Problem Solving Flashcards
problem solving
recognizing there is a problem, analyzing and solving it, verifying the effectiveness of the solution
recursive and cyclical, applicable to future situations
takes into account both bottom-up and top-down information (higher-order cognitive process)
problem space theory
initial state, problem state which contains all intermediate states - possible steps to arrive at a solution, and goal state
operators are the actions to take to arrive at the goal state
well-defined problems
have correct answers and rules and procedures to arrive at them (can be solved by algorithms)
requirements are unambiguous, all information needed is present
has constraints that tell you how to reach the outcome
ill-defined problems
have many paths to take to arrive at many possible correct answers, you don’t necessarily know when you’ve arrived at a correct answer
requires added information and context, problem is ambiguous, situational
has few limitations = you must create your own path
behavioural approach to problem solving (Thorndike)
problem solving is reproductive: we use previous knowledge (examples and rules) and consciously search through possible solutions - trial and error
Law of Effect
part of the behaviourist approach to problem-solving
any response that does not produce a satisfying effect gets weaker, and any that does gets stronger
Gestalt approach to problem solving
problem solving is productive: we manipulate and restructure information in our minds (multiple POVs, reframe, reconsider, rethink)
insight
- a solution suddenly occurs to you which your are confident in
- only accounted for by Gestalt approach, during restructuring
- occurs because we see things as wholes, not sums of parts (bistable figures are viewed all-or-none)
- some problems are best solved by insight because they require restructuring
- insight results from impasse (realizing you cannot solve the problem by normal thinking - you have no choice)
restructuring
thinking flexibly about ways to represent the problem, changing its representation in our mind
getting over mental sets
like restructuring a bi-stable figure to see it the other way
heuristics
commonsense, rules of thumb, educated guesses, intuition (shortcuts to problem solving based on past experience)
help to reduce processing power
when do we use heuristics
when we are faced with too much information to process, time to make a decision is limited, decision is unimportant, too little information, a heuristic comes to mind in that moment
working backwards heuristic
solve a problem by focusing on the final result
means-end analysis heuristic
breaking down the larger goal into smaller sub-goals and re-evaluating progress at each step (flexibility)
using forward and backward moves and constantly evaluating the difference between current and goal states, takes into account the full problem space
mental set heuristic
tendency to use solutions that have worked in the past, leads to inflexible thinking
tells you what to pay attention to in a given situation
functional fixedness
tendency to view objects only for their intended purpose because of prior experience
what is an essential part of problem solving?
ignoring irrelevant distractors - not an innate skill, develops in young children and declines in old age
fixation in problem solving
focus on a specific characteristic of a problem - inhibits people from finding a solution
insight problem vs. non-insight problem
a solution pops into your consciousness vs. you have to consciously work through the steps to arrive at the solution
evidence for insight vs. non-insight problems (Metcalfe & Wiebe)
Ps working on a non-insight problem could accurately predict how close they were to arriving at a solution, insight problem Ps could not
evidence that both types rely on different cognitive processes
Maier’s two-string problem
two ropes too far to reach by the Ps have to be tied together - tie an object to swing on as a pendulum
easier to solve when Ps are given a cue, but Ps don’t recognize it as a cue (not part of their problem solving process)
shows lack of consciousness into the nature of insight
test of functional fixedness
divergent thinking
thought process that generates many solutions to find one that works best
convergent thinking
thought process that leads to conventional solutions
analytical intelligence
basic academic problem solving skills (IQ)
practical intelligence
ability to deal with real world tasks (street smarts)
creative intelligence relationship to problem solving
using existing knowledge and skills to deal with novelty
measured using ideational fluency
positive relationship between creative intelligence and problem solving (moving past fixations)
ideational fluency
number of ideas a person can generate about a topic
how do experts view problems?
experts take longer analyzing a problem and less time thinking about steps to take (spend time deciding what to do, then quickly do it), take a more holistic view - with experience, you develop a more efficient way of navigating a problem, less time fixating on details
experts are stuck in conventional thinking (have a strong mental set)
computers vs. humans in problem solving
humans are processors that use heuristics instead of algorithms (educated guesses can sometimes lead to the wrong response)
computers have enough processing power to consider all possible moves at once (so faster at solving well-defined problems)
well-defined vs. ill-defined experiment
anagrams with task constraint (make a type of music) or no constraint (make a word)
more activity in the right PFC for ill-defined problems (organizing cognitive processes, hold and organize cognitive load)
Moravec’s paradox
everything that’s hard is easy, and everything that’s easy is hard - related to AI problem solving which cannot learn ill-defined problems, but is good at solving well-defined ones (not good with uncertainty)
problem space
includes initial and goal states, intermediate paths (sub-goals) and operators (actions), task constraints (allowable moves)
contains all possible moves and solutions
Tower of Hanoi
well-defined problem - set goal and constraints
brute force approach to moving through a problem space
considering all possible moves without foresight - guarantees a solution but not effective (cognitive load, time and energy)
leads to combinatorial explosion
combinatorial explosion
a result of a brute force approach - computing too many alternatives leads to system shut down like decision fatigue
hill climbing strategy/heuristic
difference reduction strategy - moving in the direction that will bring you closer to your goal, not considering the entire problem space
doesn’t always work because sometimes you have to move away from the goal to solve it
hobbits and orcs problem
solution has many intermediate steps which sometimes require you to move away from the goal to get there in the end (hill climbing wouldn’t work)
how do novices view a problem?
novices are more conscious of their task performance progress (additional cognitive load) and spend more time in trial-and-error
make lots of fixations on details instead of viewing the problem more generally (eye-tracking x-rays)
try to run toward a solution rather than analyze the problem
analogical problem solving
making comparisons between two situations with similarities in underlying structure or meaning, applying the solution from one (source problem) to another (target problem)
why is it difficult to use analogical problem solving?
people need a hint to use an analogy to solve the problem, don’t do it by themselves because the two scenarios differ in structure details and surface content
when are we most likely to use analogical problem solving?
when both scenarios share structure details and surface content
why is it important to use analogical problem solving?
using analogies that share structure but not surface content helps us come up with novel ideas (DNA double helix idea came from a dream about a spiral staircase)
Einstellung effect
bias to use familiar methods to solve a problem - leads to rigid thinking and overlooking more efficient methods
evidence for the development of functional fixedness
candle problem in children with pre-utilization (prior knowledge and experience with the objects) and without = no fixedness in children without
children less vulnerable to effects of fixedness
evidence for mental sets
water jug problem - when problems are presented in an order where the first rely on the same solution, Ps tend to try to keep using that solution even when a more efficient solution would work (if given randomly, there’s no effect)
four features of insight
- suddenness (solution pops into your mind)
- ease (solution comes quickly and fluently)
- positive (pleasant experience)
- confidence (belief in the solution)