Problem Solving Strategies

Problem Solving

• Problem solving involves moving from an initial problem state to a desired goal state.
• It's a multi-step cognitive process with three main stages: recognizing and representing the problem, analyzing and solving it, and assessing the solution's effectiveness.
• The first stage emphasizes focusing on relevant information to accurately understand the problem.
• The second stage involves navigating the problem-solving cycle.
• The third stage includes storing the solution in an appropriate form for future use.

The Problem-Solving Cycle

• The problem-solving cycle includes these steps:
  • Defining the problem
  • Analyzing the problem
  • Identifying possible solutions
  • Choosing a solution
  • Planning a course of action
  • Implementing and evaluating the chosen solution
• This cycle is recursive: you might need to repeat steps or the entire cycle multiple times.
• The problem-solving cycle ensures resolution.
• It is applicable and adaptable across various scenarios.
• A solution should address the current problem, and also provide a generalizable version for new situations.
• It's important to generalize solutions in memory for adaptive behavior.
• Effective memory for solutions prioritizes the core essence over specific details.

Problem Types

• Problems are categorized as either well-defined or ill-defined.

Well-Defined Problems

• Well-defined problems have unambiguous requirements.
• All information required to solve the problem is available.
• Solving them typically involves applying algorithms.
• Examples include puzzles and games like chess or sudoku.
• These problems have goal directedness, clear task constraints (steps), and a single, expected outcome.

Ill-Defined Problems

• Ill-defined problems have ambiguous goals or methods to overcome the problem.
• They often require additional information.
• Solutions are highly situational.
• Examples include deciding how to make new friends or planning a vacation.
• Social or self problem-solving falls into this category.
• These problems have few limitations or rules and multiple possible solutions or expected outcomes.
• Individuals with temporal lobe epilepsy (TLE) and hippocampal damage have difficulty describing solutions to social problems, indicating the role of episodic memory.
• Ill-defined problems create a higher cognitive load in right lateral prefrontal cortex when solving anagrams.

Cognitive Load

• Cognitive load is the amount of information held in mind at one time.
• Working memory capacity is limited, which can lead to cognitive overload with ill-defined problems.
• Ill-defined problems do not have schematic solutions, increasing cognitive load demand.

Moravec's Paradox

• Artificial intelligence (AI) excels at solving well-defined problems, but struggles with ill-defined problems and simple skills.
• Everything that seems easy is hard for AI, and vice versa.
• AI defined by algorithms and deep neural networks handles certainty well but not uncertainty.

Problem Space

• Well-defined problems can be represented as an information processing approach using algorithms, within a "problem space".
• The “problem space” illustrates strategies for moving towards a solution.
• It includes initial and goal states, intermediate paths and operators (actions), and task constraints.
• The Tower of Hanoi is an example.
• Each move must adhere to the constraints: only one disc can be moved at a time, and a larger disc cannot be placed on a smaller one.

Navigating Problem Space

• Brute force approach: a systematic algorithm that explores all possible steps from the problem to the goal state.
• Brute force is guaranteed to find a solution, but it's often inefficient and can lead to combinatorial explosion and decision fatigue.
• Heuristics are strategies to select moves in a problem space to avoid combinatorial explosion and decision fatigue.
• Thinking aloud procedures are used to measure complex thinking to understand strategies.

Thinking Aloud Procedure Types

• In concurrent verbalizations you describe what you are doing as you do it (how you solving the problem).
• Retrospective verbalizations describe what you did at an earlier time, and they are influenced by metacognitive processes.

Heuristic Types

• Trial and error involves trying out solutions and eliminating those that don't work.
  • Trial and error is considered "lower-level thinking”.
  • It works well for limited outcome problems.
  • But it doesn't work well for multi-outcome problems like solving a Rubik's Cube.
  • Experts solve Rubik's Cubes with algorithms over trial and error.
• Hill climbing strategy involves selecting the operation that appears to bring you closer to the goal.
  • This method can lead to a false outcome, where a 'local maxima' (subgoal) is mistaken as the final goal.
  • The hill climbing strategy does not work if problems require you to move away from the goal.
• Means end analysis is a more flexible approach than hill-climbing.
  • It involves assessing means to make the current state more like the goal state.
  • Means end analysis involves identifying sub-problems to complete goal.
  • Includes forward and backward movements.
  • It constantly evaluates the difference between current and goal states.
  • It involves identifying sub-problems to complete the goal, envisioning the end goal, and determining the best strategy for attaining the goal given the current situation.
  • It highights the importance of recursion.
  • It uses sub-goals and a step-by-step approach to getting to a solution.

Expertise in Problem Solving

• Expert problem solvers have more knowledge than novices.
• Experts also use better rules and strategies than novices when solving problems.
• Experts spend more time in the problem definition process.
• They also represent a problem differently than non-experts due to familiarity with information.
• Expert radiologists use 'global' visual processes when viewing scans, and avoid focusing on unnecessary details.
• Experts recruit broader and more brain areas to process information related to their expertise.
• Experts engage in holistic brain processing and activate the right hemisphere of the brain while novices activate left side of the brain.
• In chess, experts chunk information based on prior knowledge.
• There is limited transfer between domains of expertise.