What is problem solving?

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PSYC 221 Fall Semester 2013 Cognitive Psychology: Lecture Twelve Problem-Solving - What is problem solving? (Or what isn’t problem solving?)  You’re not solving a problem if the answer that you are trying to find is immediately apparent  E.g. Asking: “What your mother’s first name?”  it is not really problem solving, because you can access the answer the immediately  Problem solving instead involves a series of stages of processing  When you begin the problem there isn’t a readily apparent solution  E.g. Solving a multiplication problem like 79x23 - You would be mentally carrying digits over and so on - Once you arrive at the answer, and you’re asked the same question again, the second time you answer won’t be considered problem solving, it would just be retrieving the answer from memory from the first time you solved it  Problem solving usually involves a series of intermediate stages of processing Example: “Three Men and a Rowboat” Problem (Well-Defined Problem) - 3 men want to cross a river - They find a boat, but it is a very small boat - It will only hold 200 pounds - Men are names Large, Medium and Small - Large weighs 200 pounds - Medium weighs 120 pounds - Small weighs 80 pounds - How can they all get across? - Clue: They might have to make several trips in the boat - Solution:  Small and Medium cross the river together first  Either Small or Medium return back with the boat  Large then crosses the river alone  Whoever is left over from the first trip, comes back to pick up the other guy  Then both Small and Medium cross the river together again Well-Defined Problems  Constraints are present  There are set of rules  There are conditions that influence what can happen  There are clearly defined information  Like a math problem

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Cryptarithmetic Problems: Constrained by the rules of arithmetic  GERALD + DONALD = ROBERT (D = 5, T = 0, L +1 = R)

Some strategies we have work well with ill-defined problems (Means-End Analysis “Reasoning”) Ill-Defined Problems  Usually take longer for us to solve compared to well-defined problems (usually 20 minutes)  Constraints are not present  Example: “When conduct experiments what’s a good variable or measure that we can use to understand problem solving?”  Reaction time (not very reliable)  Verbal Protocol Analysis (not very reliable) - Self-Report  Can’t compare 10 different subjects solving a problem and expect all of them to say the same thing  Not just how the subjects say but also what the experimenter or the tester record this self-report  Depends on interpretation of the experimenter  If you’re forcing subjects to verbalize their process, you might be making them solve the problem different way that they usually do  Cognitive processes happens so quickly that we might not even be aware of it  Not very reliable but still the best that we have, as of yet Difference Between A Well-Defined Problem and Ill-Defined Problem - With the latter we don’t really know what these rules are - We don’t know what the constraints are Part I: Mental Blocks  Sometimes when people solve problems, they are not as efficient as they should be because mental blocks trip them up 

Functional Fixedness: You think of something you have as being useful only for its main function  Hints can lessen functional fixedness  If people are stuck trying to solve a problem because they are functionally fixed, this is due to them thinking that the materials they have are only focused on their original uses (a hint can lessen the function fixedness)

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Negative Set: Solving a problem in a way that is less efficient, rather than solving it in a really simple way  Why do people do things in a difficult way?  Sticking to a strategy that has worked in the past but is less efficient than a simpler strategy  Usually these people whom use the negative set usually settle for a way that they first found to complete the task

Example: Old Experiment “Candle Problem” (90 years old) - Task: Attach the candle to the wall - Equipment Given: Candles, match box and thumb tacks - Solution: Tack the match box to the wall and then melt the candle wax to the top of the match box and so the rest of the candle can adhere to that - Variations of the Candle Problem  Subjects in one condition were given the materials in boxes  Candles in a box, tacks in a box, matches in a box  Thought of objects in their container role (boxes in their container role “Functional Fixedness”)  Didn’t think that boxes could be used as something else other than a container  Subjects in the other condition were given the materials outside the boxes  Solved the problem faster Example: Two-String Problem (Another Example Similar to the Candle Problem) - Strings coming down from ceiling - Strings are too far apart to be tied together - However, there is other stuff - Tie pliers to one of the strings as a weight and swing the string and then get the other string and tie them together  Pliers are used as a weight rather than a grip  Get subjects to use the pliers as a weight before the task  Hint, become less functionally fixed  Or reverse, have them use the plier to grip and twist something before the task  Become more functionally fixed Example: MacGyver - Opposite of someone who is functional fixed - Always small materials he would carry (string, crocodile clips and etc) Water Jug Problem: B – A – 2C = 100 ml (Desired Quantity)  Negative Set problem

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Three jugs with different capacities and want a certain desired quantity, how do you get it from these three jugs? Jug A holds 21 ml Jug B holds 127 ml Jug C holds 3 ml Solution: Fill Jug B, Take away water from Jug B by pouring water until Jug A is full and then fill up 2 Jugs C.

Nine-Dot Problem:  Draw no more than 4 straight lines (without lifting the pencil from the paper) which will cross through all nine dots  Reason: People don’t solve it quickly because they assume that you’re not allowed to draw outside the perimeter of the nine dots. Matchstick Problem:  Given six matchsticks, arrange them to form four equilateral triangles with each side one stick long.  Solution: 3D Pyramid  Reason: People don’t solve it quickly because they assume that you’re not allowed to think outside the perimeter Part II: Solving Problems with Analogical Reasoning - Problems can be solved successfully with analogical reasoning - One Famous Example: Figuring out how neurotransmitters bind to receptor sites and this made sense when people started thinking about the shape of the receptor site for the neurotransmitter dopamine will be different to the receptor site of different neurotransmitters like norepinephrine or serotonin (Analogy: Lock and Key) - It helped to come up with an analogy in order to understand how this process worked - One Famous Experiment: Study carried out to see if the experimenters could get the subjects to use analogical reasoning  Problem: Tumor Radiation Question – Subjects were told that someone had a tumor in their body (stomach) that needed to be radiated (course of radiation therapy) and that they needed to radiate the area in the body where the tumor was with strong enough radiation to destroy the tumor, but at the same time not damaging the surrounding tissue  Solution: Use multiple beams of radiation aimed at different angles that intersect the tumor at a single point which has higher concentration of radiation that is strong enough to destroy the tumor  Before Task: Fortress Attack Story - Castle with a bad guy inside, good guys looking to attack the castle and defeat the bad guy - Land mines that surround the castle

PSYC 221 Fall Semester 2013 - Story Number 1 (Condition 1): Attack from under ground - Story Number 2 (Condition 2): Attacking the castle from all angles - Provided useful analogy - Priming for solving the problem - When people heard Story Number 1 it did not help them come up with a solution, whereas Story Number 2 did (Priming  Reasoning of the Analogy from they use to solve the problem) - Analogical reasoning is good for solving ill-defined problems (E.g. Global Warming and Climate Change) Part III: Solving Problems with Means-End Analysis - When computer scientists wanted to see if they could figure out how to make a chest playing program and other computer algorithms that solve problems  Started talking about Means-End Analysis. - Means-End Analysis involves setting the - Herbert Simon  Won a Nobel Prize in Economics  Interest in Artificial Intelligence (A.I.)  Making a computer program to play chess with Allan Newell  The algorithm that he came up with is called Means-End Analysis which is good for thinking about how to solve ill-defined problems  Main Point: Means-End Analysis the algorithm involves works to reach sub-goals (Taking baby steps), you want to move in a particular direction towards the overall goal but mostly focused on the sub-goal and the sub-goal after that  Good for solving well-defined problems - How can you become a Clinical Psychologist with a Vancouver Private Practice?  Get good marks in classes (3rd Year, 4rth Year Courses)  Graduate Record Exam (GRE) = Entrance Exam for Graduate School  Reference Letters (Good Reference Letters)  MA program  Involves more courses  Become a TA in undergraduate courses to make more money and support yourself  Master’s Thesis  Master’s Degree  PHD Program  more courses, Doctorial Dissertation and write a Comprehensive Exams on Entire field of Program (Examining Orally or Writing)  Practicum  Main Point: Take baby steps to different sub-goals

PSYC 221 Fall Semester 2013 Tower of Hanoi Problem (Means-End Analysis, Well-Defined Example) - Move discs from one peg to another peg - This puzzle originally came to India before it showed up in Europe - Rule: Can’t put a larger disk on top of a smaller disk - Good example of a well-defined problem - Means-End Analysis: More immediate sub-goals that lead to the main goal  Good for solving both Well-Defined and Ill-Defined Problems Part IV: Creativity and Insight - Creativity:  Sometimes there is a real mystique about creativity “That person is special because s/he is so creative”  Creativity is domain specific  someone can be creative in one domain but not be very creative in other domains.  Creativity is less “romantic” or “magical” than a lot of people think, and in fact for a long time we’ve know about a series of stages that are involved in the creative process.  When people have insights, really this is one of the stages of the creative process, but there’s a difference between someone having an insight and someone talking about intuition.  Creative solutions can be reached by groups  Brain Storming  Many heads are better than one when trying to come up with a solution  Brain Storming: Any idea at all can be raised - Silly - Irrelevant - First Stage: People are encouraged to say anything and see if the idea sticks - Second Stage: Separating the good ideas from the nonsense - The Four Stages of Creative Processing: 1. Preparation: Research, may involve some tentative attempts to figure out how to solve the problem on successful ones 2. Incubation: Problem is put aside, sometimes people will put the problem aside for weeks, maybe even a month and then come back to it and are able to solve it more easily, probably because they were locked into one way of thinking about how to solve the problem and sometime spent away from the problem allowed them to approach it from a different perspective (different mental set or maybe they had a mental block before)  Incubation can help to overcome mental blocks  Good for ill-defined problems

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Not so good for problems solved in very small steps (E.g. computer programming done in very small steps)

William James - We learn to swim in the winter - We learn to ice-skate in the summer - Main Point: We can learn about a task even though we are not working on it - We tend to do better in problem solving when we’re not constantly thinking about it. 3. Illumination: When a person can see the solution (The “aha” moment)  It can happen in a form of a sudden insight 4. Verification: Checking to see if the solution to the problem makes sense.  Check to see if answer makes sense Archimedes - King from Syracuse wanted his crown to be solid gold - Is the King’s crown solid gold? - Task: Density and Volume of the crown without damaging the crown and disappointing the King - Measuring volume of crown by submerging the crown in a container of water and figuring out how much the water rises, then finding out the volume of the crown by finding the amount of water displaced by it  “Eureka” Wolfgang Köhler - When the 1st World War broke out, a German Gestalt Psychologist on a Spanish Island had no desire to make his way back to Germany and get involved in the war and therefore he decided he would stay on the island:  Studying animal cognition  Studying insight in chimps - Famous Chimp “Sultan”  get Sultan to solve problems usually involved hanging food up in the air and seeing if Sultan could figure out how to get the food down  One Condition: 2 sticks that would screw together (like a pool cue) to make a long stick to get knock the food down  Second Condition: There were instances where Sultan couldn’t figure out how to get the food down, but there was boxes and then he figured out that by stacking the boxes one on top of the other he could reach the food  Third Condition: Sultan stacked both boxes and used the stick that he screwed together and managed to get even higher to get the food Insight - When we have insight, it is one of the stages of the creative process but there - Insight are sudden, we don’t have an impending sense of them

PSYC 221 Fall Semester 2013 - We don’t know when we’re going to have an insight - “Warmth Rating”  Hold/Cold (getting warmer, oh you’re on fire)  doesn’t work with insight problems because we can’t feel how warm or cold we are to getting an insight - People get self-report while solving problems, to describe if they are feeling like they are getting close to the solution (“Warmer”) E.g. Matchstick Problem  Roman Numerals Equation Insight Problem Example: How can 27 pigs be put into 4 pens so that there is odd number in each pen? - Can’t kill a pig - You’re not thinking about whether you’re getting warmer or colder - You don’t have a sense of when you’re getting close or not - Solution: Set it up so there is 3 pens in 1 pen and put 9 pigs in each of the 3 pens Insight ≠Intuition - Intuition = gut feeling - Intuition does not have any scientifically significant evidence Frontal Cortex is the most important area for problem solving - Frontal cortical area  executive processing, control of cognition, and is the most active when people are solving problems - Phineas Gage  Frontal cortical dysfunction  Railway worker who accidentally had a spike go through his head and frontal cortex  Had a lot of problems after that  difficult for him to solve problems - When people either have damage or a disease (schizophrenia) that disrupts frontal cortical function then you can see lower levels of activation in the frontal cortex when people are solving problems - PET scans show that schizophrenics have little or no activation in the frontal cortical compared to the normal people when solving problems - Studies of Frontal Cortical Activation when problem solving  Tower of London Tower of London Test - When people solve this test, there is an easy version or a hard version - If they need to solve an easy version, there is less activation in the frontal cortex and the parietal cortex, whereas, there is more frontal and parietal cortical activation when solving the harder version Morality and Problem Solving - “Philosophy” - Impersonal versus personal reasoning - Ask ethical questions when subject is in the scanner

PSYC 221 Fall Semester 2013 - “Saving a group by killing one person” - Most people would decide to kill that one person to save four - Impersonal killing versus personal killing (pushing a button versus pushing someone of a bridge)  Different areas of the brain were activated Part V: Problem Solving and Sleep - Thinking about a problem before you go to sleep and then waking up with the solution to the problem (it’s like working on it when you’re sleeping) - REM sleep consolidated learning and memory - Sleep helps to increase the synchrony of temporal lobe processing and hippocampal lobe processing -Experiment: People got better at doing a task with practice  Some people instead of doing additional practice  just went home and got a good night’s sleep  next day, their performance improved  A good night’s sleep got them to improve just as much as an additional practice session  Other people were deprived of sleep (kept them awake or only allowed them to have deep sleep)  performance in task declined - When people are in different sleep states, we can measure using EEG when they are sleeping to identify which sleep state they are in  Deep Sleep = Slow Wave Sleep  REM Sleep = Associated with Dreaming (EEG waves looks quite different when in REM Sleep) - When deprived of REM Sleep people do not perform well in problem solving tasks - REM Sleep is more important than Deep Sleep for problem solving - Sleep aids problem solving  getting ideas when sleeping  Sometimes having to make a decision (hard decisions) make you want to spend a lot of time thinking about it  “Don’t know what to do? Sleep On It”  Does it work?  Sometimes you wake up and you feel like you know what to do  You feel more confident that you know what to do  Sleep helps some people make decisions  Going into more detail next week - Decision-Making - Traps that people fall into when trying to make decisions