1. Thinking & Problem Solving
Thinking: process used to transform or manipulate information
Problem solving: manipulation of data with a specific goal in mind, using a specific solution
Remember that understanding and creating not same thing, may use different mechanisms

2. Studying Problem Solving
Types of problems
Well-defined problems
Ill-defined problems
Well-d : clear goal, small set of info to start with, and sometimes rules
Real-life examples: How to get car to mechanic after an accident
How to earn enough money for down-payment on house
Ill-d : opposite; no goals, no starting info, no steps to take that are clearly spelled out
Complete a perfect paper Or clean the house (could be well defined if limits set) or learn to crochet
Research uses only well-defined b/c
easy to present to subject, take little time, easy to change, easy to score,
We will be talking mostly well-defined problems

3. Studying Problem Solving
Methods
Logic puzzles
Introspection
Researchers often use puzzles to study problem solving
Why use puzzles? What do they have to do with everyday thinking?
Everyday thinking very fast and automatic
We all have different backgrounds, so it’s hard to find an example of everyday thinking (test) that would be equally challenging for everyone
introspection – detailed observation of steps taken as a problem is worked through

4. Classic Problems and Solutions
Generate-and-test technique
Generate-and-test technique
Think of a number of ideas about how to solve problem (generating)
Test each one to see if it works (testing)
(whether it works often depends on rules of the solving process or requirements about goal)
example: you are very sick and need to get to the hospital
Call an ambulance, call police, call a friend, drive yourself, take a bus, take a taxi
One problem with this technique
less effective if it has too many possible solutions; time-consuming, requires a system to keep track of what has been tried, frustrating
Ex. moon puzzle
But is useful if there are not a lot of solutions

5. Classic Problems and Solutions
Means-ends analysis
You start with a current state of something, have in mind the wanted end state (goal)
List possibilities like before, but instead of simply trying them randomly, selection directed by how the solution changes difference b/t start and goal
Poor  I want to have an opulent lifestyle
Med school, getting into med school, finding a job…
Some things may require you to break solution into smaller problems (subgoal)
Directs search for a solution more, but might cause you to overlook a solution,
Get so caught up in a subgoal, take longer to get to goal than another way ?
Current State
Goal

6. Classic Problems and Solutions
Working backwards
Example of working backwards
Start from goal and work backwards
Can have subgoals
Similar problem with my filing cabinet
Usually solver does not make a move and then wait to see what happens
Instead moves are planned ahead of time (solitaire)
Works best when there is only one, unique solution to a problem

7. Classic Problems and Solutions
Backtracking
Think of tree with lots of different choices and subchoices or a maze
I go down one path, see where it leads me (picking most logical one if you can)
If it doesn’t work out, go back up to the point where I could have made another choice and chose something else
It’s like saying to yourself, I don’t know if this is true, but let’s just suppose that is
Process of elimination

8. Classic Problems and Solutions
Backtracking
Five women, with different dogs, diff occupations, and diff # of children
Cathy and irish
Teacher no children
Owner of lab is surgen
Linda not sheepdog
Sonya lawyer
Sheepdog not 3 kids
Retriever 4 kids
Judy 1 kid
Executive retriever
First rec could be debbie or linda

9. Classic Problems and Solutions
Solving by analogy
Not simple blind trial and error
People have to have deeper understanding to solve problem, have to see a pattern/principle/schema
Solve a new problem by finding similar problem and making comparison
Tumor problem
General story of fortress
Two groups read both, but only one told that there was a clue in first story, 75% solved it
Group w/o hint only 10%

10. nine-dot problem six-matches problems
Blocks to Problem Solving
Mental set
Times when you can’t find a solution
Reasons for it
Mental set – tendency to adopt a framework/idea, instead of other possible ones
And when you do, don’t think about other one to solve problems, make assumptions
Only takes a few trials for this effect to set in
nine-dot problem six-matches problems

11. Blocks to Problem Solving
Mental set
Solutions to problems
Error/assumption: going outside “box”
Error: putting them in 2D
Figure (p. 370) Answers to the nine-dot and the six-matches problems.

12. Blocks to Problem Solving
Mental set
Functional
fixedness
String problem.
Two strings, goal to tie together, but not long enough to grab both at same time
On table is screwdriver, pieces of cotton, book of matches,
Solution: use screwdriver as weight

13. The mutilated checkerboard problem.
Blocks to Problem Solving
Incomplete or incorrect representation
Initally misunderstand a problem, or focus on wrong info
Q: can you fit 31 dominoes (fill 2 squares) onto broad (2 cut away)?
64 squares on normal board, this one has 62
A: no, (b/c squares are same color, can’t be near each other
The mutilated checkerboard problem.

14. A tic-tac-toe board representation of the numbers game.
Blocks to Problem Solving
Incomplete or incorrect representation
List of Numbers 1-9, goal to pick three numbers add to 15
Each player crosses off one number at a time to pick it
Now if you had originally seen tictactoe grid it would be easy
Representations were a list of numbers or a board
A tic-tac-toe board representation of the numbers game.

15. Problem Solving Techniques for solving problems
Lack of problem-specific expertise
Chess game, one player playing 4 opponents, all at same time, but his playing ability does not change, weird b/c he’s not allowed any extra time
Player could recognize pattern more quickly than other players
Not that he was better at planning, He had more knowledge than others

16. Problem Solving Techniques for solving problems
Lack of problem-specific expertise
Experts vs. novices
Have more knowledge in that area
Deeper level representation
Check for errors more often
Experts, takes about 10 yrs
Know – expert
Rep - spend more time understanding problem than novices
errors

17. Figure 10-10 A generic problem space.
The Problem Space Hypothesis
Figure A generic problem space.
Every possible state for a situation shown = Circles/nodes
Goal of being rich
Lines = what has to be done to go from one state to another

18. The Problem Space Hypothesis
Path
Not all states will lead to the desired goal
Path – a progression that will lead from start to goal
“good” problem solving finds fastest path

19. The Problem Space Hypothesis
Figure (p. 377) A part of the problem space for the Towers of Hanoi problem, showing the solution.

20. Expert Systems Why bother studying this? Extreme example
Depression = if we understand how people create solutions
goal: pay bills, start: broke, solutions: sleep or find a job
One practical application
We could make machines/systems that replace human experts
Which would be helpful if
Too few experts
Avoid bias/overload

21. Creativity Unconscious processing/ incubation Everyday cognitions
We have been talking about solving problems using step by step methods
But we also sometimes seem to just get a solution out of the blue, aha, eureka
Called insight (Gestalt could be talked about here)
Two ways to think about where it comes from (special process in its own – people can have more or less creativity, like intelligence or
Uses other processes)
Uncon: special process
sleep on it;
Still working on problem even if doing something else
Everyday: For example, many artists do drafts, noticing new mistakes and correcting them

22. Critical Thinking
Critical thinking: looking at solutions and evaluating them`
`to` do a “good” job critically thinking, ````Perkins suggests that person should question solutions