Multi-step reasoning derives conclusions or selects actions by combining abstractions, premises, and rules. It works alongside intuition: intuition suggests a direction, while discrete reasoning steps move toward a result. section 19.4.2
Solving an unfamiliar problem
A student who memorized familiar exam questions may fail when given a new problem. A student who builds an abstract model of the situation can reason through the unfamiliar case, anticipate possible outcomes, and plan a response. section 19.2.2
Reasoning supports abilities that pattern matching alone does not provide:
- Handling novel situations with little or no new data. section 19.2.2
- Constructing abstract models of situations, oneself, and other people. section 19.2.2
- Anticipating possible futures and performing long-term planning. section 19.2.2
- Interleaving exact, discrete reasoning with approximate, experience-based intuition. section 19.4.2
Table 19.1 The two poles of abstraction
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Value-centric abstraction
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Program-centric abstraction
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|---|---|
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Relates things by distance
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Relates things by exact structural match
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Continuous, grounded in geometry
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Discrete, grounded in topology
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Produces abstractions by “averaging” instances into “prototypes”
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Produces abstractions by isolating isomorphic substructures across instances
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Underlies perception and intuition
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Underlies reasoning and planning
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Immediate, fuzzy, approximative
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Slow, exact, rigorous
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Requires a lot of experience to produce reliable results
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Experience-efficient; can operate on as few as two instances
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Compare value-centric abstraction, which supports perception and intuition, with program-centric abstraction, which supports reasoning and planning through exact structural matches. section 19.4.2
