A student reads a story about a general who splits his army into small groups approaching a fortress simultaneously from multiple routes. Later, the same student is given Duncker's radiation problem and fails to solve it. After being told 'think about the previous story,' the student immediately produces the correct multi-beam solution. What does this best illustrate?
AThe student lacked sufficient working memory to hold both problems in mind simultaneously
BThe structural similarity between the two problems is too weak to support analogical transfer
CPrior exposure to a source analog is not sufficient for transfer; noticing the structural correspondence requires active retrieval
DAnalogical transfer only works when problems share surface features as well as structure
This is the Gick and Holyoak radiation experiment. The structural similarity is strong — both involve converging from multiple directions to achieve an effect impossible from one direction alone — but subjects did not spontaneously access it. The retrieval hint dramatically improved transfer rates. This shows that the cognitive bottleneck is noticing the correspondence, not comprehending the source or the target. Prior exposure is necessary but not sufficient; transfer requires actively mapping the relational structure from source to target.
Question 2 Multiple Choice
Expert physicists and novice students each sort a set of mechanics problems. Experts group by underlying principle (conservation of energy, Newton's second law); novices group by surface appearance (inclined plane problems, pulley problems). According to structure-mapping theory, whose categorization will enable better analogical transfer to novel problems?
AThe novice's, because surface features are processed faster and require less working memory
BThe expert's, because structural categories preserve relational patterns that generalize across new problem contexts
CNeither — categorization style does not affect analogical transfer
DThe expert's only for familiar problem types; the novice's is superior for genuinely novel problems
Structure-mapping theory predicts that productive analogies rest on relational structure, not surface features. When a novel problem arrives in an unfamiliar surface form, the expert who has indexed problems by deep structure can recognize the correspondence and transfer the solution. The novice's surface-based indexing fails because the new problem doesn't look like a familiar inclined-plane or pulley problem — even if the underlying physics is identical. Expert development largely consists of rebuilding problem categorization around structural rather than surface features.
Question 3 True / False
In Gentner's structure-mapping theory, an analogy between the atom and the solar system is considered productive because both share the relational structure of a central body with orbiting satellites — not because electrons physically resemble planets.
TTrue
FFalse
Answer: True
This is the core claim of structure-mapping: productive analogies preserve relational patterns, not object-level surface properties. Electrons and planets share no surface attributes — they differ in size, charge, and behavior. But both systems share the relational structure 'central attractive force causes smaller bodies to orbit.' This shared relational structure allows knowledge about orbital mechanics to generate valid inferences about atomic behavior. Analogies that rest only on surface similarity without structural correspondence tend to mislead rather than illuminate.
Question 4 True / False
Having previously read an analogous source problem is sufficient to produce spontaneous analogical transfer to a structurally similar target problem.
TTrue
FFalse
Answer: False
Gick and Holyoak's experiments directly falsify this. Subjects who read the fortress story immediately before the radiation problem still failed to spontaneously use the analogy at high rates. The structural correspondence is real and strong, but it does not activate automatically. Only when given an explicit retrieval hint ('think about the earlier story') did transfer rates rise sharply. This means that teaching students analogous examples does not automatically build flexible transfer unless learners are also trained to identify and apply structural correspondences.
Question 5 Short Answer
What does the Gick and Holyoak radiation experiment reveal about the conditions required for analogical transfer, and why is this finding important for how we design instruction?
Think about your answer, then reveal below.
Model answer: The experiment shows that analogical transfer requires noticing the structural correspondence between source and target — prior exposure to the source analog alone is insufficient. Subjects who had just read the analogous fortress story did not spontaneously apply it to the radiation problem; only those given an explicit retrieval hint achieved high transfer rates. For instruction, this means that teaching by analogy requires helping students with the mapping step: learners must be prompted to identify which relational structures carry across contexts, not simply exposed to analogous examples.
This finding matters because it challenges the assumption that 'learning by example' automatically produces flexible transfer. Students who can recite an analogy may still fail to apply it when a new problem appears in an unfamiliar surface form. Effective instruction in analogical transfer involves teaching students to explicitly categorize problems by deep structure — a practice that builds what expertise research calls 'deep relational knowledge' and is what separates experts from novices in problem categorization.