Problem Solving and Reasoning

Question 1

Dunker (1926) definition of Problem Solving

Answer 1

A problem arises when a living organism has a goal, but does not know how this goal is to be reached.
Solution is not in memory
Goal directed

Question 2

Mayer (1992) definition of Problem Solving

Answer 2

A sequence of mental processes or operations performed on information in a subject’s memory.
Behaviour due to cognitive processes

Question 3

Tautological Problems

Answer 3

Always true

Question 4

2 Research Methods of Studying Problem solving

Answer 4

• Protocol analysis:
  Ask people how they solve a problem
  Record ‘thinking aloud
• Computer simulations

Question 5

Well-defined Problems

Answer 5

Clear start state, goal state and operators

3x = 6, what is x?
Real world problems messy
Find basic principles from easy tasks
Generalise to complex problems

Question 6

Ill-defined Problems

Answer 6

Lack the qualities of well defined problems
More like real life
Search strategies not used
Harder to theorise about

Question 7

State Space Diagram

Answer 7

Well-defined Problems
No knowledge necessary
Solved quickly
Can be systemically changed
Tower of Hanoi

Question 8

Solving Well-defined problems
1 Prune the state space
2 Exploratory strategies
3 Hill climbing

Answer 8

Prune the state space
- Apply heuristics
Exploratory strategies
 - Weak heuristics e.g. avoid loops
Hill climbing
- Pick a move that takes you closer to goal

Question 9

Means-Ends analysis - Newell & Simon (1972)

Answer 9

ToH can be broken into subgoals
Evaluate task: How do start & goal differ?
Apply operator to reduce difference
If obstacle prevents this – re-evaluate
Create subgoal: remove obstacle
Solve subgoal
Set/solve next subgoal if necessary
HOWEVER: Not all problems have clear subgoals & ID's

Question 10

Problem Solving by Analogy - Mayer (1992)

Answer 10

Analogical reasoning occurs when we abstract a solution strategy from a previous [base] problem and relate that information to a new [target] problem that we are trying to solve. Indeed, we engage in analogical reasoning when we solve a new problem by using what we know about a related problem that we can solve.

Question 11

Isomorphic Problems - Hayes & Simon, 1977

Why is the ToH problem easier to solve than the Monsters and Globes problem? (3 reasons)

Answer 11

1. Harder to learn rules for change problem
   Change rules – 3.5 mins
   Move rules – 1.5 mins
2. Illegal moves not clear for change problem so harder to verify
   Change rules – 5.7 secs
   Move rules – 4.7 secs
3. Rules more consistent with real world knowledge for move problem
   easier to learn
   Easier to spot illegal moves

Question 12

Why does external representation affect the difficulty of problems?

Answer 12

External representation affects difficulty
Changes load on working memory
If WM load is raised…
If options are harder to identify…
…then planning ahead is prevented

Question 13

Duncker’s Radiation Problem can be solved how?

Answer 13

By analogy. Map the features of the fortress story [base] onto this one [target] and infer missing detail.

Question 14

Problem Solving Schemas - Gick & Holyoak (1983)

Answer 14

Crit problem solving by analogy
Schema = abstract description of common features & general principles
Domain specific
Schema make transfer easier
But:
Multiple stories needed to create schema
Target problem must be similar → activation

Question 15

Features of Inductive Reasoning

Answer 15

Inferring rules
Making generalisations
Detecting order out of chaos
Cannot be valid, but can be plausible

Question 16

Features of Deductive Reasoning

Answer 16

An inference that must be true as long as given information is correct
New information is not created

Question 17

Features of Conditional Reasoning

Answer 17

If you are thirsty there is tea in the pot 
There will be tea in the pot anyway!
The rule is expressed as ‘If p then q’
Modus Ponens
Modus Tollens

Question 18

Features of Biconditional reasoning

Answer 18

If you do well, then you will get a prize.
Must use the biconditional interpretation (if and only if) otherwise there is no point to the rule
Affirming the Consequent - e.g. if it rains then i will get wet - There are other events that could make me wet instead of rain
Denying the Antecedent - ‘not raining’

Question 19

Deductive reasoning
Evans (1993) - important for intelligent behaviour
Johnson-Laird (1991) ……?

Answer 19

You need to make deductions in order to formulate plans and to evaluate actions; to determine the consequences of assumptions and hypotheses; to interpret and to formulate instructions, rules and general principles; to pursue arguments and negotiations; to weigh evidence and assess data; to decide between competing theories and to solve problems. A world without deduction would be a world without science, technology, laws, social conventions and cultur

Question 20

Mental Models

Answer 20

Construct a model of a state of the world consistent with the premises
Attempt to form a tentative conclusion
Attempt to build new models that falsify the conclusion
If there is falsification, attempt to find a new conclusion that applies to all models

Question 21

Deduction Rules - Rips (1990)

Answer 21

The mind works with abstract rules of logic in order to make inferences
The abstract logical form of premises etc. is extracted
The relevant rules are chosen
The rules are applied in order to make inferences
The inferences are converted back into their original entities

Question 22

2 problems with theories of deduction

Answer 22

Facilitation (check who is drinking illegally) 
Social contract theory (cheating module in our brain)