In this study I examine the question, what is the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry? The quality of prior knowledge is analysed in terms ofschemas that provide a measure of the degree of organisation of prior knowledge. Problem-solving performance and schema activation of a group of high- and low-achieving students were compared. As expected, the high achievers produced more correct answers than the low achievers. More significantly, schema comparison indicated that the high achievers accessed more problem-relevant schemas than the low achievers. In a related task which focused on the problem diagram, both groups accessed almost equal numbers of geometry schemas. The results are interpreted as suggesting that high achievers build schemas that are qualitatively more sophisticated than low achievers which in turn helps them construct representations that are conducive to understanding the structure of geometry problems.
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Chinnappan, M. The accessing of geometry schemas by high school students. Math Ed Res J 10, 27–45 (1998). https://doi.org/10.1007/BF03217341
- Content Knowledge
- Mathematical Knowledge
- High Achiever
- Target Problem
- Geometric Knowledge