Thought and Knowledge Chapter 9 p294-307 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 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 1
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. Buddhist Monk: Graph 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 2
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? 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 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. 3
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 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: 1. You can only move one right at a time 2. You can move only the top ring on a peg 3. You cannot put a larger ring on a smaller ring Task invented in 1883 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 90 th day of the summer, the lake was entirely covered. On what day was the lake half covered? Use working backward heuristic! 4
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 Nine-dot problem: Mental set Connect dots by drawing four continuous straight lines without lifting your pencil from the paper Nine-dot problem: Mental set Answer: 5
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! 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. Coke Beer 17 21 Average correct: 72% Expertise Chess Faster problem solving if expert Baseball Repeat the following exactly: Man on 1 st base with one out hits a ground ball to the short stop who pivots and throws to the 2 nd baseman who catches the ball, pivots and throws to the 1 st baseman. Expert: 6-4-3 double-play, end of inning Both use chunking and schemas to assist memory which helps problem solving 6
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 Decision making Chapter 9 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 7
Decision making Decision making biases (p317) Confirmation bias Belief persistence Heuristics Bias Representativeness heuristic Availability heuristic Anchoring and adjustment Framing effect 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 Availability heuristic Are there more words that have K in the 1 st position or 3 rd position? Availability heuristic How easily examples come to mind Generally correct, but can lead to errors 2 factors influence Recency Familiarity 8
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 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? 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? 9
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) 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 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/ 10
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? 11