Problem Solving and Decision Making Study Pack
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Last updated May 28, 2026
Problem Solving and Decision Making Study Guide
Break down how the mind tackles problems and makes decisions, from algorithms and heuristics to cognitive biases like availability and anchoring. Covers functional fixedness, mental set, loss aversion, and Kahneman and Tversky's prospect theory.
Key Takeaways
- •Problem solving moves through distinct stages: recognizing a problem exists, representing it mentally, selecting a strategy, executing that strategy, and evaluating the outcome.
- •Algorithms guarantee a correct solution by exhaustively testing possibilities, while heuristics are mental shortcuts that trade accuracy for speed and efficiency.
- •Common problem-solving obstacles include functional fixedness (failing to see novel uses for objects) and mental set (defaulting to previously successful but now inappropriate strategies).
- •Decision making under uncertainty relies heavily on cognitive heuristics such as availability, representativeness, and anchoring, each of which can introduce systematic errors called cognitive biases.
- •Prospect theory, developed by Kahneman and Tversky, holds that people weigh potential losses more heavily than equivalent gains — a phenomenon called loss aversion — causing departures from purely rational choice.
- •Insight, sometimes called the 'aha moment,' represents a sudden restructuring of a problem's mental representation rather than a gradual, stepwise solution process.
- •Confirmation bias leads decision makers to seek and favor information that supports existing beliefs, undermining the quality of both problem solving and judgment.
The Structure of Problem Solving
Problem solving is a goal-directed cognitive process that begins the moment a person recognizes a gap between a current state and a desired outcome. Understanding how that process unfolds — from initial representation to final evaluation — is essential for analyzing why people succeed or fail when they encounter novel challenges.
Problem Recognition and Representation
- •A problem exists when there is a perceived discrepancy between the present situation and a goal; without recognizing this discrepancy, no solving process begins.
- •Mental representation determines which features of a problem are attended to; representing a problem inaccurately is one of the most common sources of failure.
- •Problems are often categorized as well-defined (clear start state, goal state, and legal moves, as in chess) or ill-defined (vague goals and ambiguous constraints, as in writing a novel).
Stages of the Problem-Solving Process
- •After representation, a solver selects a strategy, executes it through a series of steps, and monitors progress toward the goal.
- •The final evaluation stage involves checking whether the solution actually satisfies the original goal — a step that is frequently skipped under time pressure.
- •Problems can require working backward from the goal state to the initial state, particularly when the goal is clearly defined but the starting moves are not obvious.
Strategies for Solving Problems
People rely on two broad classes of strategies when working through problems: systematic procedures that guarantee solutions and intuitive shortcuts that work most — but not all — of the time. Choosing between them involves a tradeoff between reliability and cognitive effort.
Algorithms
- •An algorithm is a step-by-step procedure that, if followed correctly, will always produce the right answer — for example, using long division or a spell-checker that tests every possible spelling.
- •Algorithms are effective but cognitively expensive; they become impractical when the problem space is very large, such as trying every possible move sequence in a chess game.
Heuristics
- •A heuristic is a cognitive shortcut that reduces the effort required to reach a solution by narrowing the search space, though it does not guarantee accuracy.
- •The means-ends heuristic involves comparing the current state to the goal, identifying the most significant difference, and taking an action that reduces that difference.
- •Working backward is a heuristic strategy useful when the end goal is clearly defined; a solver starts from the goal and reasons in reverse to identify necessary prior steps.
- •Analogical reasoning applies the structure of a previously solved problem to a new one — effective when the underlying relationships match, but misleading when superficial similarities mask structural differences.
Insight and Restructuring
- •Insight is a sudden, discontinuous shift in how a problem is represented, often following an impasse, producing an immediate sense of certainty about the solution.
- •Insight problems — such as the classic nine-dot puzzle or matchstick arithmetic — typically require breaking an incorrect assumption built into the solver's initial representation.
- •Research suggests that insight involves unconscious spreading activation that eventually crosses a threshold, though the precise neural mechanisms remain under investigation.
Obstacles That Impede Effective Problem Solving
Even skilled thinkers routinely fall into well-documented traps that prevent them from finding solutions that are, in principle, within their reach. These obstacles stem from the way prior knowledge and habitual thinking constrain perception of a problem.
Functional Fixedness
- •Functional fixedness is the tendency to perceive an object only in terms of its conventional, familiar use, blocking recognition that the same object could serve a different function.
- •A classic demonstration is the candle problem (Duncker, 1945): participants fail to tack a box of thumbtacks to the wall to serve as a candle platform because they represent the box solely as a container.
- •Functional fixedness is reduced when objects are presented in unusual orientations or when their contents are removed, making the object's alternative affordances more salient.
Mental Set
- •A mental set occurs when a solver defaults to a strategy or sequence of steps that worked in previous problems, even when a simpler or more direct solution exists in the current situation.
- •Luchins's water-jar experiments demonstrated mental set clearly: after repeatedly solving problems with a three-jar formula, participants applied that formula to problems that could be solved in one simple step.
- •Mental set is adaptive in stable environments but becomes a liability when problem structure changes and flexibility is required.
Confirmation Bias in Problem Framing
- •Confirmation bias causes people to interpret ambiguous evidence as consistent with their initial hypothesis about a problem's cause or solution, narrowing the search space prematurely.
- •In the 2-4-6 task (Wason, 1960), most participants test only sequences that confirm their initial rule hypothesis rather than testing sequences that could falsify it.
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Algorithms vs. Heuristics
Explain the difference between algorithms and heuristics in your own words. What does each one offer, and what are the tradeoffs involved in choosing one over the other?
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