Value and Limitations of Analogs in Teaching Mathematics.
Graeme S. Halford, Gillian M. Boulton‐Lewis · 1989
Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representation 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 ta:get. 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 arc listed. (Author/YP) **************************A******************************************** A Reproductions supplied by EDRS are the best t;lat can be made from the original document. *********************************************************************** Value and Limitations of Analogs in Teaching Mathematics Graeme S. Halford and Gillian M. Boulton-Lewis University of Queensland and Brisbane College of Advanced Education U.S. DEPARTMENT OF EDUCATION Office of Educatronal Researen and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER tERt() Trus document nas teen reproduceu as received from the person or organqatron ongInating if C Minor changes have been made to unprove reproduction quality Popnts of new or opinions stated this doc u merit do not neCassahly rep-wen} offic$04 Of RI postion or pore', 'PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY Cit-raeme-S OtraSprA TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC). Paper presented to the Third Conference of the European Association for Research on Learning and Instruction, Madrid, Spain, September 4-7, 1989. To be published in A. Demetriou and M. Shayer (Eds.), (title not known), London: Routledge and Kegan Paul. Running head: Analogs in Mathematics This work was supported by a grant from the Australian Research Grants Scheme. Author's address: Professor Graeme Halford, Psychology Department, University of Queensland, St. Lucia, 4067, AUSTRALIA