psych cognition ch 12 problem solving and creativity

Problem solving

problem = state of the world you wish were true but currently isn’t

… and solving the problem you mean changing the world in your desired way but how to change isn’t immediately obvious

types of traditional problem solving

problem solving via SEARCH

problem solving as INSIGHT

problem solving using KNOWLDGE

Problem characterized by 3 things

goal: state of affairs you wished existed

current state: how the world is currently

actions/operators: things you can do to change the state of the world

problem space

problem states - possible states of the world that may be reached

and actions/operators

Ex: eight-tile puzzle

can involve the problem solving method of SEARCH

Problem solving by search

finding the correct ‘path’’ or ‘route’ thru the problem space

problem solving search heuristics for choosing the next operator include:

• random search

  • picking moves at random.. inefficient

• hill climbing

• means/ends

• working backwards

Hill climbing

one always chooses an operator such that the new state is CLOSER (or more similar) to the goal state than the current state

• its like physically moving closer to the goal from where you are currently

hill climbing problems

it can word for some problems but moving CLOSER to the goal isn’t always the bestt thing

*local maximum

Local maximum

when moving in the direction of increasing similarity fails to each the goal

• then you get stuck and reach a ‘point of no return’ an d actually end up further from the goal even tho it felt like you were moving closer

Hill climbing evidence

the 3 disk tower thingy

• at some point, you have to make a move that feels counterintuitive and like you’re getting further from the goal, but actually that brings you closer to the goal!

Means-End analysis

this allows the pursuit of SUBGOALS

• they allow one to temporarily move away from the goal… in order to each it in the end

and it:

• characterizes the biggest different between the current state and the goal

• selet operator that reduces the difference

  • if the operator cannot be applied in the current conditions…. we create a SUBGOAL to change the conduits to allow the operator to be applied

Means-end example

Goal: want to take son to school from home

different: the distance from home to schoool

operator: car can reduce that distance

conditions: car is broken and doesn’t start

• subgoal: need to fix the car

• difference: need a new battery

• operator: go to the mechanic to put in a new battery

• conditions: mechanic isn’t present to do that

  • sub-sub-goal: need mechanic to put the battery in

  • difference: distance/klnowlegde

  • operator: phone can inform the emchanic

  • ETC

**mothod can be used to solve the tower of Hanoi on the first try

Means Ends analysis - tools

tool = means of achieving and END

acquiring. tool may be a subgoal one pursues in order to achieve the ultimate goal and to acquire the tool, you might have to move AWAY for the ultimate goal

Tool usage

tools used too be seen as unique to intelligent human behavior but that’s false

• animal behavior were only thought to be related to learning-by-association

  • classical conditioning

  • trial-and-error

BUT Animals actually did learn to use tools like chimpanzees using sticks and boxes, and birds using hooks to reach food

Animal intelligence

they also do more than just hill climbing… they’re able to temporarily move away from their goal in order to achieve it (or to acquire a tool to achieve it)

Working backwards

one particular application of means-ends

• planning a series of moves thru thinking in ‘reverse’, and where your large problem gets converted into a smaller one

Problem solving by INSIGHT

sometimes you just need to find the right representation!

• when you find the right representation, the solution appears immediately as an insight, a sudden realization. because the traditional ‘search’ didn’t work

insight problem - necklace

insight = using the all 3 links of one chain to join the other 3 chains - this is more unconventional and requires insight

insight example/experiment

Metcalfe and Wiebe

ppnts had insight and non insight problems and every 15 seconds they rated how ‘warm’/close they were to the solution

• to see like if this problem solving really came suddenly/abruptly or if it actually happens gradually (and just w/o us noticing)

non insight: (like math problem)

• in the algebra problem they knew each step gets them closer to the solution

insight (solutions require correct representation)

• there’s a steeper slope between ‘warmth’ and the solution time because tis more abstract and this problem that insight IS A SUDDEN jump and different from the gradual other noninsight problems

Thinking outside the box

solution can be easier or harder depending on how the problem is represented

• there can be certain limitations/bounds suggested thru certain framings

Problem solving using knowledge

we often have knowledge relevant to a current problem, but it can be helpful or harmful

functional fixedness

tendency to use objects in customary/conventional ways

• and it can prevent us from finding solutions to problems

• and INSIHGT though, can help us realize the unconventional functions of objects that are the solution

functional fixedness candle problem/experiment

boxes can be represented as containers

or boxes can be shown empty w materials outside the box…

• when boxes shown as empty, % solving problem WAS SIGNIFICANTLY HIGHER because the usual/copventional function of the object was de-emphasized

Mental Set

habitual ways people have of thinking

• box = container, not candle holder

• paintbrush = painting, not as a weight in a pendulum, etc

it can be acquire as a result of repeatedly solving the SAME type of problem in the SAME way (almost like systematically)

Water jug problems (mental set) experiment

6 problems = same abstract solution/method so the ppnts would ‘learn the way’

but 7 and 8 had simpler solutions (but could also be solved using the same previous method)

when ppl formed the mental set thru the first 6 problems, much less of them solved 7 and 8 using the easier solution, and those who solved only 7 and 8 (absent mental set) all solved the problem w the easier method

• ppls tend to apply old solutions to new problems…. can be an issue

Effect of Problem Wording

it influences what knowledge if brought to bear

mutilated checkerboard problem (problem wording)

mutilated checkerboard experiment experiment

4 different wordings of checkerboard:

• all squares blank

• alternating squares black or pink

• alternating squares LABELED black or pink

• alternative squares labeled bread or butter

then they were given hints in 15 minute increments…

RESULTS:

• blank condition took the LONGEST to solve the problems

• both black/pink had the middle results

• bread/butter had the SHORTEST time taken to solve

**ppnts solved problem faster when the wording led them to think abt two squares being in PAIRS (like bread and butter… black/pink would be less obvious as ‘pairs’)

Wording effect, Russian marriage problem

basically you have to create 31 HETEROsexual pairs, but 2 men die so where’s 32 women, but 30 men.. so it’s really not possible

• its a lot more obvious here tho than the checkerboards maybe because of the wording!!!! even tho concept is technically the same

**this is an example of knowledge helping us see the solutions

Problem solving by ANALOGY

when a problem solver notes a correspondence between a NEW problem and an OLD one that suggest a new problem solution

Famous analogies in science

also Mestral: invented velcro after noticing burrs sticking to his dog

2 Stages of analogically problem solving

1. observe correspondence between base (old) and target domain (new problem) **realizatoin occurs here

   1. focus on overall system of relations rather than concrete elements or features (this makes sense lol)

2. then IMPORT knowledge from the base to the target

   1. this is like when the building on existing info in the new problem occurs

Analogies experiment/test

Gick and Holyoak

• ppnts read the General Story (base)

• then asked to solve the Tumor Problem (new) (analog of the General Story)

2 conditions:

• were aware that General Story could help solve the Tumor Problem

• were not aware

RESULTS:

• those with the hint/awareness = 90%+ correct vs no hint: 20%

  • ppnts could easily recognize the analogy/make correspondences when they were aware, but did NOT notice the analogy on their own

noticing analogies in different ways (experiment)

they:

• provided an ABSTRACT summary of the General Story (gave them the general idea/principle)

• provided diagrams summarizing the GS

• gave TWO analogs (GS and another story w the Dif elements but same solution/idea)

Analogy via principle/general idea

2 conditions

• told just the GS

• told the GS AND the principle “if you need to accomplish smth big, you can apply small forces from many directions“

RESULTS: they had the same % correct solutions so IT DID NOT HELP ppnts see the analogy

Analogy via Diagram

2 conditions

• story + diagram

• story only

REUSLTS: no significant difference, diagram didn’t rly help ppnts see analogy

Analogy + second analog

2 conditions

• GS (analog 1) + second analog

• GS plus random other story (not an analog)

they were then asked to compare the two stories and solve the tumor problem

RESULTS: TWO ANALOGS performed significantly better than one… so comparing two analogs helped promote problem solving

because: its results in the creation of an abstract representation that can be applied to new problems (ppnts were able to extract info and represent the relations between different elements)

Role of Comparison

COMPARISON IS NECESSARY to get the advantage of two analogs

• just having read the two stories isn’t enough… active comparison NEEDS to have occurred

PS by analogy summary

analogies = hard

• ppl rarely notice the fact that the info from one story can help solve another

BUT comparison helps and promotes abstract representation and therefore problem solving by analogy

Creativity

involves divergent thinking (non normative thinking)

• generate many solutions

• generate different solutions

• generatie solutions different from others

Insight and creativity…

many problems’ solutions (like related to insight) would be considered acts of creativity

Incubation

first you define the problem and gaining knowledge abt the problem area

THEN INCUBATE: when you work on something else/put your mind elsewhere

“I can’t remember now, it’ll come to me later“

sometimes getting the answer requires taking a break and letting it come to you later BECAUSE THIS allows for some other CUE to activate new pathways that might help what you’re looking for

Incubation as release from blocking

blocking - when you get stuck from using the same cue over and over again

so incubation can promote release from blocking because:

• incubation allows old representations to be replace by new ones

there was one representation blocking the problem but now after incubation, we have room for a NEW representation, and thus a solution

Incubation test/experiment

Smith and Blankenship

Conditions:

• yes incubation period OR no incubation period

• were given misleading info or NOT given misleading info

if misleading info causes blocking, then incubation should be effective

Remote Associates Test (RAT) experiment

you get seed words and need to find the 1 target word that would go with all the seed words (misleading hints would be given w the seeds)

between the 4 different groups... the main point is that there was a larger incubation effect when misleading information was given then when no misleading info (like between no incubation vs incubation)

what’s important is that PPL FORGET MISLEADING INFO, and the incubation effect was larger when misleading info was presented, but was forgotten during incubation

Barriers to Creativity

existing knowledge can block/inhibit creativity

The full creative process

creativity often involves a key insight, but the entire process of deleting a novel idea or product can involve many steps… SO BASICLLY insight yes is a component of creativity, but its not the same

Creativity as an interactive process

inventions require many iteratioins/ developments overtime… and if an insight does lead to some new invention, it’s likely followed up by iterations

Expertise/experts

those w exceptional problem solving skills in a domain

What makes experts better?

cognitive mechanisms? or experience/knowledge

Research into expertise

1. chess

2. physics

3. memory

Expertise in Chess

search tree = broad and deep

• larger number of possible moves, and the game lasts for a lot of moves

hill climbing and means-end/subgoalign doesn’t work either because problem space is huge

chess exceeds WM because so many pieces and types and stuff

Reasons to study chess

involves:

• complex skill

• recorded games

• International rating system (novice, master, etc)

Assessing Chess Experts experiment

chess is abt predicting what the other person will do in response to your move so experiment wanted to measure how many moves players considered, how far ahead, etc

Masters vs intermediates = same # moves considered, same # positions considered, same deepest move considered,

THE DIFFERENCE: masters had more ability to reconstruct chess positions

• because its more about their ability to REMEMBER the game (like past examples and scenarios they’ve seen), and less differences about how they PLAY the game itself

Testing Chess Memory

Chase and Simon

2 conditions:

• real valid chess positions/possibilies

• completely random/imposisble chess positions

for random positions, chess experts vs masters vs beginners all had SAME results (low)

for REAL possibilities, MASTERS = MUCH BETTER at recalling chess boards

**chess experts have better memory for chess positions but not better memory in general

****and experts recalled more pieces in CHUNKS (they’re able to categorize more deeply bc of their knowledge)…. and also they evaluate positions faster because their retrieval is quicker

Gary Kasparov

Less Search w Expertise

As ppl acquire expertise, they do less and less search and rely more on KNOWLEDGE

• the knowledge allows them to use better problem representations

  • which allow them to solve problems for little or no search

Memory Experts performance is also based on…

knowledge

SF

SF digit span was 7 ± 2 BUT he practiced and it became over 80 digits

he was a runner and used his knowledge of running to ‘chunk’ numbers as finishing times in races so

for ex: numbers between 346-420 = encoded running times for a mile

• and over time, his encoding strategies became more and more elaborate to include ages and years?…

*it’s about organization of chinks and about developing elaborate knowledge structures that allow for superior encoding stuff

Rajan Mahadevan

recited 31811 digits of pi from memory

• he started studying at 3yo

• digit span is 43 but letter span is only 13… so it's about practice and expertise in a SPECIFIC TOPIC

IT DOESN’T APPLY TO ALL

Ten Year Rule

it takes ten years or ~10,000 hours of practice to become an expert

Child Prodigies??

they mostly just started practicing at a young age and did not reach their highest performance levels until after ~10yrs

Theory of deliberate practice

practice is ALL that matters for attaining expertise AND NO ONE IS ACTUALLY BORN W PARTICULAR TALENTS

Violin example

it was rly just about hours practiced.., but also sort of how serious/focused the practice was…?

Kinds of Practice

Deliberate practice = practice directed toward IMPROVING

Coaches and Mentors

they are able to instruct performers on best practice techniques and especially in early stages, you can rly only get as good as your instructor is so

limits on practice

motivational constraint

resource constraint

effort constraint

• elite/masters have REST PERIODS in their schedules!

Practice vs talent

can be correlational, but some differences are ‘innate abilites’ (like height in basketball but)

well defined problems

starting states, goal states, operations that are well defined

ill-defined problem

starting and goal states and operations = unclear

• ex: finding a mate, etc when there’s TOO MANY VARIABLES and no clarity