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Just Think of It!

• Thinking- Processing of information to solve problems and

make judgments and decisions

In This Chapter

Problem Solving

Thinking Under Uncertainty

Intelligent Thinking

Problem Solving

Blocks to Problem Solving

Solution Strategies

A Problem Is…

• A situation in which there is a goal, but no clear path to reach the goal- Well-defined problem - Ill-defined problem

Can you solve the problem?

• Instructions: Connect the nine circles using four straight lines without lifting your pen or pencil from the paper or retracing any of your lines

• You should attempt this problem on a separate sheet of paper so that you can keep a record of your attempts

• Once you have a four-straight-line solution, the next goal is to connect the nine circles with three straight lines using the same constraints as in the four-straight-line version

Blocks to Problem Solving

• Interpreting the problem- Fixation: Inability to create a new interpretation of

a problem

• What did you do?- Nine circle problem: Did you try to keep your

lines within the mental square created by the circle?

• If you did, you cannot solve the problem

Problem Solving: Two Steps

Interpreting

Trying to solve

Blocks to Problem Solving

Interpretation blocks- Functional fixedness

• Involves inability to see that an object can have a function other than its typical one

- Solutions• Entails thinking about the possible novel uses of all

objects in the problem environment

- Example• If you need a screwdriver but don't have one, a dime

could be used to serve the purpose of a screwdriver

Blocks to Problem Solving

Strategy blocks- Mental set

• Includes tendency to use previously successful solution strategies without considering others that are more appropriate for the current problem

- Solution• Involves new way of interpreting a problem that provides an

immediate solution (insight) when searching for new problem-solving approaches

- Example• In the two-letter series problems, mental set likely hindered you

because you viewed the letters in the series as single entities and looked for relationships between them, not each of the letters as part of some larger entity

Insight Problem

• Insight- New way to interpret a

problem that immediately yields the solution

• Do you know what part of the brain is engaged with insight?

Instructions: The equation shown is not correct. To create a correctequation, you can move only one matchstick (but not remove it). OnlyRoman numerals and the three operators, +, -, and = are allowed.

Overcoming Blocks: Key Questions

• Is my interpretation of the problem unnecessarily constraining possible solutions?

• Can I use any of the objects in the problem in novel ways to solve the problem?

• Do I need a new type of solution strategy?

Solution Strategies

• Algorithm- Step-by-step procedure that guarantees a correct

answer to a problem

• Example- Using multiplication correctly guarantees you the

correct solution to a multiplication problem

Solution Strategies

• Heuristic- Problem-solving strategy that seems reasonable

given your past experiences with solving problems, especially similar problems

- May pay off with a quick, correct answer, but it may lead to no answer or an incorrect one

Types of Heuristics

• Anchoring and adjustment heuristic- Uses an initial estimate as an anchor and then

this anchor is adjusted up or down

• Example- When meeting a new person, your first

impression forms an anchor of that person, and you may not process subsequent information about that person as fully as it should be processed

Types of Heuristics

• Working backward heuristic- Attempting to solve a problem by working from the goal

state backward to the start state

• Example- Water lilies growing in a pond double in area every 24

hours. On the first day of spring, only one lily pad is on the surface of the pond. Sixty days later, the entire pond is covered. On what day is the pond half covered?

- If you work backward with the fact that the pond is completely covered on the 60th day, you can solve this question easily…half of the pond must be covered on the 59th day.

Types of Heuristics

• Means-ends analysis heuristic- Breaking down the problem into subgoals and

working toward decreasing the distance to the goal state by achieving these subgoals

• Example- When trying to write a major term paper, students

should be encouraged (and perhaps shown) how to break down this big task into smaller tasks that, when completed, will result in a final, large term paper

Means-End Analysis

• Let's try to solve the Tower of Hanoi problem using means-end analysis

• Instructions: The problem is to create the same configuration of disks on Peg C as on Peg A in the starting state. Rules, however, govern your moves. You can only move one disk at a time, and you cannot place a larger disk on top of a smaller disk. Try to solve this problem efficiently by minimizing the number of moves that have to be made.

• The most efficient solution involves seven moves.

The Tower of Hanoi Problem

The events in our everyday lives are not as well-defined as the allowable moves in a Tower of Hanoi problem.

Thinking Under Uncertainty

Judging Probability

Hypothesis Testing

Probability and Uncertainty

• Probability of an event- Is the likelihood that the event will happen

• Probabilities range from 0 (never happens) to 1 (always happens)

• An event with 0.5 probability of occurring is maximally uncertain because it is equally likely to occur and not occur

• Uncertainty of events - Involves attempt to reduce uncertainty about the

world by trying to find out how various events are related to each other

Judging Probability

• Two main heuristics used to make judgments about probabilities (Tversky and Kahnerman)- Representativeness heuristics- Availability heuristics

Let's take a closer look at each of these.

Judging Probability

• Representativeness heuristic- Includes rule of thumb for judging the probability of membership

in a category by how well an object resembles that category:• The more representative, the more probable

- Tends to be used because the mind categorizes information automatically

• Example- You hear about a person who likes to write, read, and interpret

poetry - Is it more likely that this person is:

• A hockey fan? OR• An English professor who likes hockey?

The Over-lapping Set Diagram for the Linda Problem

• The overlap (the green area) of the two sets (all bank tellers and all people active in the feminist movement) indicates the probability of being both a bank teller and active in the feminist movement

• Because this area is a subset (part) of each of the two sets, its probability has to be less than that for either of the two sets

• This is the conjunction rule

Judging Probability

• Conjunction fallacy- Involves incorrectly judging the overlap of two

uncertain events to be more likely than either of the two events

• Conjunction rule- States that the likelihood of the overlap of two

uncertain events cannot be greater than the likelihood of either of the two events because the overlap is only part of each event

What do you think?

If a coin lands heads up 8 times in a row, is there a greater chance of it being tails on the

9th toss?

Judging Probability

Did you commit the gambler's fallacy when answering the question on the previous slide?• Gambler's fallacy- Erroneous belief that a chance process is self-correcting in

that an event that has not occurred for a while is more likely to occur

• Example- People believe that short sequences (e.g., a series of 9 coin

tosses) should reflect the long-run probabilities- If a coin lands heads up 8 times in a row, people think there

is a greater chance of it being tails on the 9 th toss

Judging Probability

• Availability heuristic- Rule of thumb that the more available an event is in our

memory, the more probable it is- Suggests event may be prominent in memories because it

happened recently or because it is particularly striking or vivid

• Examples- We can think of more words beginning with the letter “r” than

words with “r” in the third position of a word because we organized words in our memories by how they begin, not by their third letters

- Deaths from shark attacks are highly publicized, creating greater fear of this mode of death than of diabetes, which is a far more likely cause of death

Availability Heuristic

Because airplane crashes are so visually dramatic and highly publicized by the media, they tend to be very available in our memories. This availability leads us to greatly overestimate our likelihood of dying in a plane crash.

Relying on Heuristics

• Why do we rely on heuristics?- Heuristics are adaptive and often lead to a

correct conclusion or judgment- Heuristics stem from System 1 processing (e.g.,

fast, intuitive, and largely unconscious thinking)

Hypothesis Testing

Confirmation bias

Illusory

correlation

Belief perseverance

Person

-who reasoning

Hypothesis Testing

• Confirmation bias- Tendency to seek evidence that confirms one's beliefs

• Four–card selection task (Watson)- The four cards below have information on both sides. On one

side of a card is a letter, and on the other side is a number. Consider this rule: If a card has a vowel on one side, then it has an even number on the other side. Select the card or cards that you definitely must turn over to determine whether the rule is true or false for these four cards.

Hypothesis Testing

• Illusory correlation- Erroneous belief that two variables are related

when they actually are not- Tendency to focus on instances in which there

seems to be a relationship between the variables in question, ignoring all disconfirming instances

Hypothesis Testing

• Belief perseverance- Tendency to cling to one's beliefs in the face of

contradictory evidence

• Person-who reasoning - Questioning a well-established finding because

you know a person (one instance) who violates the established finding

Testing Medical Hypotheses

• Both doctors and patients have been found to overestimate these conditional probabilities

• Physicians' estimates ranged from 1 percent to 90 percent, with a 90 percent chance of breast cancer being the most frequent estimate

• Gigerenzer recommends conversion of all of the percentages (probabilities) into natural frequencies, or simple counts of events

• In doing this, the majority of doctors understood the problem

Gerd Gigerenzer

Natural Frequency Tree Diagram for Cancer Problem in Eddy (1982)

Intelligent Thinking

Intelligence Tests

Controversies about Intelligence

Once Upon an Intelligence Test

• First attempts to develop intelligence tests- Took place in late 19th century England and in

early 20th century France- Were embedded in the nature-nurture

controversy

Intelligence Tests

• Francis Galton: Nature emphasis- Motivated by eugenics - Believed in genetic determination of

intelligence - Proposed intelligence could be determined

by measuring various aspects of the human brain and nervous system

- Developed tests of sensory abilities and reaction time and tested thousands of people

- Invented the basic mathematics behind correlational statistics

- Found his measures were not good predictors of intelligence

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Intelligence Tests

• Binet and Simon: Nurture emphasis - In France in the early part of the 20th

century worked on the problem of mental retardation when France switched to mass public education

- Developed first accepted test of intelligence (1905) to diagnose children who were subnormal

- Used concept of mental age• Age typically associated with a child's

level of performance• Remedial age required when mental age

was < chronological age

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Intelligence Tests: Terman

• Lewis Terman- Revised Binet and Simon's test for American

school children (Stanford-Binet, 1916)- Used the classic intelligence quotient

formula by Stern• IQ = (mental age/chronological age) X 100• When a child's mental age as assessed by the

test was greater than the child's chronological age, the child's IQ was greater than 100

• When a child's mental age as assessed by the test was less than the child's chronological age, the child's IQ was less than 100

- Note that the IQ formula itself is no longer used

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Intelligence Tests

• David Wechsler- Was Chief Psychologist at

Bellevue Hospital in New York City in the 1930s

- Was in charge of adult patients of diverse backgrounds

- Developed his own tests, the Wechsler Bellevue Scale, in 1939 (later called the Wechsler Adult Intelligence Scale – WAIS)

• Provides test scores for a battery of both verbal and performance tests

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Intelligence Tests: Psychometric Properties

Standardization

Reliability

Validity

Psychometric Properties

• Standardization- Process that allows test scores to be interpreted

by providing test norms- Requires that test must be given to a large

representative sample of the relevant population; scores of this sample serve as norms for interpretation

• Examples- Terman - Wechsler

Sample Performance (Nonverbal) Test Items

Psychometric Properties

• Deviation IQ scores- To calculate a person's deviation IQ, Wechsler

compared how far the person's raw score was from the mean raw score in terms of standard deviation units from the mean

- To make the deviation scores resemble the IQ formula, he set the mean to 100 and the standard deviation to 15

- Using the information above, how would you complete this equation?

- Deviation IQ score =

Deviation IQ Scores on the WAIS

Psychometric Properties: Reliability

• Reliability: Extent to which the scores for a test are consistent- Test-retest method

• Test is given twice to the same sample, and the correlation coefficient for the two sets of scores is computed

- Alternate form reliability• Different forms of the test are given to the same sample at

different times and the correlation coefficient is computed for performance on the two forms

- Split-half reliability• Reliability is determined by correlating performance of two

halves of one given test

Psychometric Properties: Validity

• Validity: Extent to which a test measures what it is supposed to measure or predicts what it is supposed to predict- Content validity

• Test covers the content that it is supposed to cover

- Predictive • Test predicts behavior that is related to what is being

measured by the test

• Important to note- If a test is valid, it will also be reliable- A test can be reliable, but not valid

Controversies About Intelligence

General vs. specifi

c

Nature vs.

nurture

Theories of Intelligence

• Argued that intelligence test performance is a function of two types of factors • A g factor (general

intelligence) • Some s factor (specific

intellectual abilities such as reasoning)

• Believed that the g factor was more important• People who did well on

one subtest usually did well on most of the subtests

• People who did poorly on one subtest usually did poorly on most of the subtests

Charles Spearman

Theories of Intelligence

•Argued for the importance of several mental abilities: Verbal comprehension, number facility, spatial relations, perceptual speed, word fluency, associative memory, and reasoning•Identified these abilities via factor analysis

L. L. Thurstone

Theories of Intelligence

•Proposed two types of intelligence, which have been of interest to researchers in aging•Fluid intelligence refers to abstract reasoning, memory, and the speed of information processing•Crystallized intelligence refers to accumulated knowledge and verbal and numerical skills

Cattell and Horn

Theories of Intelligence

Theories of Intelligence

•Introduced triarchic theory of intelligence that proposes three types of intelligence•Analytical intelligence•Practical intelligence•Creative intelligence

Robert Sternberg

Theories of Intelligence

•Intelligence by itself is not sufficient to explain such thinking•Ability to think and act rationally, which is not assessed by standard intelligence tests, is another meaningful component•“Dysrationalia” is used to describe failure to think and behave rationally despite having adequate intelligence

Keith Stanovich

Nature vs. Nurture

• Most contemporary psychologists believe that both heredity (nature) and environmental experiences (nurture) are important in determining intelligence

• The disagreement is over the relative contribution of each part to intelligence, definition of intelligence, and its origins

The Case for Nature

• Genetic similarity studies are important in determining the relative contribution of nature and nurture to intelligence- Identical twins have 100% genetic similarity- Fraternal twins and siblings have 50% similarity- Two unrelated people have 0% similarity

Why do these findings make a case for the nature position?

The Case for Nurture

• There are also results that support environmental influences on intelligence- If identical twins are raised together, the

correlation between their intelligence test scores is +0.86

- If the identical twins are raised apart, the correlation falls to +0.72

Both Nature and Nurture

• Twins and sibling data- Average correlation between fraternal twins

raised together (+0.60) is less than that for identical twins reared apart (+0.72), indicating the influence of heredity

- Average correlation is greater than that for ordinary siblings reared together (+0.47), indicating environmental influences because the environment influences of fraternal twins is more similar than for ordinary siblings at different ages

Both Nature and Nurture: Evidence to Consider

• Adoption data- There is a modest correlation between intelligence

test scores of adopted children with their parents, and this correlation disappears as the children age

- Correlation between the scores for adopted children and their biological parents, however, increases as the children age

- This stronger relationship between a person's intelligence and that of their biological parents means that nature plays a larger role in determining a person's intelligence than environmental experiences

Controversies About Intelligence

• Heritability- Index of the degree of variation of a trait within a

given population that is due to heredity- Determines a reaction range, but the quality of a

person's environmental experiences determine where the individual falls within this range

Caveats

• Heritability is a group statistic and not relevant to individual people

• Heritability has nothing to do with the differences that have been observed between populations, such as the difference in scores for Asian versus American schoolchildren

Controversies About Intelligence

• Flynn Effect- Suggests that in the United States and other

Western industrialized nations, average intelligence scores have improved steadily over the past century

- Proposed explanations involve many environmental factors such as better nutrition and more education