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Thought and Knowledge

Thought and Knowledge. Thought and knowledge. Problem solving Goal-directed cognitive activity Start at initial state and aim for goal Active effort to generate solutions Overcome obstacles along the way Decision making Evaluate options Choose between alternatives

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Thought and Knowledge

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  1. Thought and Knowledge

  2. Thought and knowledge • Problem solving • Goal-directed cognitive activity • Start at initial state and aim for goal • Active effort to generate solutions • Overcome obstacles along the way • Decision making • Evaluate options • Choose between alternatives • Learn to problem solve by • Discovery • Memorizing answers • Observing an example

  3. Problem solving • Well defined vs. ill defined problems • Stated goal and clear start/end points? • Understand the problem • Attention to relevant information • Selective attention: what to ignore/attend to? • Problem representation • Understand info given and how it can be used • Ignore irrelevant info • Can use symbols, matrix, tree diagram, graph

  4. Representation: Graph • Buddhist Monk Problem • Exactly at sunrise, a Buddhist monk set out to climb a tall mountain. The narrow path was not more than a foot or 2 wide, and it wound around the mountain to a beautiful, glittering temple at the peak. The monk climbed the path at varying rates of speed. He stopped many times along the way to rest and to eat. He reached the temple just before sunset. At the temple he fasted and meditated for several days. Then he began his journey back along the same path, starting at sunrise, and walking as before at varying speeds with many stops along the way. However his average speed going down the hill was faster than his average climbing speed. • Prove that there must be a spot along the path that the monk will pass on both trips at exactly the same time of day.

  5. Buddhist Monk: Graph

  6. Problem solving strategies • Algorithms • Exhaustive search; step-by-step procedure • Always correct • Heuristics • Selective search; educated guess • “Rule of thumb” • Analogies • Use similar ideas to get solution • Means-end • Goal directed • Use “subproblems” and “subgoals” • Working backward • Start at goal

  7. Algorithm or heuristic Unscramble S P L O Y O C H Y G • Algorithm • 907,208 combinations • Heuristic • Throw out all YY combinations • other heuristics?

  8. Tumor problem • Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. To operate on the patient is impossible, but if the tumor isn’t destroyed the patient will die. A kind of ray, at a sufficiently high intensity, can destroy the tumor. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but will not affect the tumor. How can the rays be used to destroy the tumor without injuring the healthy tissue? • Only 10% of participants solve problem

  9. Tumor problem: Analogy approach • Consider the following information to assist you with the answer for the above problem. A general who hoped to capture a fortress needed a large number of soldiers but all the roads leading to the fortress were planted with mines. Small groups of soldiers could travel to the fortress safely, since the mines would only be detonated by larger groups. By dividing the army into small groups and sending each group by a different path, the general was able to capture the fortress when the small groups converged from all directions onto the fortress.

  10. Tumor problem: Analogy • Mappings • Attack  Radiation • Fortress  Tumor • Attacking troops  Rays • Small bodies of men  Weak rays • Multiple roads  Multiple paths • Destroy villages  Damage healthy tissue • Gick & Holyoak’s (1980) results • Attack  Radiation story • Strong hint 92% correct • No hint 20% correct

  11. Tower of Hanoi: Means-end analysis • http://www.mazeworks.com/hanoi/ • Goal: Move all three rings from the left peg to the right peg: • Rules: • You can only move one right at a time • You can move only the top ring on a peg • You cannot put a larger ring on a smaller ring Task invented in 1883

  12. Water lilies problem • Water lilies are growing on Blue Lake. The water lilies grow rapidly, so that the amount of water surface covered by the lilies doubles every 24 hours. • On the first day of summer, there was just one water lily. On the 90th day of the summer, the lake was entirely covered. On what day was the lake half covered? • Use “working backward” heuristic!

  13. Influencing factors and bias • Mental set • Tendency to rely on particular strategy • Functional fixedness • Tendency to use objects in typical ways • Some problems require restructuring • Think “outside the box” • Familiarity • Restructure problem so familiar • Expertise • Use knowledge to assist problem solving

  14. Nine-dot problem: Mental set • Connect dots by drawing four continuous straight lines without lifting your pencil from the paper

  15. Nine-dot problem: Mental set Answer:

  16. Mair’s 2-string problem • Goal: tie strings together • Obstacle: strings too far apart to reach • Can use other objects in the room (paper, nails, chair, pliers) • Functional fixedness: break out of typical ideas!

  17. Coke Beer 17 21 Card trick: Familiarity • The cards have information about four people sitting at a table. One side of the card is a person’s age and on the other side of the card is what the person is drinking. The rule is that if a person is drinking beer, then the person must be over 21 years old. Select the fewest cards you have to turn over to determine if the rule is violated. • Average correct: 72%

  18. Expertise • Chess • Faster problem solving if expert • Baseball • Repeat the following exactly: • Man on 1st base with one out hits a ground ball to the short stop who pivots and throws to the 2nd baseman who catches the ball, pivots and throws to the 1st baseman. • Expert: 6-4-3 double-play, end of inning • Both use chunking and schemas to assist memory which helps problem solving

  19. Problem solving: Influencing factors • Insight • Aha! Moment • Continuous vs. discontinuous debate • Influence of right hemisphere? • Incubation • Set problem aside • Allow unconscious influence to help • Relax mental set

  20. Decision making Chapter 9

  21. Thought and knowledge • Problem solving • Goal-directed cognitive activity • Start at initial state and aim for goal • Active effort to generate solutions • Overcome obstacles along the way • Decision making • Evaluate options • Choose between alternatives

  22. Decision making • Decision making biases (p317) • Confirmation bias • Selective inattention • Belief persistence • Heuristics  Bias • Representativeness heuristic • Availability heuristic • Anchoring and adjustment • Framing effect

  23. Representativeness heuristic • Which outcome is more likely? • THHTHT or HHHTTT • Decision based on comparison to ideal • Heuristics can be helpful • But, can also lead to incorrect decisions! • Conjunction errors • “Linda is a bank teller and a feminist.” • Influence of stereotypes as heuristics

  24. Availability heuristic • Are there more words that have K in the 1st position or 3rd position? • Availability heuristic • How easily examples come to mind • Generally correct, but can lead to errors • 2 factors influence • Recency • Familiarity

  25. Anchoring and adjustment • Multiplication problem • A: 8x7x6x5x4x3x2x1 • B: 1x2x3x4x5x6x7x8 • Results: • A grp median: 2,250 • B grp median: 512 • Correct answer: 40,320 • Anchor: begin with first approximation • Adjustment: changes based on added info • Real world application • First impressions

  26. Decision making • Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two programs have been proposed. • Opt A: 200 people will be saved • Opt B: 1/3 probability that 600 will be saved, but 2/3 probability that no one will be saved • Which program do you favor?

  27. Decision making • Imagine that the US is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. • What if 2 different programs are proposed • Opt. C: 400 people will die • Opt D: 1/3 probability that nobody will die and 2/3 probability that 600 will die • Which program do you favor?

  28. Framing effect • Tversky & Kahneman (1981) • Identical deep structures (A/B vs. C/D) • A vs. B: focus on lives “saved” • 72% chose A: “risk averse” • C vs. D: focus on number of deaths • 22% chose C: “risk taking” • Framing: Subtle changes can change decision • Advertisement: 80% lean or 20% fat? • Physician choices (p 316)

  29. Why are we imperfect? • Why use heuristics? • Less effort • Economical • Faster to answer • Usually correct • Effective • Reduce errors • Approximation • Examples/Problems purposefully created to create “errors” • Help us understand cognitive process

  30. Thought paper • TV show: Deal or no deal? • How does each heuristic influence play? • Representativeness heuristic • Availability heuristic • Anchoring and adjustment • Framing effect http://www.nbc.com/Deal_or_No_Deal/game/

  31. Review: Problem solving & decision making • What are problem solving and decision making? • How do we represent information? • Strategies? Pros and cons of each? • What are some typical problems? • What are the factors that influence problem solving? • What factors bias decision making? • Why do we use heuristics?

  32. Extra slides

  33. Checkerboard: Framing • A checkerboard that has two diagonally opposite corners cut off is left with 62 squares. If you have 31 dominos, each capable of covering 2 squares on the checkerboard, can the dominos be arranged so that they cover the whole board? • Is it possible to cover 31 black and 31 white squares on the board with the 31 dominos?

  34. Checkerboard: Framing • Answer: No, because 2 of the squares have been removed, leaving 30 of 1 color and 32 of the other. • Changing the wording changes the way you think of the problem!

  35. A 4 D 7 Card trick • You have 4 cards in front of you. From left to right they are labeled: A, 4, D, 7. If a card has a vowel on one side then it has an even number on the other side. How many cards do you have to turn over to find out whether or not the rule is ever violated? • Average correct: 15% • Heuristic: a guess - a simple rule – a shortcut

  36. Problems:Working backward • Flip it or Dip it • In the game, 3 people flip coins. One person loses and 2 people win each game. The one who loses must double the amount of money that each of the other 2 players has at the time. The 3 players agree to play 3 games. At the end, each has lost 1 game, and each has $8. How much $ did each start out with? • * = loser

  37. Thought paper • Work on more problems at home: • Did you use different methods to represent the problems? • What difficulties did you encounter? • How did you overcome the barriers to solve the problem? • HOW can you use this problem-solving information for real-life problems??

  38. From the last class… • The rules for combining sounds to make words are called: _____________. • With respect to spoken language, semantics refers to: _____________ . • The deep structure of a sentence refers to: ________________ . • According to the linguistic relativity hypothesis, language: • A. shapes how we think and perceive the world • B. shapes the way we think but not our perceptions of the world • C. shapes our perceptions of the world, but not the way we think • D. has only a minimal influence on thought processes and perception

  39. Decision making • A nearby town is served by 2 hospitals. About 45 babies are born each day in the larger hospital. About 15 babies are born each day in the smaller hospital. Approximately 50% of all babies are boys. However, the exact percentage of babies who are boys will vary from day to day. Some days it may be higher than 50%, some days lower. For a period of 1 year, both the larger and smaller hospital recorded the number of days on which more than 60% of babies born were boys. Which hospital do you think recorded more such days? • Larger hospital • Smaller hospital • About the same (within 5% of each other)

  40. Representation • Mary is 10 years younger than twice Susan’s age. Five years from now, Mary will be eight years older than Susan’s age at that time. • How old are Mary and Susan? • Representation: ??? • Answer: ???

  41. Representation: Symbol • Mary is 10 years younger than twice Susan’s age. Five years from now, Mary will be eight years older than Susan’s age at that time. • How old are Mary and Susan? • Representation: Use symbols = aka algebra! • M = 2S – 10 • M + 5 = S + 5 + 8 • 2s – 10 + 5 = s + 5 + 8 • 2s – 5 = s + 13 • 2s = s + 18 • S = 18 • M = 18 * 2 = 36 – 10 = 26 • 18 + 5 = 23 • 26 + 5 = 31

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