3 Knowledge, Expertise, and Transfer
Learn how prior knowledge shapes problem representation and strategy choice, when analogies support transfer, and how to use experience flexibly without falling into mental set.
How guides problem solving
affects both how a solver understands a problem and which strategy seems suitable. Solvers do not simply read a task and apply a neutral procedure: they interpret its features through what they already know. This can help them recognize relevant patterns, but it can also steer them toward an unhelpful familiar approach.
Representing problems through meaningful relationships
A is an internal account of what is given, what is sought, and which relationships matter. helps fill in information that is not stated explicitly and directs attention toward some features rather than others. The representation matters because it can suggest a strategy before the solver chooses particular procedures or equations.
In a classic study of physics problem solving, experts tended to group problems by the underlying principle needed to solve them. Novices tended to group them by visible features, such as the objects or physical settings. As a result, an expert might represent problems involving different objects as instances of the same principle, while a novice might see them as unrelated. Recognizing a principle such as conservation can point toward a systematic solution.
What contributes—and where it is limited
is not simply having more facts. Knowledge organized into connected, retrievable structures helps experts notice meaningful relationships and choose relevant procedures. However, is usually domain-specific: experience solving problems in one field does not automatically provide in another.
Knowledge can also hinder performance. A familiar assumption or procedure may be applied where it does not fit, so experience is useful only when the solver considers whether it matches the current problem.
Using analogies to strategies
occurs when a solver uses a relation or strategy from a known problem to solve a new one. The problems need not look alike on the surface; the important feature is a useful correspondence between their underlying structures.
For example, two apparently different situations may share the structure of reaching a goal by coordinating several smaller actions. Recognizing that structural match can suggest a strategy for the unfamiliar problem. The example is useful only if the solver retrieves the earlier situation and recognizes how it maps onto the new task.
In experiments by Gick and Holyoak, a hint to use an earlier story helped people apply its solution to a structurally related problem. Comparing multiple examples could also help learners derive a more general problem schema and improve .
When is more likely
is not automatic. It is more likely when learners understand the original learning well, attend to structural relationships rather than surface details, and can explain when a strategy applies. A strategy learned in only one narrow context may remain tied to that context.
A useful analogy is not merely a resemblance: the solver must identify a relevant relationship and judge whether it carries over to the new task. This is why retrieval and checking the structural match matter.
When experience becomes a
A is a tendency to reuse a previously successful method even when another method would be simpler or more suitable. In Luchins’s classic water-jar studies, participants solved a series of problems using a recurring procedure. When a later problem allowed a simpler solution, some continued using the established procedure rather than noticing the shortcut. The example shows how learning can guide strategy selection while also narrowing the solver’s search.
is related to, but distinct from, . uses a prior problem to find a potentially useful approach. occurs when a familiar approach dominates despite a poor fit. The same can therefore help or hinder, depending on whether the solver checks how well the old strategy fits the new problem.
Using knowledge flexibly
Flexible problem solving uses as a starting point, not as a command. A solver can follow this sequence:
Represent the problem: Identify what is given, what is sought, and the important relationships.
Generate candidate principles or analogies: Consider familiar structures that might apply, rather than focusing only on familiar objects.
Check the fit: Identify the conditions under which a candidate strategy works and compare them with the current problem.
Consider alternatives: Look for a simpler approach or a different representation.
Monitor the result: If the approach does not make progress or conflicts with the problem’s constraints, revise the representation or strategy.
These steps help make adaptive: knowledge supplies useful starting points, while deliberate checking can prevent habitual methods from becoming barriers.