ERIC Number: ED315293
Record Type: Non-Journal
Publication Date: 1989
Reference Count: N/A
Value and Limitations of Analogs in Teaching Mathematics.
Halford, Graeme S.; Boulton-Lewis, Gillian M.
Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a structure-preserving mapping from a base or source to the target. Although concrete aids can provide valuable assistance to concept acquisition, their oft-noted failure to provide the anticipated benefits has been a source of some puzzlement. It is suggested that the reason for the failure may be the processing loads imposed by structure mapping. Some representative mathematical concepts are examined, together with typical concrete representations, and the nature of the processing loads analyzed. These loads can be reduced by recoding concepts into more abstract form, but it is argued that structure mapping also plays a role in abstraction. Analysis of this process provides insight into sources of difficulty, and recommendations are made for improving the efficiency of instruction. Thirty-nine references are listed. (Author/YP)
Publication Type: Reports - Research
Education Level: N/A
Sponsor: Australian Research Grants Scheme.
Authoring Institution: N/A