PSY 323 – Cognition Chapter 12: Problem Solving

What is a problem? Problem Solving Mental processes that occur when people work toward determining the solution to a problem Problems Math, chemistry, physics problems; Writing a term paper Selecting the movie you want to watch Finding a roommate Finding a solution for a chess problem

Gestalt Approach Representing a problem in the mind Solving a problem involves a reorganization or restructuring of problem representation How people represent a problem matters a lot. Many different ways to solve a crossword puzzle 

Restructuring & Insight Insight problems Those that require Aha! Solutions for insight problems often require gestalt process (re-organizing representation)

Restructuring & Insight Metclafe & Wiebe (1987) Attempted to distinguish between insight and noninsight problems Researchers felt that participants working on insight problems would not be good at predicting how close they were to a solution; noninsight problem solvers would be more methodical and thus better at determining how close they were See next slide 

Example Insight Problems: The Triangle Problem Show how you can move 3 of the circles to get the triangle to point to the bottom of the page Metcalfe & Wiebe (1987)

Example Insight Problems: The Chain Problem A woman has 4 pieces of chain. She wants to join the pieces into a single closed loop of chain. To open a link costs 2 cents and to close a link costs 3 cents. She only has 15 cents. How can she do it? Metcalfe & Wiebe (1987)

Example Noninsight Problems: Algebra! Solve for x: (1/5)x + 10 = 25 Factor 16y^2 - 40yz + 25z^2 Metcalfe & Wiebe (1987)

Studying Insight Two classes of problems: Insight and Non-insight Subjects gave “warmth” ratings every 15 seconds Warmth ratings during the final minute  Metcalfe & Wiebe (1987)

What does this mean? Interpretation Insight problems really do have an “Aha!” moment Instant problem solving Non-insight problems have specific steps to be taken No “Aha!” moment Gradual problem solving

Obstacles to Problem Solving What prevents us from finding a solution? We often get fixated, and keep applying the same approach to solve problems Functional Fixedness Restricting the use of an object to its familiar functions Duncker (1945) Group 1: Presented with small cardboard boxes containing the materials Group 2: Presented with the same materials, but outside the boxes, so the boxes were empty

Functional Fixedness: The Candle Problem You are in a room with a corkboard on the wall. Your task is to mount the candle on the board so it will burn without dripping wax on the floor. Matches in a matchbox Tacks Candles Duncker’s (1945)

Obstacles to Problem Solving Results The group that had been presented with the boxes as containers found the problem more difficult Interpretation Functional fixedness gets in the way of the solving of problems

Obstacles to problem solution… Adamson (1992) Replicated Duncker’s candle problem experiment Group 1: Got the matches in the matchbox Group 2: Got the matches and matchbox separately so matchbox was empty Results 

Obstacles to problem solution… Maier’s (1931) Participants’ task was to tie together two strings that were hanging from the ceiling The strings are separated so that you can’t reach one of them while holding the other. You have a chair and pliers. Two-string problem 

Obstacles to problem solution… Results 60 percent of the participants did not solve the problem When researcher set the string into motion by “accidentally” brushing against it, 23 of 37 participants who hadn’t solved the problem after 10 minutes proceeded to solve it within 60 seconds Interpretation Functional fixedness for the 60% Restructured representation of how to solve problem occurred

Obstacles to problem solution… Mental Set A preconceived notion about how to approach a problem determined by a person’s experience or what has worked in the past

Mental Set: Luchins’ Water Jug Problem Task: Participants given three jugs of different volumes; required to use these jugs to measure out specific amount of water for 8 problems All problems can be solved by B - A - 2C

Solution for Problem 1 A: 21 B: 127. C: 3 Desired: 100 B - A - 2C = Desired Quantity

Problems 7 and 8 All eight problems can be solved as B - A - 2C But problems 7 and 8 can be solved in fewer steps

Mental Set Experiment Procedure Mental set group: Solve problems in order No mental set group: Solve 7 & 8 first Results  Luchins (1942)

Luchins’ Methodology Interpretation The mental set created by solving problems 1 to 6 inhibited them from using the simpler solution for 7 and 8. Luchins (1942)

Problem solving: the information processing approach Newell & Simon (1972) Artificial Intelligence approach Treat problem solving as a search process They used the Tower of Hanoi problem to illustrate 

Newell & Simon (1972) Problem Space

Newell & Simon (1972) Means-end analysis: Reduce the difference between the initial and goal states by reaching sub-goals (intermediate goals).

Importance of how a problem is stated… Problem solving is more than just finding the path to reach a goal How problems are stated and presented affects problem solving a great deal

Restrictions: Goal state Initial state Acrobat Problem Only one acrobat may jump at a time. Whenever two acrobats are on the same flagpole, one must be standing on the shoulders of the other. An acrobat may not jump when some is standing on his or her shoulders. A bigger acrobat may not stand on the shoulders of a smaller acrobat. Goal state Initial state Acrobat Problem Kotovsky et al. (1985)

Importance of how a problem is stated… Results Participants took an average of 5.63 minutes to solve the problem But when the experimenter changed the problem slightly, the problem became much more difficult

Reverse Acrobat Problem Kotovsky et al. (1985)) Restrictions: Only one acrobat may jump at a time. Whenever two acrobats are on the same flagpole, one must be standing on the shoulder of the other. An acrobat may not jump when some is standing on his or her shoulders. A smaller acrobat may not stand on the shoulders of a bigger acrobat. Goal state Initial state Reverse Acrobat Problem Kotovsky et al. (1985))

Reverse Acrobat Problem Interpretation The second problem became much harder because the idea that a smaller acrobat cannot stand on the shoulders of a bigger acrobat is inconsistent with what we know about the world Problem solving is much more than just analyzing problem space Kotovsky et al. (1985)

The Mutilated Checkerboard Problem Task: A checkerboard consists of 64 squares. These 64 squares can be completely covered by placing 32 dominos on the board so each domino covers two squares. If we eliminate two corners of the checkboard, can we cover the remaining squares with 31 dominos? See whether you can solve this problem. A solution would be either a “yes” or “no” answer plus a statement of the rationale behind your answer. Kaplan & Simon (1990)

Kaplan & Simon (1990) tested 4 groups of subjects. Each group received different boards.

The blank board group took much longer and needed many more hints. Results: The bread and butter board group solved the problem fastest and with fewest hints. The blank board group took much longer and needed many more hints. Kaplan & Simon (1990)

Importance of how a problem is stated… Interpretation Participants who were presented boards that emphasized the difference between adjoining squares, found the problem to be easier to solve How a problem is stated is a major determinant related to success Kaplan & Simon (1990)

What does this show? Kaplan & Simon (1990) Used think-aloud protocol to gain a better understanding of what was actually taking place during this experiment Helped them to conclude that the Gestalt idea of restructuring a problem leading to insight took place

Using analogies to solve problems… Analogy The process of noticing connections between similar problems and applying the solution for one problem to other problems Analogical Transfer Transfer of one’s experiences from solving one problem to solving another similar problem

Telling an analogous story The Russian Marriage Problem In a small Russian village, there were 32 bachelors and 32 unmarried women. The matchmaker succeeded in arranging 32 satisfactory marriages. Then one drunken night, two bachelors, in a test of strength, killed each other. Can the matchmaker come up with 31 heterosexual marriages among the 62 survivors?

Experts are good at solving problems… People who, through intensive study, have become acknowledged as being knowledgeable about their field They solve problems in their field better and faster than novices

Experts Possess More Knowledge About Their Fields Chase & Simon (1973) Chess master vs. beginners Memorize chess pieces positioned for a real chess game for 5 seconds Reproduce the arrangement shortly after

Actual Game Random Game Chase & Simon (1973)

(a) The chess master is better at reproducing actual game positions Chase & Simon (1973) (a) The chess master is better at reproducing actual game positions (b) Master’s performance drops to level of beginner when pieces are arranged randomly

Experts Possess More Knowledge About Their Fields Interpretation Chess master did not have a superior STM (as some had suggested); rather he had stored many of the patterns that occur in real chess games in LTM The chess master’s advantage vanished when the board was arranged randomly – familiar patterns were destroyed Chase & Simon (1973)

Experts’ Knowledge is Organized Differently than novices’ Chi et al. (1981) Give 24 physics problems to experts (professors) and novices (students with one semester of physics) Ask each group to organize them See next slide 

Chi et al. (1981): Results Same physics principals Look the same NOVICES EXPERTS Look the same Same physics principals

Experts Spend More Time Analyzing Problems Lesgold (1988) An expert will try to understand the problem and underlying concepts before diving in Example: Drawing a picture before writing equations

Experts Are No Better Outside of their Domain Voss et al. (1983) Gave a problem involving Soviet agriculture to three groups Expert political scientists Novice political scientists Expert chemists Only the expert political scientists solved the problem well

Experts do not always know best Kuhn (1970) Younger scientists are often responsible for revolutionary discoveries Frensch & Sternberg (1989) Experts are worse than novices at situations that require flexible thinking

Divergent Thinking Creativity tests employ divergent thinking Open-ended thinking; no “correct” answer Asking participants to determine as many uses as possible for familiar objects like bricks

Creative Cognition Task Finke (1990) Attempted to train people to think creatively Asked participants to randomly select three object parts

Creative Cognition Task Finke (1990) Preinventive forms were the ideas (“inventions”) that preceded the creation of the finished creative product that participants came up with Example 

Finke (1990): Results A panel of judges rated 360 created objects 120 were rated as “practical inventions” 65 were rated as “creative inventions” Anyone can be creative - you don’t need training or even practice

Credits Some of the slides in this presentation prepared with the assistance of the following web sites: www.tamu.edu/faculty/.../Ch%2012%20Problem%20solving.p... archlab.gmu.edu/people/jthompsz/11-ProblemSolving_1.ppt archlab.gmu.edu/people/jthompsz/11-ProblemSolving_2.ppt