1. A.P. Psychology - Chapter 8
Problem Solving
A.P. Psychology - Chapter 8

2. Can you solve the following problems:
In the Thompson family there are five brothers, and each brother has one sister. If you count Mrs. Thompson, how many females are in the Thompson family.
Fifteen percent of the people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these can you expect to have unlisted phone numbers?

3. Answers to the Questions
#1  There are 2 females ~ Mrs. Thompson & her one daughter, who is the sister to each of her brothers.
#2  None ~ you won’t find any unlisted phone numbers in the phone book.

4. Types of Problems Problems of Inducing Structure
Require people to discover the relations between
numbers, words, symbols or ideas
Analogy problems
Series completion problems
Problems of Arrangement
Require people to arrange the parts of a problem in a way that satisfies some criterion – usually there are many ways, but only a few form a solution
Problems of Transformation
Require people to carry out a sequence of transformations in order to reach a specific goal

5. Problems of Inducing Structure
What word completes the analogy?
Merchant: Sell :: Customer : ________
Lawyer : Client :: Doctor : __________
What number or letter completes each series? __
A B M C D M __

6. Problems of Arrangement
The String Problem
Two strings have from the ceiling but are too far apart to allow a person to hold one and walk to the other. On the table are a book of matches, a screwdriver, a few pieces of cotton. How could the strings be tied together?
Insight
Sudden discovery of the correct solution following incorrect attempts based primarily on trial & error
Often helps to solve Arrangement Problems

7. Problems of Transformation

9. Barriers to Effective Problem Solving
Irrelevant Information
Many problems include information that is irrelevant to solving the problem
Leads people astray
Functional Fixedness
The tendency to perceive an item only in terms of its most common use
Ex. In the string problem, people see a screwdriver in terms of its most common use, not as a possible weight.
Mental Set
Exists when people persist in using problem-solving strategies that have worked in the past
Unnecessary Constraints

10. Approaches to Problem Solving
Working Backward
Search for Analogies
Forming Sub-goals
Use intermediate steps
Change Representation of the Problem
Change how you see the problem
Algorithms
Methodical, step-by-step procedure for trying all possible alternatives in searching for a solution
Ex. Anagram IHCRA – you would list out all the possible arrangements of the letters
Heuristics
A guiding principle or “rule of thumb” used in solving problems or making decisions

11. Try some more problems The Tower of Hanoi – move rings from peg A to peg C. You can only move the top ring on a peg and you can’t place a larger ring above a smaller one

12. Try some more problems
The water lilies on the surface of a small pond double in area every 24 hours. From the time the first water lily appears until the pond is completely covered takes 60 days. On what day is half of the pond covered with lilies?
A teacher had 23 pupils in his class. All but 7 went on a museum trip and thus were away for the day. How many students remained in class that day?

13. Decision Making
Evaluating alternatives & making choices among those alternatives
Herbert Simon
Theory of Bounded Rationality
People tend to use simple strategies & focus only on a few facets of available options resulting in “irrational” decisions

14. Selecting an Alternative
Elimination by Aspects
Gradually eliminate less attractive alternatives
When any alternative fails to satisfy criterion, it is eliminated
Additive Strategy
List personally important attributes then rate choices based on each

15. Which Strategy Do We Use?
John Payne (1976)
When there are few options with few attributes to evaluate by  additive strategies
More options & more factors  elimination by aspects
We adapt out approach to the demands of the task
Tversky & Shafir (1992)
We delay our decisions when alternatives are not dramatically different
We struggle with conflict & so seek out additional info

16. Risky Decision Making Making choices under conditions of uncertainty
Strategies
Expected value – extrinsic reward
Subjective utility- intrinsic worth
Subjective probability – personal estimates of worth

17. Heuristics in Judgements of Probability
Amos Tversky & Daniel Kahneman
Availability Heuristic
Estimated probability based on the ease with which relevant instances come to mind
EX. Divorce Rate based off of how many of your friends are divorced
Representativeness Heuristic
Estimated probability based on how similar the event is to the typical prototype of that event
EX. Flipping a coin 6 times
1. T T T T T T
2. H T T H T H

19. Pitfalls in Reasoning about Decisions
Law of Small Numbers
Misleading results tend to happen in smaller samples – small samples lead to flukes
Misplaced faith in small numbers explains why people are often willing to draw general conclusions based on a few individual cases
Chance of getting all “heads” flipping a coin 5 times is much better than 100 times
Gamblers Fallacy
Odds of a chance event increase if an event has not happened recently

20. Pitfalls in Reasoning about Decisions
Overestimating the Improbable
Overestimation of the dramatic, vivid – but infrequent events
Confirmation Bias
Seeking info that supports your decisions while ignoring disconfirming info
Belief Perseverance
Hanging onto beliefs in the face of contradictory evidence
Actual Mortality Rates for Causes of Death
Asthma
2,000
Accidental Falls
6,021
Tuberculosis
400
Suicide
11,300
Tornados 25