1. Problem Solving EDU 330: Educational Psychology Daniel Moos

2. Problem Solving: Warm-up Activity Problem: There are three hobbits (H), three orcs (O), and one boat (b) on the side of the river: Starting Point: HHH OOO b ------------------------- Goal: To get all three hobbits and all three orcs across the river. Ending Point: ------------------------- HHH OOO b Rules: (1) The orcs and hobbits must travel by boat to the other side of the river (2) The boat cannot hold more than two (3) The orcs cannot outnumber the hobbits at any point (either in the boat or on land)

4. Problem solving: General model 1.Realize the problem exists 2.Understand the nature of the problem 3.Compile relevant information 4.Formulate and carry out a solution (heuristics) 5.Evaluate the solution

5. Problem solving: Definitions (I) Well defined vs. Ill-defined problems Two roads diverged in a yellow wood, And sorry I could not travel both And be one traveler, long I stood And looked down one as far as I could To where it bent in the undergrowth; Then took the other, just as fair, And having perhaps the better claim Because it was grassy and wanted wear, Though as for that the passing there Had worn them really about the same, And both that morning equally lay In leaves no step had trodden black. Oh, I marked the first for another day! Yet knowing how way leads on to way I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I, I took the one less traveled by, And that has made all the difference. Robert Frost 8n + 13 - 3n = -12

6. Problem solving: Expertise (I) AreaExpertsNovices Representing a problem Planning for problem solving Problem solving efficiency See relationships in problems Solve problems quickly, automatically Plan carefully before attempting solutions to unfamiliar problems See problems in isolated pieces Solve problems slowly & focus on mechanics Plan briefly; quickly adopt and try solutions

7. Problem solving: Expertise (II) AreaExpertsNovices Monitoring problem solving Background knowledge Demonstrate well developed metacognition; abandon inefficient strategies Possess a great deal of integrated background knowledge Demonstrate limited metacognition; persevere with unproductive strategies Background knowledge is limited and exists in isolated pieces

8. Problem Solving: Development (1) Learning to follow rules Rule 1 (5 yr olds) Rule 2 (9 years) Rule 3 & 4 (adolescents and UGs) “Rule Assessment”: Cognitive development characterized by acquisition of increasingly powerful rules Rule sophistication increases with age and strategies compete for use at any age  due to reflection?

9. Problem Solving: Development (2) Planning is difficult for younger children Inhibition Inaccurate metacognition Cognitive “cost” Uncertain of accuracy of plan Intrinsic enjoyment of proceeding w/o plan Planning requires exploration of “parameters” before able to plan for solution

10. Problem Solving: Development (3) Analogical Reasoning: Using something you already know to help you understand something you don’t know Relational mapping: Using the relation of A to B to determine relations between C to D Example: Twins: Minnesota :: Yankees: ________ WHY DOES ANALOGICAL REASONING IMPROVE WITH AGE? Increase in content knowledge Language development New York

11. Problem Solving: Development (4) Scientific Reasoning: Generate and systematically test hypotheses; requires evidence to draw conclusion Piaget: Formal operation stage  Late developing skill, and not used spontaneously by many adults Elementary students: Can be trained, but won’t use after training ends

12. Problem Solving: Collaboration Collaborative Problem Solving Examine the developing ability to solve problems with other people and the factors that determine such collaborations Adults are more effective than children (as collaborators)… (1) Type of interaction (e.g., outline goals of the task, discuss strategies) (2) Know more about the content (although not always) What of collaborations between peers? Advantages  Motivate learners to try difficult tasks, fine tune understanding, participate in discussion Disadvantages  Limited ability to ignore distractions, use of language sufficiently to precisely communicate ideas, ability to cooperate

13. Problem solving: Application to the classroom Present problems in real-world contexts Capitalize on social interaction Provide scaffolding for novice problem solvers Teach general problem-solving strategies