Problem-Solving
What is the importance of understanding the problem in problem-solving?
Understanding the problem is the first and most critical step in problem-solving because it determines how you will approach the solution. This includes identifying the initial state, goal state, and constraints. A failure at this stage often leads to misguided efforts or incorrect solutions.
Describe the means-ends heuristic
The means-ends heuristic involves:
1. Identifying the difference between the current state and the goal
2. Creating subgoals to reduce that difference
It’s especially effective in complex problems, as it helps structure the solution path into manageable steps.
In what way do gender stereotypes affect math problem solving?
Gender stereotypes (e.g., "boys are better at math") can lead to stereotype threat, where individuals underperform because they fear confirming negative beliefs. This affects confidence, working memory, and motivation, especially in girls and women in math-heavy contexts.
What are the main methods used to represent problems?
Problems can be represented through:
Symbols (e.g., algebraic equations)
Matrices (useful for comparing multiple variables)
Diagrams (like flowcharts or graphs)
Visual images (mental or drawn representations)
Choosing the right representation simplifies complex data and can significantly improve the efficiency of problem-solving.
What is the hill-climbing heuristic, and what is its major limitation?
Hill-climbing involves choosing the option that appears to lead most directly to the goal, without backtracking.
Limitation: It can lead to local maxima, where the solver is stuck because moving forward doesn’t appear to improve the situation—even though the ultimate solution requires a temporary step back.
What’s the difference between insight and noninsight problems?
Insight problems involve a sudden realization or "Aha!" moment (e.g., riddles).
Noninsight problems are solved through methodical, step-by-step approaches (e.g., math problems).
Brain imaging studies suggest these are processed differently in the brain.
What is situated cognition and how does it affect problem-solving?
Situated cognition suggests that knowledge is tied to the context in which it is learned and used. This perspective implies that people often solve problems more effectively when they are in real-life settings, as they can draw on environmental cues and practical experience.
How does expertise influence problem-solving?
Experts excel in problem-solving within their domain because they have:
Larger, better-organized knowledge bases
Effective pattern recognition
The ability to ignore irrelevant information
However, they may be less flexible when facing novel or unconventional problems outside their field.
What are the characteristics of creative individuals?
Creative individuals often show:
Divergent thinking (generating multiple ideas)
Openness to experience
Risk-taking and intrinsic motivation
A balance of discipline and imagination
They are also typically persistent, even in the face of failure.
How does embodied cognition relate to problem-solving?
Embodied cognition emphasizes the role of the body in thinking, such as how gestures or physical movements can aid in understanding and solving problems. For example, using hand movements can help in visualizing spatial relationships or organizing thought processes.
What is a mental set, and how can it hinder problem-solving?
A mental set is a tendency to approach problems using a previously successful strategy, even when it's not appropriate for the new situation. It can block novel or more efficient solutions, especially when the solver is rigidly applying old methods.
What defines creativity in problem-solving?
Creativity in problem-solving involves producing novel and useful solutions. It requires not only originality but also appropriateness, meaning the ideas must be effective and applicable to the problem at hand.
What is the analogy approach in problem-solving?
The analogy approach involves solving a new problem by referring to a similar, previously solved problem (the source). Successful use depends on identifying structural similarities, not just surface-level features. For example, comparing the heart to a pump helps understand its function.
Define functional fixedness and provide an example.
Functional fixedness is the tendency to see objects only in their typical use.
Example: Failing to use a wrench as a paperweight because it’s only thought of as a tool for tightening bolts. It restricts creative uses of familiar objects.
How does motivation impact creativity?
Intrinsic motivation (doing something for its own sake) enhances creativity.
Extrinsic rewards can sometimes reduce creativity, especially if perceived as controlling.
However, informative feedback or recognition can support creativity when it reinforces a person’s autonomy and competence.