Investigating individual differences in the mental representation of symbol processing rule systems [Untersuchung individueller unterschiede in der mentalen repräsentation von symbolverarbeitenden regelsystemen]

Abstract

It is reported about a project from pure research in mathematics education, in which mental processes are examined which take place when rewriting terms. For this purpose, a computer based artificial world of symbolic term rewriting has been created where subjects can be observed when they work on the term rewritings based on the rules given. These rewriting rules have been constructed in such a way that subjects with different mental models can find rules matching their ideas. For the analysis, the data stored with regard to type and sequence of the rules used as well as the transcripts of the video protocols are available. It is being analysed how and in what manner a mental model of the problem to be solved is formed by the pupils of grade 10 and what consequences arise for the process of working on the problem. Three aspects are of importance: How is an idea created of the problem to be solved according to the individual preference for a predicative versus functional mental modelling (process orientated versus feature orientated)? What effect does the preference for a certain way of looking at the problem have (moving or acquiring symbols versus replacing the characteristics of symbols)? What idea of the rules does the subject have (rules as an independent process of modification versus rules as in input-output-relationship)?.