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Novick, L. R. & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition. Vol 17 (3). 398--415.

  author = 	 {Laura R. Novick and Keith J. Holyoak},
  title = 	 {Mathematical problem solving by analogy},
  journal = 	 {Journal of Experimental Psychology: Learning, Memory, and
  year = 	 {1991},
  OPTvolume = 	 {17},
  OPTnumber = 	 {3},
  OPTpages = 	 {398--415},

Author of the summary: Jim Davies, 2003, jim@jimdavies.org

Cite this paper for:

Experiment 1:

Participants solved word algebra problems. Prediction is that transfer and adaptation is difficult even if you know the mapping. They predicted worse to better solutions through the following hint types: Trend was significant (p < .003). The one hypothesis not confirmed was the difference between retrieval hint and concept mapping hint.

"The fact that only 50% of the subjects in the number-mapping condition were successful at transfer strongly suggests that the adaptation process is a major source of difficulty, separate from the difficulty of the mapping process."

They also found that schema quality correlates to analogical transfer strength, and that schema quality is related to transfer but not to nonanalogical solution.

Experiment 2:

Among the Hypotheses were: Experiment 1 was supported again, this time with only 32% of people getting it right given number mapping!

In the protocol studies, mapping of concepts was barely mentioned. "It appears that the process of mapping the concepts occurred so quickly that usually it was not verbalized." But mentions of mapping numbers was abundant. "These mappings always occurred in the course of attempting to adapt the source solution to the target problem."

Summary author's notes:

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Last modified: Wed Jan 29 12:35:04 EST 2003