Transcript Sensation and Perception
Chapter 11
Problem Solving and Creativity University of Utah Joel Cooper
Changes to the syllabus
Next Week Chapters 12 and 13 No supplementary readings Following week, Lecture on parapsychology Reading from “why people believe weird things” to be posted online.
Problem Solving
A dealer in antique coins got an offer to buy a beautiful bronze coin. The coin had an emperor’s head on one side and the date 544 B.C. on the other. The dealer examined the coin, but instead of buying it, he called the police. Why?
In 544 B.C. Christ had not been born, so a coin from that time would not be marked "B.C." (before Christ).
More Problems
What is the next letter in the following sequence?
O T T F F S S 1 2 3 4 5 6 7
More Problems
You have 10 red socks and 20 brown socks in your bureau drawer. If you reach into it in the dark, how many socks must you take out to be sure of having a pair that matches?
Problem Solving
Initial State Current situation Define the problem Goal State Desired objective Obstacles Choices made about limitations Strategy choices Limited resources
Problem Representation
The importance of determining what information is relevant and what information is irrelevant is the process of problem representation People pay attention to the wrong information People need to focus on the right information
Sample Problem
15% of the people in Topeka have unlisted numbers. You select 200 names at random from the Topeka phone book. How many of these people will have unlisted numbers?
Did you say 30?
The correct answer is zero
Sample Problem
A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in.
What should have he said? Three. The doorman lets in those who answer with the number of letters in the word the doorman says.
Strategy Formation
Select a strategy to solve the problem Analysis Breaking into sub goals Study for exam sub goals Read textbook & class notes Identify most relevant topics Create study questions & answers on note cards Learn all concepts on note cards Test self with note cards Recycle through learning and testing until mastery is achieved
Strategy Formation
Select a strategy to solve the problem Synthesis Organize to aid solution Symbols Matrixes Diagrams Let L = Lucy, S = Sean, 2L=3S, S=10 Alex Jarod Henry Mango Peach x x 0 0 x x Steak x 0 x
Strategy Formation
Divergent thinking (Analysis) Generate multiple solutions to problem Convergent thinking (Synthesis) Narrow down to best answer
Types of Problems
Well-structured problems Clear path to the solution Math problems Anagrams Ill-structured problems Dimensions of problem are not specified or easy to infer Finding an apartment Writing a book
Methods for Studying Problem Solving
Error analysis or reaction time Global measures of performance Verbal protocols Participants speak their thoughts out loud while solving problems Strategies become evident in protocols Computer simulation Create models that can recreate human data
Strategies to Solve Problems
Algorithms Systematic procedure guaranteed to find a solution Heuristics Useful rule of thumb based on experience Efficient but does not guarantee a correct solution
Heuristics for Problem Solving
Mean-ends analysis Working forward Working backward Generate and test
Heuristics for Problem Solving Mean-ends analysis Working forward Working backward Generate and test
Means-End Analysis
Compare your current state with the goal and choose an action to bring you closer to the goal Break a problem down into smaller sub goals Win at Monopoly You start by buying properties, continue to buy until you get a set, buy houses, then buy hotels, wait for others to land on spaces, etc. May not work if sub goals cannot be identified
Step 3 A&O or O Step 2 A&O or A Step 1 A or O
Apples Oranges Apples & Oranges
Each box is labeled incorrectly. You may select one fruit from one box. How can you label each box correctly?
Heuristics for Problem Solving Mean-ends analysis Working forward Working backward Generate and test
Working Forward
Start at initial state and work to goal state Math problems (2 + 6)/(4 * 1) = ?
Complete the math inside parenthesis first, then divide the quantities to get to solution
Heuristics for Problem Solving Mean-ends analysis Working forward Working backward Generate and test
Working Backward
Figure out the last step needed to reach your goal, then the next-to-the-last step, and so on You have lost your keys Try to remember the last time you used them and work backwards Work backwards from goal state
Heuristics for Problem Solving Mean-ends analysis Working forward Working backward Generate and test
Generate and Test
Trial and error strategy Create possibilities, test them and discard the ones that are incorrect Your car will not start Wait a moment and try again, may be flooded Check to see if there is gas, if no success Check to see if the battery is charged… etc. This may not be the most efficient strategy
Tower of Hanoi
Move all the discs from the left peg to the right one. Only one disc may be moved at a time. A disc can be placed either on an empty peg or on top of a larger disc. The goal is to move all the discs using the smallest number of moves possible
Recognizing the Isomorphic
From variants of the Hobbit/Orc problem, Reed (1987) found that participants have difficulty recognizing that a past problem’s solution will help them to solve the current problem Difficulty in recognizing crucial commonalities Surface features of the problem distract Current research focuses on factors that help the transfer of solutions
Insight and Problem Solving
Insight is the apparent sudden solution to a problem some time after the problem has been presented Metcalfe & Weibe (1987) Participants were given either insight or algebra problems to solve Insight: A prisoner was attempting escape from a tower. He found in his cell a rope which was half long enough to permit him to reach the ground safely. He divided the rope in half and tied the two parts together and escaped. How could this be?
Algebra: (3x 2 + 2x = 10)(3x) = ?
Insight
Metcalf & Wiebe (1987) Results
Participants indicated how close they were to solution every 15 seconds 1 being very cold to 7 being very warm On the insight problem there is a sudden shift in warmth rating On the algebra problem there is a consistent getting warmer pattern
Insight
Gestalt View of Insight
Wertheimer Sudden rearrangement of elements creates “insight” Productive thinking goes beyond previously learned associations Kohler Animal Model of Insight Sultan stacked boxes to get banana
Insight
Current Debate Is insight a special process or just a normal process in problem solving?
Insight
Schooler, Ohlsson & Brooks (1993)
Logic, Insight ≠ Structures Participants solved insight and logic problems Half participants verbalized strategies The control group did not verbalize as they solved the problem
Insight
Schooler, Ohlsson & Brooks (1993) Results
90 80 70 60 50 40 30 20 10 0 Insight Logic Verbal Control
Insight
Incubation
Time away from a problem provides new insights or otherwise facilitates the problem solving process Release from a problem solving set, or functional fixedness Retrieval of new information by changing context Recovery from fatigue
Obstacles
Obstacles to Problem Solving
Mental set Functional fixedness Incorrect or incomplete representation of the problem Lack of domain knowledge
Obstacles
Mental Set
Seeing a problem in a particular way instead of other plausible ways due to experience or context This usually causes you to adopt an ineffective strategy and can prevent problem solving Make assumptions without realizing it Difficult to approach the problem in a new way
Mental Set?
150’ 75’ ?
Two flagpoles, 150’ high. A 150’ rope suspended from each end reaches 75’ from the ground. How far apart are the flagpoles?
Obstacles
Functional Fixedness
An inability to assign new functions and roles to elements of a problem Two string problem Duncker’s candle problem
Obstacles
Problem I
Two strings are suspended from the ceiling Goal : Tie the strings together Problem : Too far apart to hold one and reach for the other Materials : Chair piece of paper pair of pliers What is the Solution ?
Obstacles
Problem II Functional Fixedness?
Materials : Box of thumb tacks Candle Matches Objective : Mount candle on wall to make light What is the Solution ?
Obstacles
Transfer
Negative Transfer Solving prior problem makes it more difficult to solve later problem Positive Transfer Solving earlier problem helps to solve later problem Gick & Holyoak examine factors contributing to positive transfer
Obstacles
Water Jugs
Jug A 21 14 18 9 20 23 14 28 Jug B 127 163 43 42 59 49 36 76 Jug C 3 25 10 6 4 3 8 3 Goal 100 99 5 21 31 20 6 25
Obstacles
Einstellung phenomena and (or) Negative Transfer
Tendency to solve problems in a particular way when a different approach might have been more productive Problems 1-5: B-2C-A Problems 6-8: A-C Problem 8 can’t be solved B-2C-A 80% who see all 8 problems use B-2C-A 1% of controls use B-2C-A 64% fail to solve #8 vs. 5% of controls
Obstacles
Gick & Holyoak (1980)
Give participants one problem to read, with a solution Then give them a second problem, which can be solved using a similar solution
Obstacles
Gick & Holyoak (1980)
3 groups of participants Control group that only tried to solve the radiation problem A group previously given the analogous General/Fortress problem & solution A group given the General/Fortress problem and told that its solution would help in solving the radiation problem
Obstacles
Gick & Holyoak (1980) Results
100 90 80 70 60 50 40 30 20 10 0 Control Analogy Analogy & Hint
Obstacles
Transfer Recap
Negative Transfer Solving prior problem makes it more difficult to solve later problem Positive Transfer Solving earlier problem helps to solve later problem Gick & Holyoak examine factors contributing to positive transfer
Obstacles
Factors Affecting Use of Analogies
Similarity Number of examples exposed to Gick and Holyoak conducted a study in which the dictator story was just one of three other stories before radiation problem Only 20% got the problem correct participants heard Whether schema for problem is activated If the two problems are separated by a delay or if they are presented in different contexts, almost none of the participants use the analogy
Expertise
Expertise
Not a general ability Have an extensive knowledge that they use to organize, represent, and interpret information in their environment This affects their abilities to remember, reason, and solve problems
Expertise
Chase & Simon (1973) & DeGroot (1965)
Participants were chess masters and beginning chess players Studied a chess board that had the pieces randomly displayed or a chess board with pieces in the middle of a game.
Beginners and experts had to recall as many pieces as they could
Expertise Experts vs. Beginners Under what condition did the experts remember more?
Expertise
Results
Master chess players and beginning players recalled a similar number of pieces from the random board Master chess players remember significantly more chess pieces from the game board in play than did the beginning chess players
Expertise
Experts Differ From Novices
Better schemas Well organized knowledge in specific domain Less time to set up problem Select more appropriate strategies Faster at solving problems Are more accurate
Creativity
Process of creating something that is original and worthwhile Multiple views which emphasize The product The person\personality creating the product The creative process; the steps that the creative person followed to create the product The creative environment A synthesis of all of the above
Boost your creativity for inspiring ideas and innovation
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Do you want help 'thinking outside of the box'?
Do you need to get over a creative block?
True creativity seems to happen by itself because it is a product of the unconscious mind, that 'back part' of the mind that incubates ideas until they are ready for the light of day. Hypnosis can help you take your conscious fingers out of the creativity process and leave your unconscious mind to come up with the sorts of ideas, solutions and innovations that it is so good at. Creativity is such a great advantage in all sorts of situations: •for humor in social situations •for innovation in business •for art, music and writing •for originality in public speaking Get the
Creativity Booster
today, sit back, relax, and watch the ideas come flooding in.
Creativity
Psychometric View
Emphasis is on the measure of the product a person creates—creativity test scores Guilford (1950) Torrance (1988)
Creativity
Breaking Functional Fixedness
Coat hanger creativity test You have 2 minutes, write down all possible uses for a coat hanger.
Think outside the box
START
STOP
Creativity The Process Approach Weisberg (1988) Nothing innately special about people Hard work and dedication leads to creativity
Creativity
Personality Approach
Baron (1988) Way of looking at things Amabile (1996) Intrinsic motivation is important
Creativity
Environment
Csikszentmihalyi (1996) Historical and social context critical Contextual balance begets “flow” Flow = enjoyment when absorbed
Creativity
A Synthesis
Gardner (1993) Examined case studies of creative people Strengths and weakness’ internal and external First became a master, then creative works cameth forth
Creativity
Sternberg, Kaufman, & Pretz (2002)
Creativity is not a monolithic ability Confluence of six main resources are necessary for creativity intellectual abilities, knowledge, styles of thinking, personality, motivation, and environment Three intellectual abilities are especially important: Synthetic ability To see problems using novel perspectives and not be bound by conventional thinking Analytic ability To recognize the importance of ideas and focus energy on those worth pursuing Practical-contextual To be able to convey and sell the importance of the ideas to others
How to Improve Your Problem Solving
Follow a systematic plan Draw inferences Develop sub-goals Work backwards Search for contradictions
How to Improve Your Problem Solving
Search for relations among problems Reformulate problems Represent problems graphically Define boundary conditions