1. COMPONENTS OF PROBLEM SOLVING
Evaluation
Representation
Am I making progress?
Should I change strategies?
Have I succeeded?
What is the goal?
What do I already know?
Strategy Selection & Implementation
What skills or strategies do I have available?
Which strategy should I use for this problem?

2. Classic Problems ---------------------------- R O B E R T
D O N A L D G E R A L D
R O B E R T
What are the other letters if D = 5?
Herb Simon, Ph.D.
Professor of Psychology & Computer Science
Carnegie-Mellon University Nobel Prize (Economics) A Founder of Cognitive Science

3. What Do I Already Know That Might Be Relevant?
Classic Problems
D O N A L D G E R A L D
R O B E R T
Good Problem Solvers Ask Themselves:
What Do I Already Know That Might Be Relevant?
4. X + 10 = (& carry 1)
5. A number + itself is an EVEN number
6. EVEN + 1 = ODD
1. D = 5
2. How to add and carry
= 0 ( & carry 1)

4. Classic Problems ---------------------------- R O B E R T
D O N A L D G E R A L D
R O B E R T
What relevant knowledge do
you have?
Can you break the overall task into simpler sub-tasks?
Will it take one strategy or
will you have to shift
strategies along the way?

5. Problem Solving: Where Do Children Go Wrong?
Generating Alternatives
e.g., Piaget’s formal operations tasks
Encoding Relevant Information
e.g., Piaget’s conservation tasks
Monitoring Performance
e.g., evaluation of memory strategies

6. A DEVELOPMENTAL STUDY OF PROBLEM SOLVING
When Weights Are Added to Each Side,
Which Side Goes Down, or Do the Two
Sides Balance?

7. RULES FOR THE BALANCE BEAM SIMPLEST TO MOST COMPLEX
Rule 1: Is the weight the same?
yes = it balances
no = pick side with more weights
Rule 2: Is the weight the same?
yes = then ask if the distance is same
yes = it balances
no = pick side with more distance

8. RULES FOR THE BALANCE BEAM SIMPLEST TO MOST COMPLEX
Rule 3: Is the weight the same?
yes = then ask if the distance is same
yes = it balances
no = pick side with more distance
no = then ask if the distance is the same
yes = pick side with more weight
no = muddle through
Rule 4: use cross products for the “muddle through” cases of Rule 3

9. DEVELOPMENTAL FINDINGS FROM THE BALANCE BEAM PROBLEM
Rule 1: 5 yr olds
only consider weight
Rule 2: 9 yr olds
consider distance info if weight is equal
Rule 3: yr olds
efforts at coordinating info on weight & distance
Rule 4: rare

10. INTERVENTION STUDY ON BALANCE BEAM PROBLEM
Phase 1: Give 5 & 8 yr olds feedback on their predictions
5 yr olds move from Rule 1 to Rule 2
8 yr olds move from Rule 1 to Rule 3
Why????
Phase 2: Ask 5 yr olds to reproduce balance beam configurations (encoding practice)
now 70 % of the 5 yr olds moved from
Rule 1 to Rule 3

11. A DEVELOPMENTAL STUDY OF PLANNING: MEANS-ENDS ANALYSIS
Move the discs from the right side to the left side as shown in the 1st display
Cannot place a larger disc on a smaller disc
Move only one disc at a time

12. DEVELOPMENTAL FINDINGS FROM THE TOWER OF HANOI PROBLEM
Performance success from 3 to 6 yrs
older children can solve problems with more moves
What happens when a child can’t move a disc directly toward the goal
younger children break the rules
older children start to plan moves in advance

13. IMPORTANT PROBLM-SOLVING PROCESSES – CAUSAL INFERENCE
Contiguity
events occur close together in time
and space
Precedence
event labeled “cause” precedes event
labeled “effect”
Covariation
cause and effect consistently occur
together

14. DEVELOPMENTAL FINDINGS CAUSAL INFERENCE
Contiguity
infants in their 1st year already use both
temporal & spatial contiguity to infer causality
Precedence
By age 5 children consistently use the
order of events (A-B-C) to infer cause-effect
Covariation
By age 8 children can use consistent co-
occurrence to infer causality even with a
time delay