PSY 3217: Ch. 13: Problem Solving and Creativity

problem solving

beginning with a goal and seeking steps that will move you toward that goal

problem space

 the set of possible states and moves that can occur between the starting point and the goal

creativity

producing ideas or solutions that are novel while still being useful or appropriate to the problem

core question

Why do some approaches lead quickly to solutions while others trap us in unproductive routines?

initial space

where the problem begins

goal state

the outcome you are trying to reach

operators

actions or moves that transform one state into another

hill climbing

at each choice point, select the option that appears to move you closer to the goal, no matter what.

strength

simple, fast, and sensible when progress is monotonic or reliant on continuous forward momentum

weakness

some problems require temporarily moving away from the goal before a solution becomes possible

means-end analysis heuristic

• Compare current state w/ goal state, identify the largest difference, and choose an operation that reduces that diff.

• Useful cuz it breaks large problems into manageable subproblems. A useful subgoal does not need to solve the whole problem, it only needs to make the next stage easier.

• Current: what is true now? → Subgoal: What smaller diff can i reduce first? → Goal: what outcome am i tryna reach?

analogy

using the solution to an earlier problem as a guide for a new problem

deep structure

the underlying relationships or causal pattern that two problems share

surface features

 obvious objects, settings, or vocabulary that can make two analogous problems look unrelated

mapping

figuring out which elements of the old problem correspond to elements in the new one

Gick and Holyoak’s Tumor Analogy Study

• Participants encountered the “general and fortress” story, in which several small forces converge from different directions to avoid a minefield and capture a fortress

• Then, they attempted the tumor problem, whose solution requires multiple low-intensity rays converging on one target

• The crucial question was whether people would spontaneously notice that the two problems shared the same deep structure

• 75% solved w/ analogy, 30% solved w/ analogy present no hint, 10% solved with neither

Goldwater and Jamrozik study

• Encouraged learners to encode examples using labels for underlying relationships

• Examples were tagged w/ relational ideas such as “trade-off” or “positive feedback loop”

• Later, participants were more likely to retrieve useful analogies when the relational structure had been emphasized during learning

• Benefit was strongest when deep structure was encoded from the beginning and not added only when people were already searching for an analogy

Expertise, chunking, and chess

• Chess experts can briefly view a meaningful board position and remember far more of it than novices

• Don’t memorize each piece independently; they encode coordinated patterns as meaningful chunks

• Those chunks organize memory, guide attention, and suggest useful subgoals

well-defined problem

• Goal is clearly specified

• Allowed operations are known

• Success can usually be judged objectively

• Ex.) chess puzzle, algebra problem

Ill-defined problem

• Goal may be vague or open-ended

• Possible operations are unclear

• Several outcomes might count as success

• Ex.) “Have a great vacation”

functional fixedness

 a tendency to think of an object only in terms of its usual function

• Not always about the objects given, but how the solver represents them

• Fixedness is more likely when the conventional function is strongly emphasized by the way the objects are presented

• Overcoming fixedness requires noticing features that make an alternative use possible

problem-solving set

the assumptions and strategies a solver brings into a new problem

einstellung

rigidity that develops when an earlier method works repeatedly, making people less likely to notice a better method. (being stuck in your old habits/ways)

Luchin’s Water-Jar Problem Study

• Participants solved a series of measuring problems using three jars w/ diff capacities

• Several early problems could all be solved using the same multi-step formula

• After the procedure became habitual, participants often kept using it on later problems even when a simpler solution was available

creativity

• Involves producing something that is novel, but novelty by itself is not enough. The product must also be useful, appropriate, or valued in its context

Big-C creativity

transformative achievements associated with major artists, scientists, inventors, or composers

Little-c creativity

everyday novelty; solving a practical problem, finding an original joke, or approaching an assignment in a new way