Chapter 12 - Problem Solving Flashcards
1- Types of problem solving
Problem solving definitions
* A multi-step process to shift your current problem state to a goal state
- Math problems
- Social problems
- And everything in between
* How do we engage in this process of problem solving efficiently?
Engaging in problem solving is …
* Cyclical
- Enact steps that occur in a
loop
* Recursive
- Repeat this cycle as many
times as necessary to find a
solution
* Applicable
- Apply successful cycles
(solutions) to hew problems
Cycle:
1. Define the problem
2. Brainstorm solutions
3. Pick a solution
4. Implement the solution
5. Review the results
(and restart if not solved)
Types of problems
1. Well defined problems: (parietal cortex)
Requirements are unambiguous
All information needed to solve the
problem is present
Applying Algorithms
Puzzles
Ex: puzzle, murder mystery, math problem…
*Goal directedness
- Problems with a defined goal state
and set task constraints such that
there are clear steps. Ex: Sudoku
- Ill defined problems (prefrontal cortex)
How to overcome problem / the goal is
ambiguous
Requires added information
Situational
Ex: My laptop is broken
* Ambiguous situations that:
- Have few limitations (rules) for how to solve the problem
- Must create your own path
- Multiple solutions
* Social problem solving is a form of ill-defined problem solving
Ex: I need to figure out how to make new friends.
I want to learn a new musical instrument
*Ill-defined problems carry a load
Ex: Can you make a word with ZJAZ (ill defined…no constraints) vs. Can you make a type of music with ZJAZ (well defined…constraints)
§ Greater activity in the right lateral prefrontal cortex for ill-defined anagrams
§ Solving ill-defined problems carries a greater ‘cognitive load’
§ Cognitive load: the amount of information held in mind at one time
Moravec’s paradox
* Artificial intelligence (AI) can solve well-defined problems well, but not ill-defined problems and simple skills
* “Everything that’s easy is hard, and everything that’s hard is easy”
* AI is often defined by the use of algorithms, deep neural networks, that work well with certainty but not with un- certainty
2- Algorithms and heuristics to navigate a problem space (Useful for well-defined problems)
Problem solving algorithms
* Strategies to move through a “problem space”
* A problem space is a representation that includes:
- Initial and goals states
- Intermediate paths and operators: actions to change between states
- Task constraints (contexts, cues)
The Tower of Hanoi
* Move 3 discs from peg A to C so they are in the same initial order
* Task constraints :No disc can lie on top of a smaller one & only one disc can be moved at a time (i.e., the top disc of a pile)
1. Initial and goals states
2. Intermediate states and operators
3. Task constraints
A brute force approach
* Systematic algorithm that
represents all the possible steps
from the problem to goal state
* Guaranteed to find a solution, but
inefficient
* Combinatorial explosion:
computing too many alternatives
Narrowing down search: Heuristics
* Strategies to select moves in a problem space
* Helps avoid combinatorial explosion
* Hill climbing strategy
* Means end analysis
Hill climbing strategy
* Select the operation that brings you closer to the goal without examining the whole problem space
* This strategy can lead to a false outcome, a ‘local maxima’ (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
Example why hill climbing doesn’t always work:
The hobbits and orcs problem
* Three Hobbits and Three Orcs are on one side of a river, and they all want to cross to the other side
* There is one boat that holds 1 or 2 creatures
* If there are ever MORE Orcs than Hobbits in one place, the Orcs eat the Hobbits.
* At least one creature must bring the boat back each time.
* How can you get everyone safely
You must move AWAY from the goal to get there!!
Means ends strategy
* What “means” do I have to make the current state look like the goal state I want to be in?
* Identifying sub-problems to complete the goal
* Includes forward and backward movements and constantly evaluating the difference between current and goal states
* More flexible approach than hill-climbing
3- Analogies and experience to solve problems (Useful for ill-defined problems)
Expertise and problem solving
* Experts are more familiar with certain information and so they represent a problem differently than non-experts
* Expert radiologists use ‘global’ visual processes when viewing scans
Analogical problem solving
* Making comparisons between two situations; applying the solution from one of the situations to the other situation
Ex: the tumor story and the fortress story
* Target: the situations the person is currently in (The Tumor Problem)
* Source: the situation that shares similarity with the target (the Fortress Story)
* People aren’t very good at using analogies unless they are ”reminded”
* Without the hint, a person must look beyond surface details, and consider the general structure (the gist)
* Most success when a source and target share surface and structure
- E.g., Using a past school-related problem to solve a current school-related problem vs a current relationship-related problem
The DNA Double Helix:
Figured out what DNA looked like when looking at a spiral staircase
The Einstellung effect
* The bias to use familiar methods to solve a problem
- “I always do it this way ..”
* Can result in an inability to seek and use a better method to solve a given problem
* Leads to rigid thinking and blocks in problem solving
* Functional and Mental Fixedness
Functional fixedness:
* The inability to see beyond
the most common use of a
particular object
* “Fixed” on the function of an
object that you know
Ex: two string problem
* Only 39% of people can find
the solution within 10 minutes
* Hints help. Prior to task, swinging
arms in a solution-relevant manner
led to the solution
Ex: the candle problem
* Children of different ages solved the
‘candle’ problem
* Difference with respect to pre- utilization: experience with the objects
* No fixedness in children without
pre-utilization
* Too much experience may lead to
fixedness and the Einstellung effect
Mental fixedness: Overusing mental sets
* Responding with previously learned rule sequences even when they are inappropriate or less productive
* The tendency to respond inflexibly to a particular type of problem and not alter your response
Ex: The water jug problem
* This equation could be applied to all remaining problems: Solution: Amount = B - A - 2C
* Problem 7 and 8 can also be solved with a simpler equation: A + C (problem 7) or A – C
(problem 8)
Do people still use the more
complex equation?
YES
4- Overcoming fixations and using insight to solving problems (A link to creativity)
Insight
* A productive thinking process of forming new patterns or ways to view a problem
* Restructuring a problem in a new way leads to a sudden solution
- The Aha moment
* Gestalt switches: the experience of having a sudden switch in how you see something
Four features of insight:
* Suddenness: The solution pops into mind with surprise
* Ease: The solution comes quickly and fluently
* Positive: A pleasant experience, even before assessing ifmthe solution is effective
* Confidence: The solution is believed to be the right one
Insight: The triangle problem
The triangle shown below points to the top of the page. How can you move three circles to get the triangle to point to the bottom of the page?
Verbal insight problems
Insight problems: The necklace
* You are restructuring the problem, a key
characteristic of insight
Insight results from impasse
* mental impasse is being stuck in a solution path
* leads to sudden insight from restructuring the problem to see a new solution
Insight and the subjective experience
* Insight problem solving feels like it happens suddenly
- People cannot accurately predict performance (finding solution)
* Non-insight problem solving comes with awareness
- Step by step algorithms help predict performance
* Participants solved ten problems:
- Five verbal insight problems
- Five non-insight algebra problems
* Made ‘warmth ratings’ every 15 seconds
- A person’s feeling that they are approaching a solution
* Warmth ratings predicted performance on algebra by not insight problems
Insight is defined by the experience
* Participants shown problems and asked to rate feeling of knowing ( “Do you
feel that you will know the answer to this problem?”)
* Completed algebra and insight problems
* Feeling of knowing ratings predicted algebra but not insight problem solving ability
* Metacognitive assessments (What you know about what you know) is not accurate for insight problems
