Department of Mathematics
Title : Mapping mathematical leaps of insight using SPOT diagrams
| Speaker: Caroline Yoon Affiliation: Department of Mathematics, UoA Time: 3pm Friday, 27 September, 2013 Location: 303.B11 (Basement Maths/Stats Building) |
Abstract
| Mathematical leaps of insight—those Aha! moments that seem so unpredictable, magical even—are often the result of a change in perception. A stubborn problem can yield a surprisingly simple solution when one changes the way one looks at it. In mathematics, these changes in perception are usually structural: new insights develop as one notices new mathematical objects, attributes, relationships and operations that are relevant to the problem at hand. I will describe a novel analytical approach for studying these insights visually using “mathematical SPOT diagrams” (SPOT: Structures Perceived Over Time), which display evidence of the mathematical structuresstudents perceive as they work on problems. SPOT diagrams are used to compare the conceptual development of two pairs of participants, who investigate whether a gradient (derivative) graph yields information about the relative heights of points on its antiderivative; one participant pair experiences a leap of insight, whereas the other does not. Each pair’s SPOT diagrams reveal key differences in the structural features they attend to, which can account for the disparate outcomes in their conceptual development. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
