Chapter 11 Problem Solving and Creativity

Chapter 11Problem 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

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

Each box is labeled incorrectly. You may select one fruit from one box. How can you label each box correctly? Step 3 A&O or O Step 2 A&O or A Step 1 A or O Apples Oranges Apples & Oranges

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: (3x2 + 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

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

Two flagpoles, 150’ high. A 150’ rope suspended from each end reaches 75’ from the ground. How far apart are the flagpoles? Mental Set? 150’ 75’ ?

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 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

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

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 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 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

Chapter 11 Problem Solving and Creativity