Problem Solving

Problem Solving Definition - What is the formal definition of problem solving and why is it considered such a broad cognitive process?

Problem solving is any situation where you have a goal and you are not currently at that goal. This definition is broad enough to account for everything from complex 3D puzzles and math exams to mundane tasks like tying shoes or walking to a specific room, which are often "hidden" problems we solve automatically.

Behaviorist View - How does the behaviorist approach explain the "shaping" of a solution over time?

Initially, problem-solving is a matter of chance or trial-and-error (like a cat in a puzzle box). Through reinforcement, successful actions are "shaped" into more efficient behaviors, where the subject gradually learns to avoid useless moves and go straight to the goal-trigger.

Gestalt Approach & Restructuring - What does it mean to "restructure" a problem according to the Gestalt view?

It involves fundamentally changing your mental "map" or representation of the problem's elements. You move from a state of total confusion to a sudden Insight (the "Aha!" moment) where the solution appears clearly because you've re-imagined how the pieces fit together.

Sultan the Ape Experiment - How did Sultan's behavior with the sticks illustrate the concept of mental restructuring?

Sultan didn't just use trial-and-error; after a period of quiet contemplation, he suddenly realized he could join two short sticks together to make a long one. This represents a restructuring of the sticks from "two separate reaching tools" to "individual components of a single larger tool."

Information Processing View - What are the 4 components of a "Problem Space" according to the Information Processing model?

1. Initial State: Your starting conditions. 2. Goal State: Your desired end-point. 3. Intermediate States: The various "checkpoints" or configurations you reach along the way. 4. Operators: The mental "rules" or moves you use to transition from one state to another.

Well-defined vs. Ill-defined Problems - What is the difference between a well-defined and an ill-defined problem?

A Well-defined problem has a clear starting point, a specific goal, and a fixed set of rules (e.g., a math problem or a chess game). An Ill-defined problem has ambiguous goals or unclear paths, where it's not even certain when the "perfect" solution has been reached (e.g., "becoming a better student").

Algorithms - When is an algorithm the most effective choice for a cognitive task?

They are best for well-defined and familiar problems. An algorithm is a rigid, step-by-step procedure that guarantees a correct solution if followed exactly (e.g., a specific math formula, a computer code, or a rigid baking recipe).

Heuristics Strategy - Why do humans prioritize heuristics over algorithms when facing unfamiliar problems?

Because searching every possible state in a "problem space" for an unfamiliar task is too demanding on working memory and time. Heuristics are "rules of thumb" that are highly likely to work and drastically narrow down the search space, even if they don't guarantee a 100% success rate.

Difference Reduction (Hill-Climbing) - What is the core logic and the primary weakness of the difference reduction heuristic?

Logic: You always choose the move that makes the current state "look" most like the goal state. Weakness: It fails when a problem requires you to temporarily move away from the goal or take a "detour" to eventually reach it (e.g., walking backward to find a gate or bridge).

Means-Ends Analysis - What is the step-by-step process of using the "Means-Ends" heuristic?

1. Identify the largest difference between the current and goal states. 2. Create a sub-goal to reduce that difference. 3. If you can't reach that sub-goal, create a "sub-sub-goal" until the "ends" (goal) can be met by the "means" (available actions).

Working Backward - In what specific scenario is the "working backward" heuristic most cognitively efficient?

It is most effective when the Goal State is very clearly defined but the starting point has too many possible directions. By starting at the end and moving to the previous required step, you filter out irrelevant paths (e.g., solving a complex maze from the exit).

Analogy in Problem Solving - How can an analogy be used as a heuristic for new problems?

It involves finding a familiar "source" problem that shares the same underlying structure as your current "target" problem. If you can map the solution of the source onto the target, you can solve the new problem without needing new information or trial-and-error.

Expertise & Pattern Recognition - How does "chunking" allow experts to solve problems faster than novices?

Experts have thousands of complex patterns stored in Long-Term Memory. Instead of seeing individual pieces (like in Chess or Poker), they see "strategic clusters." This pattern recognition automates low-level tasks, freeing up working memory for high-level strategy.

Functional Fixedness - What is functional fixedness and how does it serve as a barrier to insight?

It is the tendency to fixate only on the common or typical function of an object. Ex. In the "two-string problem," people often fail to use a pair of pliers as a pendulum weight because their knowledge says pliers are only for "squeezing," preventing them from seeing the pliers as a simple "heavy object."

Knowledge Impediments (Mental Sets) - How can having a "Mental Set" (Einstellung Effect) actually hurt problem solving?

A mental set is the tendency to keep using a strategy that worked in the past, even when a much simpler or more obvious solution exists. You become "blind" to new possibilities because you are stuck on "autopilot" with an old strategy.

Strategy Selection Rule - What is the "summary rule" for choosing between algorithms, heuristics, and knowledge?

1. If Familiar/Well-defined: Use an Algorithm. 2. If Unfamiliar/No Knowledge: Use a Heuristic (e.g., means-ends). 3. If Some Knowledge: Use it to recognize patterns and automate, but watch out for functional fixedness and mental sets.