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.

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

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

Cite this paper for:

• "mapping the features of the source and target problems and the process of adapting the source solutoin procedure for use in solving the target problem were clearly distinguished." [abstract]
• "Successful mapping was found to be insufficient for successful transfer." [abstract]
• Evidence that transfer stage is difficult above and beyond mapping.
• Even with the mapping given, only 50% (exp 1) and 32% (exp 2) of Ss got it right.

Experiment 1:

• no hint (results: 19%)
• retrieval hint (results: 35%)
• retrieval and concept mapping hint (results: 37%)
• retrieval and numerical mapping hint (more specific to problems) (results: 50%)

"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:

• numerical mapping is closer to adaptation than conceptual (supported again).
• Tranfer is facilitated by understanding of reasons for the alignments in mapping. (unsupported)
• Analogical reasoning ability predicts analogical problem solving ability. (math SAT predicts it only (not verbal or analogical ability) note: these were math problems.

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:

• none