Analogical reasoning solves problems by mapping structural correspondences from a known source domain to an unfamiliar target domain. Success depends on recognizing that the domains share abstract relational structure, not surface similarity. A person might solve a marketing problem by mapping the structure of how water flows through pipes (constrain flow, increase pressure) to the abstract problem of increasing customer throughput. Failure to recognize structural correspondence leads to missed opportunities for transfer and analogy.
Provide source domain examples (story analogues) with varying structural similarity to target problems and measure problem-solving success. Show how surface similarity without structural correspondence fails while hidden structural parallels succeed when explicitly highlighted.
From your study of analogical reasoning and structure-mapping theory, you already know the core insight: analogy is about shared relational structure, not surface similarity. A solar system is analogous to a Rutherford atom not because the sun and nucleus look alike, but because both share the abstract structure of a central massive body around which smaller objects orbit at various distances. The task now is to go deeper — to understand how the cognitive system actually *performs* this mapping, why it sometimes succeeds and sometimes fails, and what the implications are for problem-solving and expertise.
The mapping process is guided by three constraints operating simultaneously. One-to-one correspondence: each element in the source maps to at most one element in the target. Structural consistency: if A maps to A' and B maps to B', then the relations holding between A and B in the source should mirror those holding between A' and B' in the target. And systematicity: deeper, higher-order relational hierarchies take precedence over isolated object matches. These constraints drive the system toward mappings that are internally coherent and richly connected rather than superficial. This explains why the water-pipe-to-electrical-circuit analogy works so cleanly: voltage maps to pressure, current to flow rate, resistance to pipe narrowness, and the governing equations map to each other — a systematic structural correspondence at multiple levels.
Where analogical mapping fails is equally instructive. People are reliably misled by surface similarity — the tendency to match elements that share superficial features even when their relational roles differ. In classic problem-solving experiments, subjects given a structurally parallel story (the "radiation problem" and the "military fortress" story analogue) fail to spontaneously apply the analogous solution to the new problem — even though they could solve it immediately when told to use the earlier story. The structural knowledge was present; the spontaneous mapping was not triggered. What does trigger it? Explicitly abstracting the structural principle from the source story — stripping away surface content and stating the underlying relational skeleton — dramatically increases spontaneous transfer to new problems. The abstract representation is what travels across domains.
This has direct implications for problem-representation and expertise. Structural abstraction — representing problems at their underlying relational level rather than their surface features — is the cognitive marker that distinguishes expert problem-solvers from novices. Novices in physics classify problems by surface features ("this is an inclined plane problem"). Experts classify by deep structure ("this is a conservation-of-energy problem"). The expert's representation discards the specific objects and settings, retaining only the causal and relational skeleton — precisely the level at which analogical mappings to new problems become visible. Developing strong analogical reasoning is thus not just about recognizing clever comparisons; it is about cultivating the habit of representing problems abstractly enough that structural correspondences to known solutions become apparent.