Understanding as experiencing a pattern

Sammanfattning: The thesis proposes that understanding is a matter of experiencing a pattern. To experience a pattern involves seeing how a task, principle, or problem space is structured; to attend to the relevant information; and to be able to use that information as it relates to the knowledge domain at hand. The every day concept of understanding, which is a term used in many ways is discussed and it is explored how it can be turned into something measurable. The overall focus of the thesis is on the process leading to understanding and the transient stage between not understanding and understanding. A more specific focus is on the role that attention play for understanding – in particular attending to relevant visual stimuli. The aim of the thesis has been to (1) use attention to visual stimuli to explore part of the processes underlying understanding by asking whether or not attending to critical areas correlates with understanding; (2) use eye tracking as well as other complementary methods to identify underlying cognitive processes and (3) evaluate and discuss the pedagogical implications of the studies conducted. The studies reported in the thesis represent two related projects. One was conducted in a controlled laboratory setting, the second in a classroom. Both were designed to explore understanding-as-experiencing-a-pattern and investigated how students attend to relevant visual information in mathematical problems in an attempt to examine part of the process leading to understanding. The results reported in the thesis do show that attention to problem-relevant areas of visual stimuli is correlated with understanding of the task and proficiency with which the task is performed. Also, a new methodology was developed for capturing the dynamic reading of mathematical representations – one that can be applied in other domains as well. By focusing on understanding-as-experiencing-a-pattern and its relation to visual attention, and by using both quantitative and qualitative measures, the thesis has provided a relatively fine-grained description of some aspects of what students are doing when they come to an understanding.

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