Problem Solving
Chapter 12
Some Questions to Consider
What makes a problem hard? Is there anything special about problems that seem to be solved in a ash of insight? How can analogies be used to help solve problems? How do experts in a eld solve problems differently than nonexperts?
What Is a Problem?
Obstacle between a present state and a goal Not immediately obvious how to get around the obstacle
How do we overcome obstacles?
Gestalt Approach
Representing a problem in the mind
Restructuring: changes the problems representation Khlers circle problem Chimps and obstacles to food
Gestalt Approach
Representing a problem in the mind
Restructuring: changes the problems representation Khlers circle problem
The circle problem
Insight in Problem-Solving
Sudden realization of a problems solution Metcalfe and Wiebe (1987)
Insight problems solved suddenly (Aha!) Noninsight problems solved gradually
Think-aloud protocol Say aloud what one is thinking (thoughts, not actions) Shift in how one perceives elements of a problem
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Insight Problems
(a) Triangle problem. (b) Chain problem.
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Insight in Problem-Solving
Metcalfe and Wiebe (1987)
Insight: triangle problem, chain problem Noninsight: algebra Warmth judgments every 15 seconds
Insight problems solved suddenly Noninsight problems solved gradually
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Metcalfe & Wiebe (1987)
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Attach the candle to the wall so it will burn without dripping wax.
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Tie the two strings together
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Obstacles to Problem Solving
Functional xedness: restricting use of an object to its familiar functions
Candle problem: seeing box as a container inhibited using it as a support Two-string problem: function of pliers gets in the way of seeing them as a weight
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Obstacles to Problem Solving
Situationally produced mental set
Situation inuences approach to problem Water-jug problem: given mental set inhibited participants from using simpler solution
Functional xedness: the elevator riddle
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Luchinss (1942) water-jug problem
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Obstacles to Problem Solving
Functional xedness: the elevator riddle: The once was man named Otto. Everyday, Otto rides the elevators from his apartment on the 15th oor to the lobby. But when he returns, he rides the elevator to the 10th oor and then walks to the 15th. But when it rains, he usually rides all the way to the 15th. Why doesnt Otto always ride all the way to the 15th oor?
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Information-Processing Approach
Newell and Simon Problem space
Initial state Intermediate state(s) Goal state
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What Is a Problem?
Well-dened problem: has a correct answer, certain procedures will lead to solution
A small problem space.
Ill-dened problem: path to solution is unclear, no one correct answer
A large problem space.
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A Problem Space
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Eating on the Hill
Crepes Sink Abos Pizza
Sandwiches
French
Delicious Indian
Aion
Gurkhas
E Asian Salvaggios Hapa Mex Pita Deli Zone Burgers Bento Snarfs Kims Pickled Petes Lemon Santiagos You and Mee Half Fast Dots Cheeba Thai Ave Shish Sink Mamacitas Tra Lings Smelly Five Guys Ks Qdoba Jimmy Thunderbird Del Taco Lollicup Johns
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Information-Processing Approach
Tower of Hanoi Operators: actions to go from one state to another.
Governed by rules that specify which moves are allowed and which are not.
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Initial and goal states for the Tower of Hanoi problem.
The operators for the Tower of Hanoi problem.
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Information-Processing Approach
Means-end analysis: reduce differences between initial and goal states
Subgoals: create intermediate states closer to goal
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Initial steps in solving the Tower of Hanoi problem, showing how the problem can be broken down into subgoals.
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The Importance of How a Problem Is Stated...
Acrobat and reverse acrobat problem
One small change in wording of problem Not just analyzing structure of problem space How a problem is stated can affect its difculty
Framing?
Initial
Goal
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Framing
Mutilated-checkerboard problem
Conditions differed in how much information provided about the squares Easier to solve when information is provided that points toward the correct representation of the problem
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Kaplan and Simon (1990)
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Analogy
Using a solution to a similar problem guides solution to new problem
Russian marriage problem (source problem) --> mutilated-checkerboard problem (target problem)
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Using Analogies to Solve a Problem
Gick and Holyoak (1980, 1983)
Noticing relationship Mapping correspondence between source and target Applying mapping
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Using Analogies to Solve a Problem
Dunckers Radiation Problem (1945)
Analogies aid problem solving Often hints must be given to notice connection
Surface features get in the way Structural features must be used
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Using Analogies to Solve a Problem
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3 Steps for analogical problem solving
Noticing that there is an analogous relationship between source story and target story. Mapping the correspondence between target and source stories. Applying the mapping to generate a parallel solution to the target problem
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Using Analogies to Solve a Problem
Lightbulb problem (Holyoak and Koh, 1987)
High surface similarities aid analogical problem solving Making structural features more obvious aids analogical problem solving
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Using Analogies to Solve a Problem
Analogical encoding: comparing two cases that illustrate a principle (Genter & Goldwin-Meadow, 2003)
Effective way to get participants to see structural features that aide problem solving
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Using Analogies to Solve a Problem
Analogical paradox (Kevin Dunbar, 2001)
Participants in experiments focus on surface features People in the real world use structural features
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Analogical Paradox
Dunbar used In vivo problem-solving research to study analogical paradox
People are observed to determine how they solve problems in the real world
Advantage: naturalistic setting Disadvantages: time-consuming, cannot isolate and control variables
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Using Analogies to Solve a Problem
Dunbar found that many groups use deep structural analogies frequently
Molecular biologists Immunologists Engineers
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How Experts Solve Problems
Experts solve problems in their eld faster and with a higher success rate than beginners Experts possess more knowledge about their elds Knowledge is organized so it can be accessed when needed to work on a problem
Novice: surface features Expert: deep structure
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How Experts Solve Problems
Novice Expert
Surface features
Deep structure
(Chi et al., 1981)
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How Experts Solve Problems
Experts spend more time understanding the problem (Lesgold, 1988) Experts are no better than novices when given problems outside of their eld Experts less likely to be open to new ways of looking at problems (e.g., Kuhn, 1970)
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Creative Problem-Solving
Creativity
Innovative thinking Novel ideas New connections between existing ideas
Divergent thinking: open-ended; large number of potential solutions Convergent thinking: one correct answer
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Creative Problem-Solving
Design xation (Jansen & Smith, 1991)
Fixated on what not to do as demonstrated by sample Fixation can inhibit problem-solving
Creative cognition: technique to train people to think creatively (Finke, 1995) Preinventive forms: ideas that precede creation of nished creative product
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Creative Problem-Solving: Preinventive Forms
(R. A. Finke, 1995)
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Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selsh (especially the captain). The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side. If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain. What is the maximum number of coins the captain can keep without risking his life?
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According to the story, fourprisonersare arrested for acrime, but the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are executed. The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats. The prisoners can see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No "communication" between the prisoners is allowed. Then, prisoner C (see image) either calls out the color of his hat, or says he doesn't know what color it is. After this, prisoner B either calls out the color of his hat, or says he doesn't know. Similar for prisoner A. If any of the three prisoners can gure out what color hat he has on his headall four prisoners go free. The puzzle is to nd how the prisoners can escape.
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