Human Cognitive Processes: psyc 345

Ch. 11: Problem Solving

Takashi Yamauchi© Takashi Yamauchi (Dept. of Psychology, Texas A&M University)

Problem solving

• Mental processes that occur when people work toward determining the solution to a problem.

• Gestalt approach

• Information processing approach

What is 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

• Well-defined problem– Math, physics, or chess problems– You can get clear solutions, and procedures to

reach the solutions. The rule is clear.

• Ill-defined problem– The rule is not clear. Don’t have “correct”

solutions. Problems in everyday situations (e.g., making your own career choice)

Gestalt approach

• How people represent a problem matters a lot.

• Solving a problem involves a reorganization or restructuring of problem representation.

Fig. 11-2, p. 398

Insight problems

• Insight problems:– Those that require Aha! like insights.

– Solutions for insight problems usually occur suddenly.

– Solutions for insight problems often require gestalt process (re-organizing representation)

Fig. 11-3, p. 399

Triangle problem: show how you can move three of the circles (dots) to get the triangle to point to the bottom of the page.

Join the three groups of the chains into a single close loop of chains. Opening a link costs 2 cents and closing a link costs 3 cents. You have only 15 cents.

Fig. 11-4, p. 400

Your assessment of how close you are to a solution

Obstacles to problem solution

• What prevents us from finding a solution?

• Functional fixedness– Focusing on and keep using familiar uses of an

object

Candle problem:

Using the materials shown below (matches in a match box, some tacks), find a way to mount a candle on the corkboard on the wall so it will burn without dripping.

Fig. 11-6, p. 402

Fig. 11-7, p. 402

Tie the strings that are 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.

Fig. 11-8, p. 403

Use jugs A, B, and C and get the quantities suggested in the right column. Try to use jugs no more than necessary.

• Fixation

• We often get fixated, and keep applying the same approach to solve problems.

Problem solving: the information processing approach

• Newell & Simon (1972)

• Artificial Intelligence approach

• Treat problem solving as a search process.

Fig. 11-10, p. 405

Tower of Hanoi problem:

Fig. 11-11, p. 406

Problem Space

Fig. 11-12, p. 407

Means-end analysis:

Reduce the difference between the initial and goal states by reaching sub-goals (intermediate goals).

Problem I

• Drive from College Station to New York City

Constraints

• Time constraint:– have only 5 days

• Economical constraint– spend no more than $500

• Psychological constraints:– have fun. Want to see many cool cities,

beautiful mountains, lakes, villages.

College Station

NYC

Initial state

goal stateSub-goal

Sub-goalSub-goal

• But problem solving is more than just finding the path to reach a goal.

• How problems are stated influence our problem solving a lot.

Initial state Goal state

Restrictions:

1. Only one acrobat may jump at a time.

2. Whenever two acrobats are on the same flagpole, one must be standing on the shoulder of the other.

3. An acrobat may not jump when some is standing on his or her shoulders.

4. A bigger acrobat may not stand on the shoulders of a smaller acrobat.

• 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.

Initial state Goal state

Restrictions:

1. Only one acrobat may jump at a time.

2. Whenever two acrobats are on the same flagpole, one must be standing on the shoulder of the other.

3. An acrobat may not jump when some is standing on his or her shoulders.

4. A smaller acrobat may not stand on the shoulders of a bigger acrobat.

• Implication:

– 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.

Fig. 11-14, p. 410

Checkboard problem:

A checkboard 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?

Yes, or not? Explain why yes / no.

Kaplan & Simon (1990) tested 4 groups of subjects.

Each group received different boards.

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.

• Why?• When a domino is placed on the board, it is

always covering two squares that are different (e.g., black and pink).

• There is no way to place dominos to cover two pink squares or two black squares.

• So, if you remove two pink squares, you can’t cover the board with dominos.

• How problems are stated and presented affects problem solving a great deal.

• Problem solving it is important to state and represent problems in many different ways.