Problem-Solving Strategies

Why This Matters

Problem-solving is at the heart of cognitive psychology—and it's one of the most heavily tested areas on exams. You're not just being asked to recall what "means-end analysis" means; you're being tested on when different strategies work best, why some approaches guarantee solutions while others trade accuracy for speed, and how cognitive barriers like functional fixedness prevent us from finding solutions. Understanding these strategies reveals fundamental principles about how the mind represents problems, searches for solutions, and sometimes gets stuck.

The strategies covered here demonstrate core concepts like algorithmic vs. heuristic processing, problem representation, cognitive flexibility, and the role of unconscious processing. When you study these, focus on the underlying mechanisms: What makes one approach systematic and another intuitive? Why do "aha" moments happen? Don't just memorize definitions—know what cognitive principle each strategy illustrates and when you'd use one approach over another.

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Systematic Search Strategies

These approaches involve methodically working through a problem space. They rely on explicit, step-by-step processing and are most effective when the problem structure is well-defined.

Means-End Analysis

• Reduces the difference between current and goal states—breaks complex problems into sub-goals that feel more achievable
• Continuously evaluates progress by comparing where you are to where you need to be, adjusting strategy as needed
• Classic example: Tower of Hanoi—demonstrates how we navigate problem spaces by targeting intermediate states

Working Backward

• Starts from the goal and reverses—particularly powerful when the end state is clear but the starting path is ambiguous
• Identifies necessary conditions by asking "what must be true right before the goal?"
• Common in mathematical proofs and planning problems where forward progress feels overwhelming

Forward Chaining

• Begins with known information and applies rules to derive new conclusions step by step
• Data-driven approach—moves from initial state toward goal by following logical implications
• Used in expert systems and AI—contrasts with backward chaining, which starts from hypotheses

Algorithm

• Guarantees a correct solution if followed precisely—no guesswork involved
• Time-consuming but reliable—think of solving an anagram by testing every letter combination
• Contrasts sharply with heuristics—trading speed for certainty

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Heuristics and Mental Shortcuts

Heuristics sacrifice guaranteed accuracy for cognitive efficiency. They exploit patterns and rules of thumb that usually work—but can lead us astray.

Heuristics

• Fast, frugal mental shortcuts that reduce cognitive load when making decisions
• Availability heuristic judges probability by how easily examples come to mind; representativeness heuristic judges category membership by similarity to prototypes
• Often accurate but systematically biased—understanding when they fail is key exam content

Trial and Error

• Tests solutions unsystematically until one works—no strategy, just persistence
• Useful when problem structure is unknown and you can't predict which approach will succeed
• Inefficient but exploratory—allows discovery of unexpected solutions

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Insight and Restructuring

These strategies involve sudden shifts in understanding rather than incremental progress. Insight occurs when we restructure our mental representation of a problem.

Insight Problem Solving

• Characterized by "aha" moments—solutions appear suddenly after a period of apparent stuckness
• Involves restructuring the problem representation, often seeing it from an entirely new angle
• Difficult to explain step-by-step—solvers often can't articulate how they reached the answer

Representation and Restructuring

• How you frame a problem determines what solutions you can see—poor representation blocks progress
• Restructuring means changing your mental model—shifting from one problem space to another
• Key insight: the same problem can be easy or hard depending entirely on how it's represented

Incubation

• Taking a break facilitates insight—stepping away allows unconscious processing to continue
• Reduces fixation on unproductive approaches by letting mental set decay
• Supports the role of implicit cognition in problem-solving—not all thinking is deliberate

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Creative and Flexible Approaches

These strategies emphasize generating novel solutions and breaking free from conventional thinking patterns.

Lateral Thinking

• Deliberately seeks unconventional angles—rejects the assumption that logic alone leads to solutions
• Uses techniques like provocation—intentionally absurd statements that disrupt habitual thinking
• Contrasts with vertical thinking—which digs deeper in one direction rather than exploring sideways

Brainstorming

• Generates quantity over quality initially—suspends judgment to encourage wild ideas
• Group technique that leverages diverse perspectives—collaboration can spark connections individuals miss
• Effectiveness depends on psychological safety—criticism during ideation kills creativity

Analogical Problem Solving

• Transfers solutions from source problems to target problems—requires recognizing structural similarity
• Gick and Holyoak's radiation problem is the classic demonstration—participants needed hints to see the military analogy
• Surface features often mislead—deep structural mapping is cognitively demanding

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Decomposition Strategies

These approaches manage complexity by breaking problems into smaller pieces. They reduce cognitive load by limiting how much must be held in working memory at once.

Divide and Conquer

• Splits large problems into independent sub-problems—solve each separately, then combine
• Reduces working memory demands—you only need to focus on one component at a time
• Effective when sub-problems don't interact—less useful when components are tightly interdependent

Problem Space Theory

• Newell and Simon's foundational framework—problems consist of initial states, goal states, and operators
• Search involves navigating the problem space—finding a path from start to goal through intermediate states
• Explains why some problems are hard—large problem spaces with many dead ends require sophisticated search strategies

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Cognitive Barriers to Problem-Solving

Understanding what blocks solutions is just as important as knowing strategies. These phenomena explain why smart people get stuck.

Mental Set and Functional Fixedness

• Mental set is the tendency to reuse strategies that worked before—even when they no longer apply
• Functional fixedness specifically involves inability to see objects beyond their typical use—Duncker's candle problem is the classic demonstration
• Both reduce cognitive flexibility—prior experience becomes a liability rather than an asset

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Quick Reference Table

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Self-Check Questions

1. Which two strategies both involve breaking problems into smaller parts, and what distinguishes how they do so?

2. A student solves a physics problem by recalling a similar problem from math class. Which strategy does this illustrate, and what cognitive process makes it difficult?

3. Compare and contrast algorithmic and heuristic approaches: When would you choose each, and what are the costs of each choice?

4. Why might an expert mechanic struggle more than a novice to find an unconventional use for a wrench? Which two barriers explain this?

5. An FRQ describes someone stuck on a puzzle who solves it immediately after taking a walk. Which two concepts from this guide explain what happened, and how do they work together?