Chapter Eight. Language and Thought. Language Problem Solving Probabilistic Reasoning

Transcription

1 Chapter Eight Language and Thought Language Problem Solving Probabilistic Reasoning

2 Part One: Language Though second nature to native speakers, languages are complex in their content, structure, and diversity. Phonetics Semantics Theories of Development

3 Phonetics The individual distinct sounds within a language are called phonemes. Each language has its own set of phonemes. Some of these are almost universal across all languages, while others are limited to specific languages or language families.

4 Semantics Semantics are meanings within a language. A morpheme is a basic unit of meaning. For example, the word workers is comprised of the morphemes work, er, and s, each of which affects the overall meaning of the word. Syntax is the set of rules governing how words can be arranged meaningfully. For example, the workers helped children, the children workers helped, and helped children the workers have the same words but different meaning (or nonmeaning).

5 Theories of language development The influence of nature versus nurture in children s language development has been extensively debated. Type of theory Behaviorist Nativist Interactionist Summary Children learn language through observational learning and operant conditioning: They experience or witness reinforcement for effectively communicating. Humans innately have a language acquisition device that allows them to quickly pick up language. Language is learned through observational learning and operant conditioning with the help of a language acquisition device.

6 Part Two: Problem Solving Problem solving happens in a variety of contexts, from entertaining logic puzzles to international crises. Approaches Barriers mental sets functional fixedness irrelevant information unnecessary constraints Cognitive Styles Kitiyama, Duffy, Kawamura, & Larsen (2003)

7 Approaches to problem solving Different approaches can be tried in problem solving. Some types of problems are more easily solved with certain types of approach. Approach Description Unscramble TCOHL Algorithmic Each possibility is Try each of the 5! = 120 systematically considered. possible orders: TCOHL, Heuristic General rules of thumb are applied. TCOLH, TCHOL, etc. H is likely to follow T or C in English, and the four consonants are likely to have a vowel in or near the middle: CHOTL, THOCL, THOLC, etc. Insight Ideas are brainstormed. Keep thinking.

8 Barriers to problem solving Algorithmic approaches are ideal because they account for every possibility. However, many situations are too conceptual to be examined algorithmically, and many that can be have so many possibilities that a computer is required to consider all of them. Other types of problem solving may be prone to limitations created by the problem solver himself or herself, such as the following. Barrier Description Mental Set using an inefficient approach that was efficient in previous similar problems Functional Fixedness not considering uses for an object different than those typical for the object Irrelevant Information fixating on information in the problem that is not relevant to the solution Unnecessary Constraints making incorrect assumptions limiting possible solutions

9 Mental Set example Students in Statistics class last year were given the following problem. Problem: Anya pulls 4 different random marbles from a cup containing 11 green marbles, 8 blue marbles, and 1 black marble. What is the probability she pulls a) at least 1 green marble, and b) at least 1 black marble? Mental Set: Statistics students know that the probability of getting at least one of something is the complement of getting none of them, so they calculate the probability of getting none and subtract it from 100%. At least one green marble: % = 97% At least one black marble, using mental set: % = 20% At least one black marble, without mental set: 4 at least one black: = 20% 20 Comment: Statistics students are used to using the mental set of 100% minus the complement for this type of problem that not one student in either period realized how simple the second problem was.

10 Functional Fixedness example Problem: Brett hurts his hand at work and needs an ice pack, but there is no ice in the freezer. Functional Fixedness: To keep his hand cold, Brett must use ice. Solution limited by functional fixedness: Go to a store to buy ice. Solution not limited by functional fixedness: Use something else cold, such as frozen food or a soda from a vending machine.

11 Irrelevant Information example Problem: Lizzie draws two cards. What is the probability that her second card is the ace of spades? Irrelevant Information: A card was already drawn. Solution using irrelevant information: 1 / 51 Solution disregarding irrelevant information: 1 / 52 Comment: Every card has a 1 / 52 probability of being the ace of spades. It is irrelevant which card is being asked about. In this case, irrelevant information tends to lead people to an incorrect answer.

12 Unnecessary Constraints example Problem: Without picking up the pencil, draw four lines that cross all nine dots at right. Unnecessary Constraint I: The lines cannot go past the dots. Unnecessary Constraint II: The lines must be at 90 or 45 angles to each other. Solution limited by unnecessary constraints: not possible Solutions not limited by unnecessary constraints:

13 Cognitive Styles Cognitive Style Focus on More common in Analytic individual elements and Western cultures details Holistic overall setting and context Eastern cultures

14 Kitayama, Duffy, Kawamura, & Larsen (2003) Participants: 40 American undergraduates at the University of Chicago, 21 Japanese undergraduates at the University of Chicago, 32 Japanese undergraduates at Kyoto University, and 18 American exchange students at the Kansai Institute for Foreign Languages. Procedure: Participants were shown a box with a line drawn down from the top middle of it. They were then given an empty box, not necessarily the same size as the first, and asked to draw in a line that was the same as the one they had seen in the first box. This was done for six boxes. Independent Variable I: what they were asked to match about the line relative length (with respect to the size of the box) or absolute length Independent Variable II: surrounding culture American or Japanese Independent Variable III: race American or Japanese Dependent Variable: line length error same absolute length original same proportional length

15 Kitayama et al. (2003), continued Results: People surrounded by Eastern culture, regardless of their own race, tended to be more accurate replicating the lines relative lengths than their absolute lengths. To a lesser extent, the same was true for Japanese people, regardless of the surrounding culture. average error (mm) American race Japanese American Japanese surrounding culture absolute length relative length

16 Part Three: Probabilistic Reasoning The natural tendency in probabilistic reasoning is for quickness, rather than accuracy, to be emphasized. Systems of thinking Heuristics and their fallacies More System 1 fallacies Probabilistic concepts Fischbein & Schnarch (1997) Tversky 92 & Kahneman (1983) Tversky 92 & Kahneman (1981) Kahneman & Tversky (1981) Windschitl & Wells (1998) Windschitl & Chambers (2004) Influence of Cognitive Load

17 Systems of thinking Thinking, especially decision-making, can be divided into two systems. System 1 is automatic, such as riding a bike or having a gut feeling on a multiple-choice question. System 2 requires conscious effort, such as riding a bike on a tricky single-track, or reasoning out an answer to a multiple-choice question. System 2 may override a decision made by System 1, but in most cases it is used to justify System 1 s decisions or is not used at all. System System 1 System 2 Order first second, if at all Processing automatic intentional Speed fast slow Cognitive load minimal signficant Tools heuristics analysis Source of conclusions intuition reasoning Fallacious conclusions very common common

18 Heuristics and thier fallacies A heuristic is a problem-solving approach that tends to be quick and efficient. Heuristics are frequently applied implicitly. Their fast, automated nature makes them very beneficial, but this often comes at the expense of accuracy. Type Application Fallacy example Availability basing estimates of likelihood on how readily examples come to mind creative Representativeness Anchoring assuming something is likely to fit into a given category if it has characteristics of that category providing a baseline for judgements on a scale believing you are more creative than Kate because you can think of more examples of yourself being creative than of her being assuming that a 6 9 Black man is more likely to be a professional athlete than a waiter assigning higher pentalties to crimes with a maximum fine of $800 than crimes with a minimum fine of $400

19 Heuristics and thier fallacies, continued Type Application Fallacy example Affect equating factual assessment with personal emotion Effort Fluency assuming higher value for things resulting from greater effort assuming higher value for things that are recognizable or otherwise easily processed believing Starbucks stock is a good investment because you like Starbucks feeling stronger allegiance to a fraternity after being hazed more readily accepting claims that have been heard before

20 More System 1 fallacies The effects below are additional examples of fallacies that commonly result from System 1 processing. Effect Definition Example Framing Effects preference for possibilities when they are described in terms of gain rather than loss Alternative- Outcomes Effects Dud-Alternative Effects increased confidence in most likely result, regardless of how likely it actually is more confidence in a likely result when listed with likely and unlikely alternatives than when listed only with likely alternatives greater confidence in a kicker that makes 70% of his field goals than one who misses 30% of his field goals greater confidence in Brett winning if each of his six opponents have a 10% chance of winning than if his one opponent has a 60% chance of winning greater confidence in McDonalds being a larger restaurant chain than Subway, Applebee s, and In-and-Out than when compared only to Subway

21 More System 1 fallacies, continued Effect Definition Example Falk Phenomenon understanding dependent events only if the events are stated in the order in which they occur Conjunction Fallacy claiming that a subcategory is more common than a category that contains it (often due to the representativeness hueristic) given two cards are taken from a stack of seven red and three black cards, believing that the probability of one card being black if the other is red depends on which card is which believing that a French-speaking person is more likely to live in France than in Europe

22 Probabilistic concepts Probabilistic reasoning is highly counterintuitive for the average person. The three fundamental concepts below are rarely well understood, leading to misconceptions that sometimes have significant consequences. Concept Definition Example Base Rates Probabilities and sample distributions are based largely on population parameters. The representativeness heuristic leads people to assume that a college student who reads a novel every week is more likely to be majoring in literature than in business, but since the base rate of business majors is 7 times that of lit Law of Large Numbers Regression toward the Mean The larger a sample is, the closer its sample statistics tend to be to the acutal population parameters. Extreme values of a random variable tend to be followed by more typical values. majors, the reverse is actually true. Getting at least 90 heads in 100 flips is far less likely than getting at least 9 heads in 10 flips, beause the more coins that are flipped, the closer the proportion of heads tends towards the expected 50%. Athletes frequently show decreased performance after appearing on the cover of Sports Illustrated, because they had to be at the very top to have been on the cover.

23 Fischbein & Schnarch (1997) Participants: 98 Israeli students Procedure: Participants took a multiple-choice quiz consisting of eight probabilistic reasoning questions. (See next two slides.) Independent Variable: grade level 5 th, 7 th, 9 th, 11 th, or grad school as future math teachers Dependent Variable: accuracy

24 Fischbein & Schnarch (1997), continued Concept Question (paraphrased) Accuracy Representativeness Which lottery ticket is more likely to win, 56% or ? Gambler s Fallacy A coin is flipped three times and lands on 69% heads each time. What is the probability it will land on heads a fourth time? Compound Events Which is more likely on two dice rolls, a 5 15% and a 6 or a 6 and a 6? Conjunction Fallacy Dan likes to help people and dreams of becoming a doctor. He was a medical attendant in the army and then started college. Is he more likely to be a student or a medical student? 36%

25 Fischbein & Schnarch (1997), continued Concept Question (paraphrased) Accuracy Law of Large Numbers Which is more likely to have more than 60% of its births be boys on a given day, a hospital that averages 15 births per day or one that 1% Law of Large Numbers Availability Heuristic Falk Phenomenon averages 45 births per day? Which is more likely, getting heads at least 2 times out of 3 coin flips or at least 200 times out of 300 coin flips? Ten people are available to form a committee. Are there more possible committees of 2 people or of 8 people? Galit has two black marbles and two white marbles in a box. She pulls out one marble and sets it aside without looking at it. She then pulls out a second marble and sees that it is white. What is the probability that the first marble was white? 26% 6% 40%

26 Fischbein & Schnarch (1997) continued Results: Most questions were answered incorrectly more often than correctly, and every grade level including college students training to be math teachers averaged more incorrect answers than correct answers. There was only a slight trend for students with more math experience to outperform younger students. 100% accuracy 75% 50% 25% 0% 5 th 7 th 9 th 11 th college grade level

27 Tversky 92 & Kahneman (1983) Participants: college students Procedure: Participants read the following description: Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. They were told to rate the likelihood of statements such as: a) Linda is a teacher in elementary school. e) Linda works in a bookstore and takes Yoga classes. b) Linda is active in the feminist movement. f ) Linda is a bank teller. c) Linda is an insurance salesperson. g) Linda is a member of the League of Women Voters. d) Linda is a psychiatric social worker. h) Linda is a bank teller and is active in the feminist movement. Independent Variable I: statistics background of participants University of British Columbia undergraduates with no statistics background, Stanford undergraduates with some statistics background, or Stanford or Berkeley graduate students with extensive statistics background Independent Variable II: obviousness of conjunction fallacy (see next slide) Dependent Variable: percent of participants who violated the conjunction rule by claiming that (h) is more likely than (f ) Results: In almost all cases, the majority of participants violated the conjunction rule.

28 Tversky & Kahneman (1983), continued Scenario Wrong Rank the likelihood of the eight possibilities on the previous slide. 89% Same as above, but with stats-educated Stanford undergrads. 90% Same as above, but with Stanford Business School graduate students, highly 85% educated in statistics and decision-making. Which is more probable, Linda is a bank teller or Linda is a bank teller and is 85% active in the feminist movement? Rate the two statements above from 1 (extremely unlikely) to 9. 82% Which argument is more convincing: Linda is more likely to be a bank teller than 65% she is to be a feminist bank teller, because every feminist bank teller is a bank teller, but some women bank tellers are not feminists, and Linda could be one of them, or Linda is more likely to be a feminist bank teller than she is likely to be a bank teller, because she resembles an active feminist more than she resembles a bank teller? Rate the likelihood of Linda is a bank teller and is active in the feminist 57% movement and Linda is a bank teller whether or not she is active in the feminist movement on a scale of 1 to 9. Which would you bet $10 on, Linda is a bank teller or Linda is a bank teller 56% and is active in the feminist movement? Same as above, but with Stanford and Berkeley social science graduate 36% students with extensive statistics background.

29 Tversky 92 & Kahneman (1981) Tversky & Kahneman did a series of between-participants experiments in which participants were asked to choose between two outcomes that were framed differently but approximately equal mathematically. One experiment is described below. Participants: Stanford and University of British Columbia undergraduates Procedure: Participants were asked, Would you rather have a sure gain of $240, or 25% chance to gain $1000? and Would you rather have a sure loss of $750, or 75% chance to lose $1000? Independent Variable: outcome gain or loss Dependent Variable: choice of outcome sure or gamble Results: Participants were much more likely to choose the sure option to get a gain but the gamble option when it could mean preventing a loss. This was despite the fact that the mathematical expectations were almost identical in each case and actually slightly worse with the sure option in the gain condition. proportion choosing sure option 100% 75% 50% 25% 0% gain loss change

30 Windschitl & Wells (1998) Windschitl & Wells (1998) did a series of between-participants experiments in which participants were each given a distribution and asked how likely they felt a specific outcome was. One experiment is described below. Participants: Iowa undergraduates Procedure: Students were told that Randy cleans 30 of the 50 classrooms at a university. Independent Variable: the distribution of the other 20 classrooms all 20 by Sylvia, or 3 by Sylvia, 7 by Amy, 5 by Lauren, and 5 by Matt Dependent Variable: how likely they think it is that Randy cleaned a random classroom, on a 21-point verbal scale from impossible to certain. Results: When the alternative outcomes were more widely distributed, people rated more highly the likelihood of Randy cleaning the given room. estimates of likelihood of Randy cleaning distribution of alternative outcomes

31 Windschitl & Chambers (2004) Participants: 44 University of Iowa undergraduates Procedure: Participants were given ten scenarios such as A random sample of U.S. children aged 7-10 was asked: Which of the following is your favorite type of food for dinner pizza or hamburger? Independent Variable: dud alternatives half the questions had two additional implausible responses, such as eggplant parmesan and grilled fish in the example above Dependent Variable: estimate of likelihood that a specific focal outcome (e.g., pizza) was the most common response Results: Additional possibilities should have decreased estimates of a specific possibility, but adding dud alternatives actually increased estimates. estimates of likelihood of focal outcome one strong one strong & two duds alternative choices

32 The effect of Cognitive Load on heuristics Heuristics advantage is their speed and ease, not their accuracy. Thus it makes sense that they are more likely to be used when cognitive load is high that is, when not much processing power is left. The studies below demonstrate this. Study Scenario Cognitive Load Results Callon, Sutton, David, who was memorize Participants with high cognitive & Dovale (2010) having an affair, got hit by a car. a 2-digit or 12-digit load rated higher the extent they felt his accident was the result of Whitney, Rinehart, & Hinson (2008) Bodenhausen (1990) Tversky & Kahneman s (1981) gain versus loss experiment Tversky & Kahneman s (1983) conjunction fallacy experiment number memorize a 5-digit letter string low point in circadian rhythm his affair. Cognitive load strengthened Tversky & Kahneman s result of keeping sure gains and trying to gamble away losses. Morning people were more prone to the conjunction fallacy at night, and vice versa.