's task demands. It is suggested that the role of externalisation in reasoning with ERs may be to facilitate the swapping of information between cognitive subsystems. A mechanism by which the use of diagrammatic ERs may facilitate self-explanation is also proposed. The thesis concludes with an argument in favour of a domain-independent 'ER curriculum'. It is suggested that direct instruction in the use of a range of ERs might equip students with wider representational repertoires and hence allow them more scope to indulge their representational preferences. Finally, several directions for future work are proposed. These include extending the representational semantics of switchERII, evaluating various types of system feedback and implementing a mechanism for checking for slips during read-off from ERs.