Problem Solving Strategies

• Cognitive abilities will not solve all problems

Today's Topics

• Define "problem solving"
• Learn about well-defined and ill-defined problems
• Learn strategies for problem solving
• Examine expertise in problem solving

Problem Solving Defined

• Problem solving is the process of moving from a problem state to a desired goal state.
• Problem solving involves
• Recognizing and representing the problem, focusing on relevant information.
• Analyzing the problem and applying a problem-solving cycle.
• Assessing the effectiveness of the solution and storing it appropriately.

Three-Part Problem Solving Cycle

• Recognizing and representing the problem
• Analyzing and solving it
• Assessing the solution's effectiveness

The Monk Problem

• Requires recognizing and representing the problem in a way that allows for a solution

Analyzing and Solving Problems

• First define the problem
• Then analyze the problem
• Identify possible solutions
• Choose a solution
• Implement the solution, evaluate its effectiveness, develop a plan of action

Characterizing The Problem Solving Cycle

• The problem-solving cycle is recursive, needing to be repeated to find a solution
• The problem-solving cycle should output a solution to a problem, and also have adaptability to generalize to new scenarios

Generalizing Solutions In Memory

• Important for adaptive behavior.
• The storage of solutions should apply to new scenarios
• Memory for solutions involves including the essence and not just specifics.

Classes of Problems

• Well-defined problems’ requirements are unambiguous
• All information needed to solve well-defined problems is present
• Algorithms can be applied to well-defined problems
• Well-defined problems include puzzles
• Ill-defined problems define how to overcome the problem, the goal of which is ambiguous
• Ill-defined problems require added information
• Ill-defined problems are situational
• Examples of ill-defined problems include fixing a broken laptop and planning a vacation

Well-Defined Problems

• Games like chess and sudoku
• Have goal directedness
• Defined goal state
• Task constraints with clear steps
• Single expected outcome

Ill-Defined Problems

• Ambiguous situations that have few limitations for how to solve the problem
• Have multiple solutions or expected outcomes
• Include social or self problem solving
• Examples include needing to figure out how to make friends, or learning a new musical instrument

Episodic Memory

• Assists in problem solving
• Temporal lobe epilepsy (TLE) patients with hippocampal damage have select episodic memory loss
• TLE problems limit the number of effective, relevant steps, or non-effective, irrelevant steps

Cognitive Load

• Solving ill-defined problems carries a greater cognitive load
• Greater activity in the right lateral prefrontal cortex for ill-defined anagrams
• Cognitive load is the amount of information held in mind at one time
• Working memory capacity is limited

Ill-Defined Problems and Schematic Solutions

• Ill-defined problems lack schematic solutions to reduce working memory capacity
• Increased cognitive load demand is observed in ill-defined problem solving

Moravec's Paradox

• Artificial intelligence (AI) solves well-defined problems well, but not ill-defined problems and simple skills
• "Everything easy is hard, and everything hard is easy"
• A.I. is defined by algorithms and deep neural networks
• These work well with certainty, not with uncertainty

Problem Space

• Well-defined problems represent an information processing approach to study problem solving via algorithms
• Strategies can be depicted to move through a "problem space"
• A problem space is a representation that includes initial and goals states, intermediate paths and operators, and task constraints

Tower of Hanoi

• The Tower of Hanoi is a problem involving moving three discs from peg A to peg C, in the same initial order
• The task constraints are that no disc can lie on top of a smaller one, and only one disc can be moved at a time

Solving By "Brute Force"

• Solving requires systematic algorithms to represent all steps from problem to goal state
• Guaranteed to find a solution, but is inefficient
• Combinatorial explosion occurs when computing too many alternatives
• Leads to decision fatigue

Problem Space Heuristics

• Problem solving involves strategies to select moves in a problem space
• Avoid combinatorial explosion and decision fatigue

Thinking Aloud Procedures

• Used to measure complex thinking, understanding strategies
• "Concurrent verbalizations" describe what you are doing as you do it (solving a problem)
• "Retrospective verbalizations" describe what you did at an earlier time, influenced by metacognitive processes

Navigating Problem Space

• Heuristics
• Involves select moves in a problem space to avoid combinatorial explosion and decision fatigue
• Includes trial and error, hill climbing strategy, and means end analysis

Trial and Error

• Considered lower-level thinking
• Try out a number of solutions, rule out what doesn't work
• Good for limited outcome problems
• No good for multi-outcome problems

Algorithms

• Champions of tasks like Rubik's cube solving use algorithms, not trial and error

Hill Climbing Strategy

• Select the operation that brings you closer to the goal without examining the whole problem space
• Can lead to a false outcome, a local maxima, or where the subgoal is mistaken as the final goal
• Does not always work because some problems require you to move away from the goal in order to solve it

Means-End Strategy

• Means end strategy is more flexible than hill-climbing
• Requires the means to make the current state look like the goal state
• Sub-problems need to be identified to complete the goal
• Includes forward and backward movements
• Constantly evaluate the difference between current and goal states

Means End Analysis

• Envisioning the end or ultimate goal
• Determine the best strategy for attaining the goal with the current situation
• Highlights the importance of recursion
• Sub-goals and step by step approach to getting to the solution

Expertise

• Experts have more knowledge, and use better rules or strategies

Expertise and Defining the Problem

• Experts spend more time defining a problem
• Participants were split into four groups defined by expertise and area of study
• Non-experts spent more time trying to develop a solution
• Experts spent more time defining the problem appropriately

Expertise and Problem Visualization

• Experts are more familiar with certain information and represent problems differently
• Expert radiologists use 'global' visual processes when viewing scans
• Experts do not focus on unnecessary details

Expertise Requires Brain Processes

• Expert radiologists recruit broader visual areas when viewing chest x-rays
• Experts recruit more brain areas related to their expertise
• Experts are better able to use domain-relevant knowledge to perform a task

Holistic Brain Processing

• fMRI was applied as expert and novice doctors solved clinical problems
• Novices activate the left hemisphere of the brain; experts activate the right side

Expertise In Chess

• When expert and novice chess players reconstruct a chess board depicting a play, experts remember more of the board
• If shown a chess board with pieces in a random layout, experts were no different than novices
• Experts chunk information on encoding based on prior knowledge

Chess Master Brain Activity

• Chess masters engage additional brain regions
• Regions are only engaged for a chess recognition task, not a geometry task

Expertise Domain Specificity

• Expertise shows there is limited transfer between domains
• An expert lyricist (rapper) is not necessarily an expert baker