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?

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

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 3. 5+5 = 0 ( & carry 1)

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?

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

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

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

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

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: 13-17 yr olds efforts at coordinating info on weight & distance Rule 4: rare

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

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

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

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

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