1. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.1 Problem Solving Well-defined versus ill-defined problems Creativity Polya’s stages of problem solving –processes and problems at each stage Improving your problem solving skills

2. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.2 Problem Solving Definition of a problem –goal state differs from initial state –actions are not immediately obvious Well-defined problem –clear goal state –clear initial state –clear set of operations Ill-defined problem –unclear goal –unclear operations –unsure about what is relevant

3. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.3 Problem Solving Creativity –synthesizing novel combinations of ideas –new, more adaptable mental picture of issue –social utility very important The study of genius –many factors divergent thinking intrinsic motivation devotion environment

4. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.4 Polya’s Four Stages of Problem Solving Polya’ terms 1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Looking backwards Information Processing terms 1. Encode problem into working memory 2. Search LTM for plan or relevant information 3. Execute plan 4. Evaluate results

5. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.5 Stage 1 Understanding The Problem Initial representation may be a crucial factor –some problems are trivial to solve in one representation and impossible to solve in another –e.g. which word does not fit –skyscraper, cathedral, temple, prayer Buddhist monk problem Very hard to change from the initial representation

6. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.6 Stage 2 Devise a Plan Many of the problem reflect two general characteristics of human cognition –limited working memory so focus on one view at a time –tendency to go beyond the given implicit inferences activation of inappropriate information from LTM e.g. the nine dot problem

7. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.7 Stage 2 Devise a Plan Three types of rigidity interfere with stage 2 –response set continue to use method that worked in the past Luchin’s problem solving set –perceptual set encode only one perspective (representation) –functional fixedness established use memory interferes with creative use of an object e.g. matchbox problem

8. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.8 Stage 2 Devise a Plan Need search strategies –overall plans and sub goals –overall plan may be too large for working memory Search space –representation of the search –all possible paths to all possible solutions –often represented as a tree diagram Example: Water jug problem –Given 2 jugs one holds 4 gallons the other holds 3 gallons there are no marks on the jugs –Problem: how to get exactly 2 gallons in the 4 gallon jug

9. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.9 Water Jug Search Space 0,0 Initial state 4,00,3 0,04,30,03,04,3 0,3 3,0 4,0 4,2 2,0 3,3 0,2 4,0

10. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.10 Stage 2 Devise a Plan Search strategies –algorithms = step by step procedures that guarantee a solution –heuristics = short cuts, no guarantee, but quicker and more efficient Common types of strategies –generate and test - trial and error –means-ends analysis set up sub goals difference reduction - each step changes only one small differences –hill-climbing - each step move closer not always a good plan e.g. missionaries and cannibals problem

11. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.11 Stage 2 Devise a Plan Protocol analysis –have subject “think out loud” while problem solving –gives information about their initial representation and search strategy –shows where errors turn up One frequent difficulty is in redirecting the search –need to change representation –try new mental operations –Reorganize Incubation helps redirection –very hard to study

12. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.12 Stage 2 Devise a Plan Incubation: three general findings –ONLY after much time and effort are already invested –burst of insight (the “aha!” feeling) –not in final form Five hypotheses about why incubation works –decrease fatigue –forget inappropriate sets and directions –added practice - divided attention with part of your mind still working on the problem –change occurrence of an external event that triggers a new association e.g. waffle iron and running shoes –unconscious processing - run automatized search strategies

13. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.13 Stage 2 Devise a Plan Incubation results in –innovation - synthesis of ideas –insight - pieces come together

14. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.14 Stage 3 and Stage 4 Stage 3: Carry out the plan –get a solution Stage 4: Evaluate the solution –“satisficing” (Simon’s Nobel prize) –humans generally do not maximize or optimize they satisfice –accept solutions that are “good enough” –too many possible solutions to check them all –may be problematic because of differing criteria for “good enough”

15. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.15 Improving Your Problem Solving Try –novel or atypical associations –working backwards –solving a similar but easier problem –diagramming the problem –visualization –brainstorming (withhold evaluation) –analogies –evaluating other people’s solution to other problems read biographies –breaking the problem into sub goals

16. Cognitive - problem_solving.ppt © 2001 Laura Snodgrass, Ph.D.16 Improving Your Problem Solving Techniques for systematizing your search –inferences - what else applies consciously draw as many inferences as possible from the goals, given, and actions –classification of action sequences record all actions tried organize equivalence classes I.e. inverse actions –state evaluation define a “quantitative” evaluation for all momentary outcomes choose actions that have evaluations closest to goals –contradictions derive inferences from the given that are inconsistent with the goal avoid actions that lead to inconsistent subgoals