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Thinking Overview Thinking Concepts Solving Problems Making Decisions and Forming Judgments The limits of everyday intuition are easily demonstrated in class. For example, Shane Frederick (cited by Kahneman, 2003) suggests a simple puzzle: “A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?” Most people report an initial tendency to answer “10 cents” because the sum $1.10 separates easily into $1 and 10 cents and because 10 cents is about the right magnitude. Frederick reported that 50 percent of Princeton students and 56 percent of University of Michigan students gave this wrong answer. Simple subtraction convinces students of their error: $1.00 for the bat – $0.10 for the ball = $0.90, not $1.00. The correct answer is $1.05 for the bat, $0.05 for the ball. Or, present the classic “horse-trading” problem. A man bought a horse for $60 and sold it for $70. Then he bought the same horse back for $80 and again sold it, for $90. How much money did he make in the horse business? Although the problem seems simple enough, most American college students answer incorrectly. David Myers reports that even most German banking executives get it wrong. The most common answer is $10. Respondents apparently reason that when the man buys the horse back for $80 he lost the $10 he made in the original deal. The man actually made $20. You can show this by comparing the total amount paid out ($140) with the total amount taken in ($160). Alternatively, present the problem in modified form. Instead of having the man buy the horse back for $80, state that he bought firewood for $80 and then sold it for $90. The problem suddenly becomes easier. You can also use this manipulation to introduce the importance of framing discussed later in the module. (Bolt) Module 23 02 21 13

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Thinking Module 23 Online link
Our brains reached full size about 300,000 years ago. Art, tool making etc. appeared only about 75,000 years ago. Vilayanur S. Ramachandran The Tell Tale Brain pg. 118 Earliest tools. Oldowan, about 2.4million years ago. Vilayanur S. Ramachandran The Tell Tale Brain pg. 119 The Thinker is a bronze and marble sculpture by Auguste Rodin, whose first cast, of 1902, is now in the Muse Rodin in Paris; there are some twenty other original castings as well as various other versions, studies, and posthumous castings. It depicts a man in sober meditation battling with a powerful internal struggle.[1] It is often used to represent philosophy. Look for Whorf Hypothesis labs or activities. Module Thinking Overview Thinking Concepts Solving Problems
Making Decisions and Forming Judgments The limits of everyday intuition are easily demonstrated in class. For example, Shane Frederick (cited by Kahneman, 2003) suggests a simple puzzle: A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost? Most people report an initial tendency to answer 10 cents because the sum $1.10 separates easily into $1 and 10 cents and because 10 cents is about the right magnitude. Frederick reported that 50 percent of Princeton students and 56 percent of University of Michigan students gave this wrong answer. Simple subtraction convinces students of their error: $1.00 for the bat $0.10 for the ball = $0.90, not $1.00. The correct answer is $1.05 for the bat, $0.05 for the ball. Or, present the classic horse-trading problem. A man bought a horse for $60 and sold it for $70. Then he bought the same horse back for $80 and again sold it, for $90. How much money did he make in the horse business? Although the problem seems simple enough, most American college students answer incorrectly. David Myers reports that even most German banking executives get it wrong. The most common answer is $10. Respondents apparently reason that when the man buys the horse back for $80 he lost the $10 he made in the original deal. The man actually made $20. You can show this by comparing the total amount paid out ($140) with the total amount taken in ($160). Alternatively, present the problem in modified form. Instead of having the man buy the horse back for $80, state that he bought firewood for $80 and then sold it for $90. The problem suddenly becomes easier. You can also use this manipulation to introduce the importance of framing discussed later in the module. (Bolt) Module Thinking Cognition Cognitive Psychologists
mental activities associated with thinking, knowing, remembering, and communicating Cognitive Psychologists study these mental activities concept formation problem solving decision making judgment formation From Lahey 9e Cognition is active Information is Obtained through senses Transformed through interpretive processes Stored and retrieved through memory Used in problem solving and language 65. In studying the behavior of five year olds in free-play situations, a cognitive psychologist would be most interested in the childrens (AP12) A. problem solving strategies B. toy preferences C. degree of cooperative behavior D. prosocial play activities E. choice of playmates The stage had now been set for people to consider the physical brain as having a relationship with perception. In 1886, years after both Weber and Miller had died, an American named James McKeen Cattell published a paper entitled "The time taken up by cerebral operations."9 The punch line of his paper was deceptively simple: how quickly you can react to a question depends on the type of thinking you have to do. If you simply have to respond that you've seen a flash or a bang, you can do so quite rapidly (190 milliseconds for flashes and 160 milliseconds for bangs). But if you have to make a choice ("tell me whether you saw a red flash or a green flash"), it takes some tens of milliseconds longer. And if you have to name what you just saw ("I saw a blue flash"), it takes longer still. From Incognito: The Secret Lives of the Brain, David Eagleman Module Thinking Concept Prototype
mental grouping of similar objects, events, ideas, or people Prototype mental image or best example of a category matching new items to the prototype provides a quick and easy method for including items in a category (as when comparing feathered creatures to a prototypical bird, such as a robin) We form some concepts with definitions. For example, a triangle has three sides. Mostly, we form concepts with mental images or typical examples (prototypes). For example, a robin is a prototype of a bird, but a penguin is not. Incorporates all the features we associate with a category (Rosch 1978) We recognize things closer to prototypes more quickly A prototype is best defined as (AP94) (A) An example of habituation (B) An example of bottom-up processing (C) The equivalent of feature abstraction (D) The hypothetical "most typical" instance of a category (E) An essential element of category membership Module In Class Exercise on Prototypes
Classroom Exercise: Introducing Prototypes Betsy Decyk has devised an exercise for introducing prototypes. Tell your students that even though you have known most of them for only a short time, you already know much about what and how they think. Have them take out a piece of paper and respond to the categories you are about to list with the very first example that comes to mind. 1. a bird 2. a color 3. a triangle (drawing a picture is just fine) 4. a motor vehicle 5. a sentence 6. a hero 7. a heroic action 8. a game 9. a philosopher 10. a writer After students have finished, say that you will predict many, if not most, of their answers even before they reveal them. Give the following: 1. a robin, sparrow, or eagle 2. red or blue 3. a picture of an equilateral triangle 4. a car 5. a short declarative statement, e.g., The boy ran home. 6. Superman, Batman, or possibly a fireman 7. a single act by a male, e.g. a rescue by a fireman 8. Socrates or Aristotle 9. monopoly or some other board game 10. Stephen King, or some other white male author Module Triangle (definition) Bird (mental image)
We form some concepts with definitions. For example, a triangle has three sides. Mostly, we form concepts with mental images or typical examples (prototypes). For example, a robin is a prototype of a bird, but a penguin is not. Explain that we tend to think in terms of the best example of a category, or prototype. Within a given culture, there tends to be considerable agreement, in fact near consensus, on some prototypes. However, they may vary across cultures. As Diane Halpern explains, if you live in Australia, you might name kiwi as a bird, most Russians would probably name Pushkin, Tolstoy, or Chekhov as an example of a writer. Decyk, B. N. (1994). Using examples to teach concepts. In D. F. Halpern (Ed.), Changing college classrooms: New teaching and learning strategies for an increasingly complex world (pp. 3963). San Francisco: Jossey-Bass. Halpern, D. (2003). Thought and knowledge (4th ed.). Mahwah, NJ: Lawrence Erlbaum. J. Messerschmidt/ The Picture Cube Daniel J. Cox/ Getty Images Triangle (definition) Bird (mental image) Module We organize concepts into category hierarchies.
To demonstrate the most popular method for measuring cognitive complexity, have your students think of a person they like and a person they dislike, then take a total of 10 minutes to write descriptions of these people. They should pay special attention to the persons habits, beliefs, ways of treating others, mannerisms, and similar attributesany aspect of the persons personality or behavior but not physical characteristics. Finally, they should add the total number of different constructs they used for the two descriptions. With this technique, researchers typically obtain a wide variation of scores from college students. In one study the scores ranged from 5 to 43, with a mean of 16. What difference does cognitive complexity make? Jerry Burger describes a number of implications. For example, among politicians and world leaders, cognitive complexity has been related to political ideology. In describing the issues of the day, conservative U.S. senators make significantly fewer complex statements than do moderate and liberal senators. Among members of the British House of Commons, extremists from either side tend to see things in the simplest manner. A cognitively complex person is also better able to take the perspective of others, that is, to see the world through their eyes. Research also suggests that cognitively complex people are more persuasive than those low on this variable. They seem to match their arguments to the audience they are trying to persuade. Finally, people who are high in cognitive complexity are better able to deal with ambiguity. Because they are better able to make sense of events in their world, they are less likely to become anxious when confronted with unexpected or unstructured situations. Burger, J. (2004). Personality (6th ed.). Belmont, CA: Wadsworth. From Bolt, build lab for this. Courtesy of Christine Brune Module Categories Once we place an item in a category, our memory shifts toward the category prototype. Tell the students that Jesus was Asian, it will blow their minds because it is so opposite their prototype of Jesus. Yes, um.the middle east is in Asia. Courtesy of Oliver Corneille A computer generated face that was 70 percent Caucasian led people to classify it as Caucasian. Module Problem solving strategies include:
Preview Question 2: What strategies do we use to solve problems, and what obstacles hinder our problem solving? Trial and error is straightforward Boys tendency to rely on more flexible problem-solving approaches doesn't just occur at the high school level; it happens as early as elementary school. Despite the fact that there are not usually sex differences in mathematical achievement in the early grades, observation of classroom behavior shows that girls are more likely to use standard calculation procedures for arithmetic whereas boys often take more flexible, unconventional problem-solving approaches. For example, when asked to calculate , girls are more likely, in a step-by-step fashion, to first add the ones digits, 8 and 6, get 14, carry the 1, add that to the tens digits 3 and 2, and end up at 64. Boys, on the other hand, might decide that 30 and 20 is 50, and 8 makes 58; then 6 more is Where do these strategy differences come from? In another study, when third- and fourth-grade students were interviewed about how they could solve arithmetic problems like those above, everyone reported that they knew about both the standard and unconventional problem-solving methods, but only the boys actually used the unconventional approaches. From Choke: What the Secrets of the Brain Reveal About Getting It Right When You Have To Trial and Error Algorithms Heuristics Insight Module Thinking Algorithm methodical, logical rule or procedure that guarantees solving a particular problem contrasts with the usually speedierbut also more error-prone--use of heuristics Check every product in the supermarket until you find guava juiceslow, but eventually you will find it. Module S P L O Y O C H Y G Algorithms
Algorithms, which are very time consuming, exhaust all possibilities before arriving at a solution. Computers use algorithms. Heuristicthrow out all YY combinations Processing every possible combination of the letters DBRI to arrive at the word BIRD is an example of the use of (AP99) (A) An algorithm (B) An expert system (C) An inference rule (D) A hypothesis (E) A heuristic S P L O Y O C H Y G If we were to unscramble these letters to form a word using an algorithmic approach, we would face 907,200 possibilities. Module Heuristics with the psych files 15:12
Heuristics are mental shortcuts that allow us to make judgments and solve problems efficiently. Heuristics are less time consuming, but more error-prone than algorithms. Heuristics with the psych files 15:12 Look for guava juice in the juice isle or ethnic food sectionmay find it quicker, may not find it at all. The practice of solving problems by using a mental shortcut is an example of (AP04) (A) An insightful operation (B) A confirmation bias (C) A hypothesis test (D) The use of a heuristic (E) The use of an algorithm 83. Mental shortcuts or rules of thumb that help solve problems and reduce mental effort are called (AP12) A. heuristics B. algorithms C. syllogisms D. propositions E. concepts B2M Productions/Digital Version/Getty Images Module Put a Y at the end, and see if the word
Heuristics Heuristics make it easier for us to use simple principles to arrive at solutions to problems. S P L O Y O C H Y G S P L O Y O C H G Y P S L O Y O C H G Y P S Y C H O L O G Y Put a Y at the end, and see if the word begins to make sense. Module Insight Insight involves a sudden novel realization of a solution to a problem. Humans and animals have insight. Chimp Problem solving: Grande using boxes to obtain food Module Try to connect these dots with three lines, without lifting your pencil from the paper or retracing any of the lines you draw. You must also end the drawing where you began it. You can take up to three minutes. Try to connect these dots with three lines, without lifting your pencil from the paper or retracing any of the lines you draw. You must also end the drawing where you began it. You can take up to three minutes. Have you finished? If you haven't, fear not; you're far from being alone. In fact, you're like 78 percent of study participants who were given the problem to solve. If you have, how long did it take you? Consider this: if I had turned on a light bulb in your line of sight while you were working on the problem, you would have been more likely to solve it if you hadn't solved it already, a full 44 percent of people who saw a lit light bulb solved the puzzle, as contrasted with the 22 percent in the original condition (the one that you just experienced) and you would have solved it faster than you might have otherwise. The bulb will have activated insight-related concepts in your mind, and in so doing will have primed your mind to think in a more creative fashion than it would as a matter of course. It is an example of priming in action. Because we associate the light bulb with creativity and insight, we are more likely to persist at difficult problems and to think in a creative, nonlinear fashion when we see it turn on. All of the concepts that are stored in our attic next to the idea of "light bulb moment" or "insight" or "eureka" become activated, and that activation in turn helps us become more creative in our own approaches. By the way, here's the solution to the dot problem. Our natural mindset may well be holding us back, but a simple prime is enough to cue it in a very different direction indeed. Works of art on the walls do the trick, too. The color blue. Pictures of famous creative thinkers. Happy faces. Happy music. (in fact almost all positive cues.) Plants and flowers and scenes of nature. All of these tend to boost our creativity with or without our awareness. That's cause for celebration. Whatever the stimulus, as soon as your mind begins to reflect on the idea, you become more likely to embody that very idea. There are even studies that show that wearing a white coat will make you more likely to think in scientific terms and be better at solving problems the coat likely activates the concept of researchers and doctors, and you begin to take on the characteristics you associate with those people. From Mastermind: How to Think Like Sherlock Holmes by Maria Konnikova Module Before class, carefully draw the following figures on the chalkboard:
Classroom Exercise: The Aha! Experience Michael Wertheimer describes a classroom activity that is intended to demonstrate the Aha! experience of achieving insight. The exercise involves the presentation of a series of brain teasers that begins with the call for simple reorganization of perceptions and proceeds to the demand for the more challenging restructuring of abstract problems. Before class, carefully draw the following figures on the chalkboard: Source: Wertheimer, M. (1999). Reorganization and productive thinking. In L. T. Benjamin et al. (Eds.), Activities handbook for the teaching of psychology (Vol. 4, pp. 218219). Washington, DC: American Psychological Association. Explain to your class that in solving problems, the pieces sometimes suddenly fall together and we perceive the solution. A reorganization or restructuring of perception produces the aha! experience we call insight. For example, the first line drawing might be viewed as a side view of a squinting face. But you can reorganize it into a soldier and a dog passing an archway; the mouth becomes the dogs tail and the squinting eye a rifle with a bayonet. Similarly, the second figure may first appear to be a ghoul looking over a fence and a couple of ears sticking up over a fence. But with restructuring we may see a custodian cleaning mud off the floor (the ghouls eyes become the soles of the janitors shoes, and the ears become the sides of a bucket). Module Chimp behavior showed a cognitive trial- and-error process rather than an actual one; they were solving the problem in their minds first, and only after an insight (the "aha" moment) tried out their solution. This is contrary to the behaviorist view that learning is conditioned by response to a stimulus, and reinforced by reward. The chimps learned by perceiving the problem, not by receiving rewards. This was a demonstration of Kohler's dynamic model of behavior, involving organization within perception, rather than passive learning through response to rewards. From all about psych-I think Module Insight (it can be seen in the brain before you are conscious of it)
Brain imaging and EEG studies suggest that when an insight strikes (the Aha experience), it activates the right temporal cortex (Jung-Beeman & others, 2004). The time between not knowing the solution and responding is about 0.3 seconds. Responding by pushing a button Because the problem required both speed and concentration, the scientists reasoned that the solution for those who solved it would likely pop as a sudden insight. The EEG readings confirmed this. They showed different results between those who solved the problem and those who could not. And better yet, just a second or two before the reported insight occurred, there appeared to be consistently identifiable brainwave activity. More interesting, the EEG readings allowed researchers to predict an aha! moment up to eight seconds in advance, because increased activity in the right frontal cortex associated with shifting mental states announced it. These researchers also found that a positive mood assists insight. In a related study, the researchers gave twenty-one subjects three words, such as head, shade, and post. They were to think of one word (lamp) that would make a compound word with all three, while hooked to an EEG monitor. Mental blocks correlated with high gamma activity in the parietal cortex, which is associated with selective attention. For those subjects with the highest gamma readings, even clues failed to move them toward a solution, suggesting that a mental fixation can block insight. They were mentally clenched, like a fist. Those who experienced sudden insight showed a drop in gamma activity levels just before they reported the insight, but there was no such drop during conventional problem-solving strategy. Theta waves, which assist the brain to encode new information, increased before an aha! moment. The researchers believed that the brain was forming new associations from whatever information it had. In SNAP: Seizing Your Aha! Moments by Katherine Ramsland From Mark Jung-Beekman, Northwestern University and John Kounios, Drexel University Module Thought Puzzle #1 Predict the next number in this sequence.
In your notes, write down your thought process. Include any dead ends. Dont talk about your process or your answer so that everyone can work on the puzzle. Sequence ____ Mental Set Tendency to approach a problem in a particular way especially a way that has been successful in the past but may or may not be helpful in solving a new problem. Module Thought Puzzle #1 Sequence 8 5 9 1 7 2 ____
____ Now think about the words rather than the numbers EightFiveNineOneSevenTwo _____ Alphabetical order Do problem solving activity. Module Thought Puzzle #1 What got in the way of solving this problem?
Mental Set - Old pattern of problem solving is applied to a new problem. Functional Fixedness A tendency to think about familiar objects in familiar ways which may prevent more creative use of those objects to solve the problem. A teacher asks students to think of as many uses for a brick as possible. By listing 50 uses, most of which the class finds new and unusual, Susan is displaying (AP94) (A) Computational learning (B) paired-associate learning (C) Hypothetical thinking (D) Divergent thinking (E) Convergent thinking Module Functional Fixedness A tendency to think only of the familiar functions of an object. 100. Failure to recognize that an object typically not used for a particular purpose can, in fact, serve that purpose illustrates which of the following? (AP12) A. Schema B. Functional fixedness C. availability D. insight E. Confirmation Bias their ability to think about information in new and unusual ways can actually be hampered when they wield too much brainpower. This seems to be even more true the more you know about a given subject. When people with lots of baseball knowledge, for example, are asked to come up with a word that forms a compound word with plate, broken and shot, they are pretty bad at this task. Baseball fanatics want to say the word is home (home-plate, broken-home, home-shot?!). This isnt correct. The real answer is glass (glass-plate, broken-glass, shot-glass). What's interesting is that baseball fans who also have a lot of cognitive horse-power relative to their peers-those higher-working-memory baseball fans---are the ones most likely to dwell on the wrong baseball-related answer. Its as if these guys (and girls) are too good at focusing their attention on the wrong baseball information. As a result, they have trouble breaking free of their knowledge and coming up with the correct answer that has nothing to do with baseball. Baseball fanatics high in working-memory have problems thinking outside their base-ball box. From Choke, WHAT THE SECRETS OF THE BRAIN REVEAL ABOUT GETTING IT RIGHT WHEN YOU HAVE TO, SIAN BEILOCK ? Problem: Tie the two ropes together. Use a screw driver, cotton balls and a matchbox. Module Thought Puzzle #2 Connect the dots with no more than 4 straight lines without lifting your pen.
* Module Thought Puzzle #2 Connect the dots with no more than 4 straight lines without lifting your pen.
* Module Thought Puzzle #2 Connect the dots with no more than 4 straight lines without lifting your pen.
Many people suffer from the Mental Set which states that they must stay within the square defined by the dots. Functional Fixedness keeps most people in a connect the dots mode. Module Figure 8.7: Applying a Mental Model
What path will the marble follow when it leaves the curved tube? Classroom Exercise: Dice Games to Demonstrate Problem Solving G. William Hill, IV, uses a simple dice game to demonstrate typical stages in solving problems. Begin by telling your students that they will be playing a game called Petals Around a Rose. You will be throwing dice and after each throw you will tell how many petals are around the rose. A specific rule determines the number of petals, and students are to discover the rule. Also tell them that the name of the game itself provides a clue to the rule. For the first few throws of the dice (in larger classes use overheads to show the dice throws or quickly draw them on the chalkboard), simply identify the correct number of petals. After the first three throws, have students attempt to guess the number of petals before telling them the correct answer. Simply inform them whether their guess is correct or incorrect; do not confirm a particular rule. Begin by throwing five dice. To facilitate acquisition of the rule, progressively reduce the number of dice. Most students will figure out the rule by the time you reduce the number to two or one. The rule is very simplea rose is defined as a die with a center dot (always an odd number). The total number of petals is the sum of all the dots that occur around the center dot (on all the dice thrown that have the dot). After completing the game, ask volunteers to describe how they solved the problem. Some may refer to insight. Others are likely to describe a process of hypothesis formation, testing, and revising. Also ask what information they attended to in attempting to solve the problem and why. Do obstacles in problem solving reflect problems in isolating relevant information or are they also the result of frustration or performance anxiety? Hill, G. W. (1991, August). Craps in the classroom: Dice games to demonstrate problem-solving. Paper presented at the Annual Convention of the American Psychological Association, San Francisco, CA. Module Manipulating Images Are these pairs of objects the same or different?
Only (A) is the same. PsychSim 5: My Head Is Spinning This activity demonstrates thinking with verbal concepts and mental images, using the concept of mental rotation, thus you may want to hold this until you cover thinking with images. The issue of mental rotation is introduced and explained with reference to the classic studies by Roger Shepard and colleagues. Students participate in a simulation involving mental rotation of the letter R in the picture plane. Their results are graphed and compared with the pattern of results from Cooper and Shepard (1973). Interestingly the more different numbers are the quicker we can tell them apart. Which is greater 5 or 7, which is greater 12 or 550, the greater the distance the shorter the response time. Vilayanur S. Ramachandran The Tell Tale Brain pg. 110 Return Module Obstacles in Solving Problems
Confirmation Bias: A tendency to search for information that confirms a personal bias. When given this problem people only test solutions that match their bias. Rule: Any ascending series of numbers. 1 2 3 would comply. Watsons students had difficulty figuring out the rule due to a confirmation bias (Watson, 1960). 2 37. A student who strongly believes that genetic influence is the major contributor to human personality is analyzing data gathered about identical twins who had been separated at birth and reunited at adulthood. The student observes many striking similarities in personality and habits within the twin pairs but does not notice differences within the twin pairs that might argue against the students belief. This students behavior illustrates which of the following? (AP04) (A) Confirmation bias (B) The availability heuristic (C) An algorithmic error (D) Metacognition (E) A mnemonic 2 4 6 Discover the rule Module Fixation Fixation: An inability to see a problem from a fresh perspective. This impedes problem solving. An example of fixation is functional fixedness. Stuck container in drain as an example On a fishing trip, Ed realizes that he has mistakenly packed the sewing box instead of the tackle box. He wants to fish but returns home because he does not have any line or hooks. Ed's failure to realize that sewing thread can be used as fishing line and that a bent needle can be used as a hook is an example of (AP94) (A) Poor problem representation (B) Cognitive accommodation (C) Backward masking (D) Functional fixedness (E) Proactive interference The Matchstick Problem: How would you arrange six matches to form four equilateral triangles? From Problem Solving by M. Scheerer. Copyright 1963 by Scientific American, Inc. All Rights Reserved. Module Candle-Mounting Problem
Using these materials, how would you mount the candle on a bulletin board? From Problem Solving by M. Scheerer. Copyright 1963 by Scientific American, Inc. All Rights Reserved. Module The Three-Jugs Problem
Using jugs A, B, and C, with the capacities shown, how would you measure out the volumes indicated? Module Figure 8.6: Six standard problems used in studies of problem solving.
Try solving the problems and identifying which class each belongs to before reading further. The problems can be classified as follows. The analogy problems and series completion problems are problems of inducing structure. The solutions for the analogy problems are Buy and Patient. The solutions for the series completion problems are 4 and E. The string problem and the anagram problems are problems of arrangement. To solve the string problem, attach the screwdriver to one string and set it swinging as a pendulum. Hold the other string and catch the swinging screwdriver. Then you need only untie the screwdriver and tie the strings together. The solutions for the anagram problems are WATER and JOKER. The hobbits and orcs problem and the water jar problem are problems of transformation. The solutions for these problems are outlined in Figures 8.7 and 8.8. Fig. 8-6, p. 311 Module Figure 8.7: Solution to the hobbits and orcs problem.
This problem is difficult because it is necessary to temporarily work away from the goal. Fig. 8-7, p. 312 Module The Matchstick Problem: Solution
From Problem Solving by M. Scheerer. Copyright 1963 by Scientific American, Inc. All Rights Reserved. Module Candle-Mounting Problem: Solution
Module The Three-Jugs Problem
Solution: a)All seven problems can be solved by the equation shown in (a): B - A - 2C = desired volume. b) But simpler solutions exist for problems 6 and 7, such as A - C for problem 6. Module Making Decision & Forming Judgments
Each day we make hundreds of judgments and decisions based on our intuition, seldom using systematic reasoning. Preview Question 3: How do heuristics, overconfidence, and framing influence our decisions and judgments? Link BBC Horizion How to make better decisions 48:48 Link How to make better decisions Module Using and Misusing Heuristics
Two kinds of heuristics, representative heuristics and availability heuristics, have been identified by cognitive psychologists. Heuristics are mental shortcuts Courtesy of Greymeyer Award, University of Louisville and the Tversky family Courtesy of Greymeyer Award, University of Louisville and Daniel Kahneman Amos Tversky Daniel Kahneman Module Representativeness Heuristic
Judging the likelihood of things or objects in terms of how well they seem to represent, or match, a particular prototype. Ivy league universities 10 Classics profs at each 4, total 40 Short , 20 Read poetry , 10 Truck drivers 400,000 Short , 100,000 Read poetry 1/100, 1000 If you meet a slim, short, man who wears glasses and likes poetry, what do you think his profession would be? More likely an ivy league professor or a truck driver? Probability that that person is a truck driver is far greater than an ivy league professor just because there are more truck drivers than such professors. Module All (except one) of these animals fit the concept of penguin
The guy is not representative of penguins Module Heuristics Availability Heuristic
How about how this influences views on race or immigration or terrorism Are there more words starting with k or that have k as the 3rd lettermake, likely, acknowledged, ask, asked, Ones with K at the start come to mined more readily How recently we heard about and event, how vivid it was, how concrete it was, how distinct it was Availability Heuristic estimating the likelihood of events based on their availability in memory if instances come readily to mind (perhaps because of their vividness), we presume such events are common Example:airplane crash Module Overconfidence Overconfidence: tendency to overestimate the accuracy of our beliefs and judgments. Even when we have 100% confidence we err about 15% of the time Students routinely misjudge how long projects and papers will take, they actually take about 2x longer than they think (Buehler 1994) We overestimate our future free time (Zauberman 2005) TED Laurie Santos looks for the roots of human irrationality by watching the way our primate relatives make decisions. A clever series of experiments in "monkeynomics" shows that some of the silly choices we make, monkeys make too. A bit dry In the stock market, both the seller and the buyer may be confident about their decisions on a stock. Mind over Money at NOVA 52:52 Module overconfidence increases with action
overconfidence increases with action. As we actively engage, we become more confident in what we are doing. Finally, overconfidence increases with action. As we actively engage, we become more confident in what we are doing. In another classic study, Langer found that individuals who flipped a coin themselves, in contrast to watching someone else flip it, were more confident in being able to predict heads or tails accurately, even though, objectively, the probabilities remained unchanged. Furthermore, individuals who chose their own lottery ticket were more confident in a lucky outcome than they were if a lottery ticket was chosen for them. And in the real world, the effects are just as pronounced. Let's take the case of traders once again. The more they trade, the more confident they tend to become in their ability to make good trades. As a result, they often overtrade, and in so doing undermine their prior performance. But forewarned is forearmed. An awareness of these elements can help you counteract them. It all goes back to the message at the beginning of the chapter: we must continue to learn. The best thing you can do is to acknowledge that you, too, will inevitably stumble, be it from stagnation or overconfidence, its closely related near opposite (I say near because overconfidence creates the illusion of movement, as oppose From Mastermind: How to Think Like Sherlock Holmes by Maria Konnikova Module You might steal more when asked NOT to
Sign posted that condemned the fact that many visitors steal the wood from Petrified Forest National Park. In the absence of the sign 3% stole wood In the presence of the sign 8% stole wood Messages that condemn yet highlight undesired social norms are common, and that they invite counterproductive results In a related study, researchers created a sign condemning the fact that many visitors steal the wood from Petrified Forest National Park. They placed the sign on a well-used pathway, along with some secretly marked pieces of wood. Then they watched to see what effect the sign would have. They found that in the absence of a sign, souvenir hunters stole about 3 percent of the wood pieces in just a ten-hour period. But with the warning sign in place, that number almost tripled, to 8 percent. Again, it is doubtful that many of the pilferers literally said to themselves, Everyone does it, so why not me? But that seems to be the message received by their unconscious. The researchers pointed out that messages that condemn yet highlight undesired social norms are common, and that they invite counterproductive results. So while a college administration may think it is warning students when it says, "Remember! You must cut down on binge drinking, which is prevalent on campus!" what sinks in may instead be a call to action: Remember! Binge drinking is prevalent on campus! From Subliminal: How your unconscious mind rules your behavior. Module The 9/11 attacks led to a decline in air travel due to fear.
Exaggerated Fear Exaggerated fear: about what may happen. Such fears may be unfounded. This is opposite ofhaving overconfidence. The 9/11 attacks led to a decline in air travel due to fear. 39.5 times more likely to die in auto accidents than in plane crashesmore traffic deaths since 9/11 because people were afraid to fly We fear what our ancestral history has prepared us to fear, confinement, heights, we fear what we cannot control, flying not driving, we fear immediate threats, takeoff, landing, we perceive the dangers of driving across many moments AP/ Wide World Photos Module We often fear the wrong things
What is most likely to kill someone your age15-24. Murder? Criminal violence? Accidents, mostly car wrecks As a group you are more likely to kill yourself than to be murdered! Are you more likely to be burglarized or steal from your work? Why We Are Dishonest, and What We Can Do about It In 2004, the total cost of all robberies in the United States was $525 million, and the average loss from a single robbery was about $1,300. These amounts are not very high, when we consider how much police, judicial, and corrections muscle is put into the capture and confinement of robbers let alone the amount of newspaper and television coverage these kinds of crimes elicit. I'm not suggesting that we go easy on career criminals, of course. They are thieves, and we must protect ourselves from their acts. But consider this: every year, employees' theft and fraud the workplace are estimated at about $600 billion. That figure is dramatically higher than the combined financial cost than robbery, burglary, larceny-theft, and automobile theft (totaling about $16 billion in 2004); it is much more than what career criminals in the United States could steal in their lifetimes; and it's also almost twice the market capitalization of General Electric. But there's much more. Each year, according to reports by the insurance industry, individuals add a bogus $24 billion to their claims of property losses The IRS, meanwhile, estimates a loss of $350 billion per year, representing the gap between what the feds think people should pay in taxes and what they do pay. The retail industry has its own headache: it loses $16 billion a year to customers who buy clothes, wear them with the tags tucked in. and return these secondhand clothes for a full refund. Add to this sundry everyday examples of dishonesty the congressman accepting golfing junkets from his favorite lobbyist; the physician making kickback deals with the laboratories that he uses; the corporate executive who backdates his stock options to boost his final pay and you have a huge amount of unsavory economic activity, dramatically larger than that of the standard household crooks. From Predictably Irrational by Dan Ariely Source, how will you die graphic Module Thinking Framing the way an issue is posed
how an issue is framed can significantly affect decisions and judgments Example:What is the best way to market ground beef--as 25% fat or 75% lean? 10% die with a surgery 90% survive Most people feel more risk when surgeons say 10% die. 9/10 college students say condom effective with 95% success rate stopping aids 4/10 say effective with 5% failure rate More people think a 1/20 event will happen than a 10/200 More people scared by numbers than %, if chemical exposure kills 10 in 10 million that is scarier than % Ground beef 75% lean is more appealing than 25% fat Framing is used to influence you. Do custody judge framing activity Does presenting Hitler in the style of an iconic image soften his appearance Module Thinking Belief Bias Belief Perseverance
the tendency for ones preexisting beliefs to distort logical reasoning sometimes by making invalid conclusions seem valid or valid conclusions seem invalid Belief Perseverance clinging to ones initial conceptions after the basis on which they were formed has been discredited Belief perseverance is the tendency to cling to our beliefs in the face of contrary evidence. If you see that a country is hostile, you are likely to interpret their ambiguous actions as a sign of hostility (Jervis, 1985). Study took two groups, one supported capital punishment, one opposedgiven new findingseach group interpreted findings to fit their beliefs. Implications for racism, gangs, republican/democrat Cure for belief bias.consider the opposite, asked to consider opposite groups were more objective. Consistency is adaptive, inconsistency thought to be undesirable (Allgeier 1979) 54 Once we make a choice or take a stand we encounter personal and interpersonal pressure to behave consistently w/that commitment (Fazio 1992) 53 It would appear that we are biased AGAINST open mindedness. Cialdini, Influence Consistency allows us to not think about pros and cons. 56 Cialdini, Influence Magic and the brain at PBS Magic and the Brain at PBS Module For example, epidemiologists estimate that it was not until 1905 that you were better off going to a physician. (Ignaz Semelweiss, noticed that doctors doubled the mortality rate of mothers at delivery.) The role of the physician predated its rational function for thousands of years, so why were there physicians? Economists, forecasters, and professional portfolio managers typically do no better than chance, yet command immense salaries for their services. Food prices are driven up to starvation levels in underdeveloped countries, based on climate models that cannot successfully retrodict known climate history. Liability lawyers win huge sums for plaintiffs who get diseases at no higher rates than others not exposed to "the" supposed cause. What is going on? The complexity and noise permeating any real causal nexus generates a fog of uncertainty. Slight biases in causal attribution or in blameworthiness (e.g., sins of commission are worse than sins of omission) allow a stable niche for extracting undeserved credit or targeting undeserved blame. If the patient recovers, it was due to my heroic efforts; if not, the underlying disease was too severe. From This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking, By John Brockman Module One of the biggest challenges in education, for example, get children to apply what they learn in school to real-world situations. Perhaps the most dire consequence is that human beings tend to be better at remembering evidence consistent with their beliefs than evidence that contradicts those beliefs. When two people disagree, it is often because their prior beliefs lead them to remember (or focus on) different bits of evidence. To consider something well, of course, is to evaluate both sides of an argument, but unless we also go the extra mile of deliberately forcing ourselves to consider alternatives which doesn't come naturally we're more prone to recall evidence consistent with a belief than inconsistent with it. Overcoming this mental weakness (known as confirmation bias) is a lifelong struggle; recognizing that we all suffer from it is an important first step. We can try to work around it, compensating for our inborn tendencies toward self-serving and biased recollection by disciplining ourselves to consider not just the data that might fit with our own beliefs but also the data that might lead other people to have beliefs different from ours. From This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking, By John Brockman Module Belief Bias example God is love. Love is blind Ray Charles is blind.
Ray Charles is God. Anonymous graffiti OBJECTIVE 8| Explain how our preexisting beliefs can distort our logic. Module Fluency Effect If the form of information is difficult to assimilate, that affects our judgments about the substance of that information. one-page description of an exercise routine instead of a recipe and similar results: subjects rated the exercise as harder and said they were less likely to try it when the instructions were printed in a font that was hard to read. Psychologists call this the "fluency effect." If the form of information is difficult to assimilate, that affects our judgments about the substance of that information. The science of the new unconscious is full of reports about phenomena such as these, quirks in our judgment and perception of people and events, artifacts that arise from the usually beneficial ways in which our brains automatically process information. The point is that we are not like computers that crunch data in a relatively straightforward manner and calculate results. Instead, our brains are made up of a collection of many modules that work in parallel, with complex interactions, most of which operate outside of our consciousness. As a consequence, the real reasons behind our judgments, feelings, and behavior can surprise us. From Subliminal: How your unconscious mind rules your behavior. Module Perils & Powers of Intuition
Intuition may be perilous if unchecked, but may also be extremely efficient and adaptive. Which is more populous San Diego or San Antonio. 62% of Americans guessed right 100% of Germans (who had never heard of San Antonio) guessed right Intuition adaptive, it allows us to make quick decisions in areas in which we are experts, chess, nursing, fire fighting for example Sway: The Irresistible Pull of Irrational Behavior 53:50 Myers on intuition Power and Perils of intuition link Irrational behavior link Myers on Intuition Module Predictably Irrational
The power of FREE! Truffle at 15 cents Kiss at 1 cent, 73% chose truffle 27% chose kiss Truffle at 14 cents Kiss at free 31% chose truffle 69% chose kiss The price difference in both cases is the same 14 cents Sofree can make you miss something (Note a Lindt truffle wholesales for about 30 cents.) So what happened when the "customers" flocked to our table? When we set the price of a Lindt truffle at 15 cents and a Kiss at one cent, we were not surprised to find that our customers acted with a good deal of rationality: they compared the price and quality of the Kiss with the price and quality of the truffle, and then made their choice. About 73 percent of them chose the truffle and 27 percent chose a Kiss. Now we decided to see how FREE! might change the situation. So we offered the Lindt truffle for 14 cents and the Kisses free. Would there be a difference? Should there be? After all, we had merely lowered the price of both kinds of chocolate by one cent. But what a difference FREE! made. The humble Hershey's Kiss became a big favorite. Some 69 percent of our customers (up from 27 percent before) chose the FREE! Kiss, giving up the opportunity to get the Lindt truffle for a very good price. Meanwhile, the Lindt truffle took a tumble; customers choosing it decreased from 73 to 31 percent. What was going on here? First of all, let me say that there are many times when getting FREE! items can make perfect sense. If you find a bin of free athletic socks at a department store, for instance, there's no downside to grabbing all the socks you can. The critical issue arises when FREE! becomes a struggle between a free item and another item a struggle in which the presence of free! leads us to make a bad decision. For instance, imagine going to a sports store to buy a pair of white socks, the kind with a nicely padded heel and a gold toe. Fifteen minutes later you're leaving the store, not with the socks you came in for but with a cheaper pair that you don't like at all. The cost of zero cost Module From Predictably Irrational by Dan Ariely
To replicate this experience in out chocolate experiment, we told our customers that they could choose only a single sweet the Kiss or the truffle. It was an either-or decision, like choosing one kind of athletic sock over another. That's what made the customers1 reaction to the FREE! Kiss so dramatic: Both chocolates were discounted by the same amount of money. The relative price difference between the two was unchanged and so was the expected pleasure from both. According to standard economic theory (simple cost-benefit analysis), then, the price reduction should not lead to any change in the behavior of our customers. Before, about 27 percent chose the Kiss and 73 percent chose the truffle. And since nothing had changed in relative terms, the response to the price reduction should have been exactly the same. A passing economist, twirling his cane and espousing conventional economic theory, in fact, would have said that since everything in the situation was the same, our customers should have chosen the truffles by the same margin of preference. And yet here we were, with people pressing up to the table to grab our Hershey's Kisses, not because they had made a reasoned cost-benefit analysis before elbowing their way in, but simply because the Kisses were free! How strange (but Predictable) we humans are! From Predictably Irrational by Dan Ariely Module From Predictably Irrational by Dan Ariely
Indeed, the draw of zero cost is not limited to monetary transactions. Whether it's products or money, we just cant resist the gravitational pull of FREE! So do you think you have a handle on free!? OK. Here's a quiz. Suppose I offered you a choice between a free $10 Amazon gift certificate and a $20 gift certificate for seven dollars. Think quickly. Which would you take? If you jumped for the FREE! certificate, you would have been like most of the people we tested at one of the malls in Boston. But look again: a $20 gift certificate for seven dollars delivers a $13 profit. That's clearly better than getting a $10 certificate free (earning $10). Can you see the irrational behavior in action ? The concept of zero also applies to time. Time spent on one activity, after all, is time taken away from another. So if we spend 45 minutes in a line waiting for our turn to get a free! taste of ice cream, or if we spend half an hour filling out a long form for a tiny rebate, there is something else that we are not doing with our time. My favorite personal example is free-entrance day at a museum. Despite the fact that most museums are not very expensive, I find it much more appealing to satisfy my desire for art when the price is zero. Of course I am not alone in this desire. So on these days I usually find that the museum is overcrowded, the line is long, it is hard to see anything, and fighting the crowds around the museum and in the cafeteria is unpleasant. Do I realize that it is a mistake to go to a museum when it is free? You bet I do but I go nevertheless. From Predictably Irrational by Dan Ariely Module EXPLORING PSYCHOLOGY (7th Edition in Modules) David Myers
Robert Cialdini illustrates the principle for sales. Assume that a man wants to buy a three-piece suit and a sweater. If you were the salesperson, which should you show him first in order to get him to spend the most money? You might think it best to sell the sweater first. Having spent a lot on a suit, the customer might be reluctant to spend more on a sweater. However, sales motivation analysts suggest the opposite. Sell the suit first because the additional cost of the sweater will not be so readily noticed. If the man has just paid $500 for a suit, an additional $75 for a sweater will not seem excessive. The same applies to other accessories, such as a shirt or shoes. As a rule, people will almost always pay more for accessories if they buy them after rather than before a more expensive purchase. The same principle holds for the purchase of accessories on a new car. After paying $32,000 for the car, the customer will hardly notice $700 for a sound system to go with it. The trick, of course, is to mention these accessories independently so that each addition will seem negligible in comparison to the much larger commitment already made. Cialdini, R. B. (2001). Influence: Science and practice (4th ed.). Boston: Allyn & Bacon. PowerPoint Slides Aneeq Ahmad Henderson State University Worth Publishers, 2008 Module Impact of Belief Bias in a Syllogism
Premise #1 Some professors wear ties. Premise #2 Some men wear ties. Conclusion Some professors are men. Does this follow logically? Premise #1 Some scarecrows wear ties. Premise #2 Some professors wear ties. Conclusion Therefore, some scarecrows are professors??? Return Module Figure 8.9: Two Versions of the Same Premise
Module Thinking Strategies: Informal Reasoning
Also known as inductive reasoning Role of heuristics Potentially problematic heuristics Anchoring heuristic Basing judgments on existing info early info has more impact Representativeness heuristic Judging whether something belongs to a class based on its similarity to other members of the class Availability heuristic Basing judgments on information most easily brought to mind Module Biases and Flaws in Decision Making
Loss Aversion Biases in Perceptions of Probability Overestimate probability of unlikely events Underestimate probability of likely events Gamblers fallacy Unrealistic Confidence in Accuracy of Predictions Module Types of Concepts Simple concepts have a single common feature
Cognition, Language, and Intelligence Types of Concepts Simple concepts have a single common feature Complex concepts Conjunctive: simultaneous presence of 2 or more common characteristics Disjunctive: presence of one common characteristic or another, or both apple Red t-shirt ball aunt moms sister female Schizophrenic person hears having voices distorted not there beliefs Superordinate concept
Cognition, Language, and Intelligence Basic Concepts Station wagon Basic concepts Vehicles Planes Propeller plane Cars Luxury sedan Sportscar Boats Glider Jet plane Kayak Sailboat Motorboat Subordinate concepts Superordinate concept Creative Problem Solving
Cognition, Language, and Intelligence Creative Problem Solving Creativity ability to act or think in novel and ways that are valued by others Convergent thinking Logical, factual, conventional, focused thinking Divergent thinking Unconventional, loosely organized and directed Breaks out of mental sets more easily Which two belong together?
Cognition, Language, and Intelligence Chinese thinking (relationship) American thinking (category) Which two belong together?