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). 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 Goal State Obstacles 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 Students will get this problem wrong if they focus on the math of the problem rather than the meaning of what is said.

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. Students will also get this problem wrong if they focus on the math, rather than a trick. This illustration helps the students to realize how important representing the problem correctly is. It is also an example of a mental set effect.

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   Mango Peach Steak Alex x Jarod Henry

Strategy Formation Divergent thinking (Analysis) Generate multiple solutions to problem Convergent thinking (Synthesis) Narrow down to best answer

Types of Problems Well-structured problems Ill-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?

Working Forward Start at initial state and work to goal state 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

Generate and Test Trial and error strategy 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 If you are connected to the internet, you can click the blue base bar and open a web page that allows you to try the tower of Hanoi game. The website is Mazeworks at http://www.mazeworks.com/hanoi/. You may also watch the computer solve the Tower of Hanoi if you like. 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 Ross, B. H. (1987). This is like that: The use of earlier problems and the separation of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 629-639.

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: (3x2 + 2x = 10)(3x) = ? Clip art image from Microsoft.

Metcalf & Wiebe (1987) Results 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 Figure 11.11 from Sternberg text.

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?

Schooler, Ohlsson & Brooks (1993) 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

Schooler, Ohlsson & Brooks (1993) Results Insight Schooler, Ohlsson & Brooks (1993) Results Performance was decreased in the Insight problem condition when they were forced to use verbal protocol while solving the problems. One interpretation of this study is that the verbal system is not used to solve these types of problems. Thus, participants had to do “extra verbal work” to describe what they were doing, thus leading to a lower success rate in the verbal condition. This is not the case for the logic problems. Participants simply had to state what they were doing, thus it did not interfere.

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 to Problem Solving Mental set Functional fixedness Incorrect or incomplete representation of the problem Lack of domain knowledge

Mental Set Obstacles 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?

Functional Fixedness Obstacles An inability to assign new functions and roles to elements of a problem Two string problem Duncker’s candle problem

Problem I Two strings are suspended from the ceiling 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?

Functional Fixedness? Problem II Materials: Obstacles Problem II Functional Fixedness? Materials: Box of thumb tacks Candle Matches Objective: Mount candle on wall to make light What is the Solution?

Transfer Negative Transfer Positive Transfer Obstacles 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

Water Jugs Jug A Jug B Jug C Goal 21 127 3 100 14 163 25 99 18 43 10 5 Obstacles Jug A Jug B Jug C Goal 21 127 3 100 14 163 25 99 18 43 10 5 9 42 6 21 20 59 4 31 23 49 3 20 14 36 8 6 28 76 3 25

Einstellung phenomena and (or) Negative Transfer 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

Gick & Holyoak (1980) Obstacles Give participants one problem to read, with a solution Then give them a second problem, which can be solved using a similar solution

Gick & Holyoak (1980) 3 groups of participants 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

Gick & Holyoak (1980) Results Obstacles Gick & Holyoak (1980) Results

Transfer Recap Negative Transfer Positive Transfer Obstacles 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

Factors Affecting Use of Analogies 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 participants heard before radiation problem Only 20% got the problem correct 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 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

Chase & Simon (1973) & DeGroot (1965) 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? Check student’s understanding of the graph by having them look at graphs and explain the results found.

Results Expertise 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

Experts Differ From Novices Expertise 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 Are you seeking inspiration for a project? 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.

Psychometric View Creativity Emphasis is on the measure of the product a person creates—creativity test scores Guilford (1950) Torrance (1988)

Breaking Functional Fixedness 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 STOP START

The Process Approach Weisberg (1988) Creativity The Process Approach Weisberg (1988) Nothing innately special about people Hard work and dedication leads to creativity

Personality Approach Baron (1988) Amabile (1996) Creativity Baron (1988) Way of looking at things Amabile (1996) Intrinsic motivation is important

Environment Csikszentmihalyi (1996) Creativity Csikszentmihalyi (1996) Historical and social context critical Contextual balance begets “flow” Flow = enjoyment when absorbed

A Synthesis Gardner (1993) Examined case studies of creative people Creativity Gardner (1993) Examined case studies of creative people Strengths and weakness’ internal and external First became a master, then creative works cameth forth

Sternberg, Kaufman, & Pretz (2002) Creativity 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 Sternberg, R. J., Kaufman, J. C., & Pretz, J. E. (2002). The creativity conundrum. New York: Psychology Press.

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