Problem Solving Approaches

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Questions and Answers

In the context of problem solving, what does it mean to represent a problem at a deeper level?

  • Breaking down the problem into smaller, more manageable subproblems.
  • Using a variety of different problem-solving strategies to approach the problem.
  • Focusing on the surface features of the problem, rather than its underlying structure.
  • Identifying the key concepts and principles that are relevant to the problem. (correct)

What is a key difference between how experts and novices approach problem solving?

  • Experts are more likely to use pre-existing knowledge to solve problems, while novices rely on more intuitive approaches.
  • Experts spend more time identifying and representing the problem, while novices spend more time choosing a solution strategy. (correct)
  • Experts are more likely to use trial-and-error methods, while novices rely on more systematic approaches.
  • Novices are more likely to focus on the surface features of the problem, while experts pay more attention to its underlying structure.

Based on the text, what is a possible reason why experts are faster at processing meaningful information?

  • They have a more extensive knowledge base and can access relevant information more quickly.
  • They are more likely to use heuristics and mental shortcuts to solve problems.
  • They have a greater ability to focus their attention and filter out irrelevant information.
  • All of the above. (correct)

What is the main idea of the text?

<p>Experts and novices differ significantly in their problem-solving approaches. (D)</p> Signup and view all the answers

Based on the text, what is a likely difference in how experts and novices might categorize physics problems?

<p>Experts categorize problems based on their underlying principles, while novices categorize them based on their surface features. (C)</p> Signup and view all the answers

What defines a problem according to the provided information?

<p>It involves an obstacle between a current state and a goal. (D)</p> Signup and view all the answers

Which of the following approaches to problem solving is proposed by Gestalt Psychologists?

<p>Problem solving involving restructuring. (D)</p> Signup and view all the answers

What is considered a characteristic of expert problem solvers?

<p>They deploy structured methods and analogies. (B)</p> Signup and view all the answers

What factor is essential in defining metacognition in problem solving?

<p>Having knowledge of one's own thought processes. (C)</p> Signup and view all the answers

How can individuals apply problem solving using analogies?

<p>By drawing parallels with similar situations. (D)</p> Signup and view all the answers

What is NOT a characteristic of a problem as defined in the content?

<p>A clear solution is readily available. (B)</p> Signup and view all the answers

Which term describes the cognitive process used when individuals reflect on their own problem solving methods?

<p>Metacognition (D)</p> Signup and view all the answers

What does the process of problem solving involve?

<p>Reorganisation or restructuring of the problem representation (D)</p> Signup and view all the answers

What is indicated by the expression 'x = r' in the context of the circle problem?

<p>The radius of the circle (B)</p> Signup and view all the answers

What characterizes an insight problem?

<p>Involves a sudden realization of a solution, often referred to as an ‘Aha!’ experience (D)</p> Signup and view all the answers

What is one example of an insight problem given in the content?

<p>Moving 3 pins to make a triangle face downwards (A)</p> Signup and view all the answers

How can experience impact problem solving?

<p>Experience can either aid or hinder the problem-solving process (D)</p> Signup and view all the answers

What do obstacles to problem solving generally refer to?

<p>Challenges that prevent effective resolution of problems (C)</p> Signup and view all the answers

Which of the following best describes the process of restructuring in problem solving?

<p>It involves changing the representation of the problem to find a solution (C)</p> Signup and view all the answers

What is an essential feature of the triangle problem mentioned in the content?

<p>It involves moving pins to alter the triangle's orientation (D)</p> Signup and view all the answers

According to the content, which statement is true about the perception of problems?

<p>Different representations can lead to novel solutions (D)</p> Signup and view all the answers

What percentage of participants with a mental set solved problem 7 using the shorter solution?

<p>Less than 25% (A)</p> Signup and view all the answers

In Luchin's water-jug problem, what was the initial state defined as?

<p>The condition at the beginning of the problem (D)</p> Signup and view all the answers

Which of the following best describes the term 'goal state' in the context of problem-solving?

<p>The desired condition at the end of the problem (B)</p> Signup and view all the answers

Which element in problem space represents permissible moves to achieve the goal?

<p>Operators (C)</p> Signup and view all the answers

What effect did beginning with problem 1 have on participants' approach to problem 7?

<p>It established a mental set that hindered finding the shorter solution. (B)</p> Signup and view all the answers

What was the main focus of Newell and Simon's problem-solving model?

<p>The transition from initial to goal states through operators (D)</p> Signup and view all the answers

Which of the following is NOT a component of a problem space as defined by Newell and Simon?

<p>Solution path (B)</p> Signup and view all the answers

What factor can significantly affect the ability to solve problems effectively according to Luchin’s findings?

<p>Prior experience with similar problems (C)</p> Signup and view all the answers

Which term describes the various conditions that exist between the initial and goal states?

<p>Intermediate states (D)</p> Signup and view all the answers

How does establishing a mental set affect problem-solving outcomes?

<p>It makes it harder to find innovative solutions. (B)</p> Signup and view all the answers

What is the primary objective in solving the Tower of Hanoi problem?

<p>To move all rings to peg C (D)</p> Signup and view all the answers

Which of the following statements about operators in the Tower of Hanoi is true?

<p>You can only move one ring at a time. (D)</p> Signup and view all the answers

What is the means-end analysis strategy used for?

<p>To reduce the distance between the initial and goal states (C)</p> Signup and view all the answers

Which of the following is NOT a rule for moving rings in the Tower of Hanoi?

<p>Larger rings can be placed on smaller ones (C)</p> Signup and view all the answers

In the Tower of Hanoi, what constitutes an intermediate state?

<p>Any configuration closer to the goal state. (B)</p> Signup and view all the answers

What is the initial state in the Tower of Hanoi problem?

<p>All rings on peg A (D)</p> Signup and view all the answers

Which strategy is employed in reducing the complexity of the Tower of Hanoi problem?

<p>Means-end analysis (D)</p> Signup and view all the answers

What role do subgoals play in solving the Tower of Hanoi problem?

<p>They help bridge the gap between initial and goal states. (B)</p> Signup and view all the answers

What happens if a large ring is placed on a smaller ring in the Tower of Hanoi?

<p>It violates the rules of the game. (B)</p> Signup and view all the answers

Flashcards

Problem Solving

The process of overcoming obstacles to reach a goal when a solution isn't immediately obvious.

What is a Problem?

A situation requiring a solution where the way forward isn't clear.

Restructuring Approach

A problem-solving technique focusing on changing the way the problem is perceived.

Search Approach

A problem-solving method that involves exploring possible solutions through systematic searching.

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Analogies in Problem Solving

Using parallels from similar situations to solve a problem.

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Metacognition

Thinking about one's own thinking process while solving problems.

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Expert vs Non-Expert Problem Solving

The different ways experts and novices approach problem-solving tasks.

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Problem Representation

How a problem is understood and depicted in the mind.

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Reorganization in Problem Solving

The process of restructuring a problem's representation to find solutions.

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Insight

A sudden realization of a problem's solution, often described as an ‘Aha!’ moment.

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Perceptual Insight

The ability to see a problem in a new light, necessary for solutions.

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Circle Problem Solution

To solve the circle problem, the solution is x = r.

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Triangle Problem

An insight problem where three pins must be moved to change the triangle's orientation.

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Obstacles to Problem Solving

Factors from experience that can help or hinder finding a solution to a problem.

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Difference in Problem Types

Insight problems may be qualitatively different from other problems.

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Method of Insight Problems

Insight problems often require a unique approach to solve them effectively.

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Expert Problem Representation

Experts spend more time understanding and framing the problem deeply.

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Focus on Underlying Structure

Experts pay attention to essential problem features rather than superficial aspects.

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Time Efficiency in Problem Solving

Experts solve problems faster by spending less time on choosing strategies after clarifying the issue.

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Meaningful Information Processing

Experts efficiently search and represent problems using significant information.

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Novice vs. Expert Speed

Experts process and solve problems faster than novices due to better problem representation.

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Luchin’s Water-Jug Problem

A problem-solving task that reveals mental set effects.

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Mental Set

A tendency to solve problems using the same methods as previously used.

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Shorter Solution

A more efficient way to solve a problem compared to established methods.

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Initial State

The condition at the beginning of a problem-solving process.

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Goal State

The desired condition at the end of a problem-solving process.

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Intermediate States

Conditions that exist in-between the initial and goal states during problem-solving.

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Operators

Permissible moves that transition between states in problem-solving.

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Information Processing Approach

A modern approach to problem-solving focusing on how information is processed.

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Newell and Simon

Researchers known for their work on problem-solving and cognitive processes.

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Problem Space

The entire set of possibilities available to solve a problem.

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Tower of Hanoi

A mathematical puzzle involving moving rings between pegs under specific rules.

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Means-End Analysis

A strategy to solve problems by reducing the differences between the current and goal states.

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Subgoals

Intermediate objectives that help achieve the overall goal in problem-solving.

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Rules in Tower of Hanoi

Specific guidelines governing the movement of rings in the Tower of Hanoi problem.

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Ring Movement

The action of relocating rings from one peg to another, adhering to specific rules.

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Pegs

The vertical posts in the Tower of Hanoi used to hold the rings.

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Study Notes

Problem Solving

  • Problem solving involves some difficulty, with a non-obvious solution.
  • Every day, people solve problems.
  • A problem arises when an obstacle exists between a current state and a desired goal, making the path unclear. (Lovett, 2002)
  • A problem is also defined as a situation where someone wants something but isn't immediately sure how to achieve it. (Newell and Simon, 1972)

Approaches to Problem Solving

  • Restructuring: Proposed by Gestalt psychologists, involves representing the problem differently, reorganizing the thought process or perception. Key aspects include:
    • How people represent problems in their minds, and
    • How problem solving involves reorganizing or restructuring the representation of the problem.
  • Search: A problem space consists of:
    • Initial state
    • Goal state
    • Intermediate steps
    • Operators (Permissible actions)
    • Problem solving is the search through this space. (Newell and Simon, 1956, 1972)
  • Analogies: Leveraging solutions from similar problems.

Creative Cognition

  • Creativity involves originality and expressiveness in creating something new.

Metacognition in Problem Solving

  • Metacognition is "thinking about thinking."
  • In problem-solving, metacognition helps identify the actual problem, understand when knowledge is insufficient, to recognize difficult parts, and to accurately monitor progress.

Obstacles to Problem Solving

  • Functional Fixedness: Inability to perceive the novel functionality of an object due to familiar usage. Causes difficulty applying an object for a different use than conventionally prescribed.
  • Mental Set: Based on past experiences, individuals might approach problems in a habitual manner, regardless of the better fit alternative. This can hinder effective problem solving.

Problem Solving and the Brain

  • Problem solving involves many brain regions, with the prefrontal cortex playing a critical role in planning complex tasks, executing strategies, reasoning, and forming connections across elements.

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