Questions: Analogical Reasoning and Structure Mapping

Question 1

Two students encounter a water-flow analogy for electrical circuits. Student A knows water flow and is learning circuits. Student B knows circuits and is told 'think of it as water.' According to structure-mapping theory, what primarily determines how useful each finds the analogy?

• A. The direction of mapping is irrelevant; only the degree of surface similarity between domains determines transfer quality
• B. Student A benefits more because concrete, physical source domains always support better analogical transfer than abstract ones
• C. The systematicity of the shared relational structure — how many mutually constraining relations carry across — determines usefulness in either direction
• D. Student B benefits less because familiarity with one domain creates cognitive interference that blocks analogical mapping

Answer: (C)

Structure-mapping theory holds that analogical usefulness is determined by relational systematicity, not surface similarity or direction of mapping. What matters is whether the mapped relations form a coherent, mutually constraining system — if A causes B and B constrains C in the source, does the same pattern hold in the target? If so, the analogy is productive in either direction. Surface concreteness or familiarity of the source domain is not itself the key variable.

Question 2

Researchers give participants two story problems with completely different surface features — one about water pipes, one about electrical circuits — but identical mathematical structure. Many participants fail to use their solution from problem one when working on problem two. What best explains this failure?

• A. The mathematical operations required by the two problems differ enough to prevent transfer
• B. Surface features (water vs. electricity) draw attention away from the underlying relational structure that drives useful transfer
• C. Participants recognize the structural analogy but choose not to apply it to avoid seeming lazy
• D. Water flow and electrical circuit problems have no real structural overlap, so transfer is not expected

Answer: (B)

This is the classic surface-vs.-structure finding: participants encode problems in terms of their salient surface features and retrieve previously solved problems based on surface similarity. When surface features are mismatched (water ≠ electricity), structural overlap goes unnoticed. This is why novices often struggle with transfer while experts — who have abstracted domain schemas — spontaneously recognize structural matches across superficially different problems.

Question 3

A high-surface-similarity analogy — where two problems share many surface features like setting, objects, and vocabulary — is typically more useful for problem-solving transfer than an analogy that shares mainly relational structure.

• T. True
• F. False

Answer: False

Surface similarity without structural match can actively mislead. If two problems share surface features but have different mathematical or causal structures, they are a bad analogy that may cause the solver to apply the wrong solution method. Conversely, low-surface analogies that share deep relational structure are highly useful once the structural match is noticed. Expertise develops partly by learning to see past misleading surface similarity to structural identity.

Question 4

According to structure-mapping theory, a candidate inference is a hypothesis about the target domain generated by projecting relations from the source domain that do not yet have known counterparts in the target.

• T. True
• F. False

Answer: True

Candidate inferences are the knowledge-generating mechanism of analogy. Once the structural mapping between source and target is established, you can look at relations true in the source that have no known counterpart in the target, and project them as hypotheses to test. The solar system analogy suggested discrete electron orbits as a candidate inference before quantum mechanics confirmed it. This is why good analogies are productive scientific tools, not just pedagogical shortcuts.

Question 5

What is the systematicity principle in structure-mapping theory, and why does it predict that analogies based on isolated matching relations are less useful than analogies based on coherent relational systems?

Model answer: The systematicity principle holds that good analogies map entire systems of mutually constraining relations, not just isolated relational pairs. A single matched relation could be coincidental; a coherent system where A causes B, B constrains C, and C explains D — mapped intact from source to target — provides a rich, reliable basis for inference. Systematic analogies generate more candidate inferences and are more resistant to breakdowns at individual points, because the coherence of the system validates each part.

Systematicity explains why the solar system analogy for the atom was scientifically productive: it wasn't one matched relation but a whole cluster (central mass, orbital motion, attractive force, comparative masses) that held together. Isolating one relation — say, 'the nucleus is at the center' — gives you much less leverage for generating new predictions about atomic behavior.