thinking & problem solving

• mental image

  • reconstruction of the object or event from memory

  • can lead to creative solutions to puzzling problems

    • Albert Einstein : Many of his creative insights derived from the use of mental imaging in the form of thought experiments.

    • The creative journey that led to theory of relativity began at age 16 when he pictured in his mind what it might be like to ride a light beam at the speed of light. He later was to say that words did not play any role in his creative thinking. Words, he said, only came into play after he was able to create mental images of new ideas he had formulated in thought experiments.

  • Women tend to outperform men in remembering the spatial location of objects (honey where is my keys)

    • Women may be better at recalling where things are placed because of their greater skill in visually scanning an image of a particular location in their minds.

    • people can experience mental images of other sensory experiences, such as “hearing” in their minds the rousing first chords of Beethoven’s Fifth Symphony or recalling the taste of a fresh strawberry or the feel of cotton brushing lightly against the cheek. Yet people generally have an easier time forming visual images than images of other sensory experiences.

concepts

• Concepts are mental categories we use to group objects, events, and ideas according to their common features

• Concepts help us respond more quickly to events by reducing the need for new learning each time we encounter a familiar object or event.

  • Having acquired the concept ambulance, we immediately know how to respond when we see one pulling up behind us on the road.

• 2 major concepts types

• logical concepts: clearly defined rules for determining membership

  • 3 sided shapes are triangles

• natural concepts: rules for determining hoe they are applied are poorly defined or fuzzy

  • justice, honor, freedom

1. Do you perceive two interlocking squares in Figure 7.2? Or might this figure represent something else?

2. Emily and Sophia played six games of chess, and each of them won four. There were no ties. How is that possible? (adapted from Willingham, 2007)

3. An airliner from France crashes just off the coast of New Jersey within the territorial waters of the United States. Although all the passengers and crew were French citizens, none of the survivors was returned to France for burial. Why not?

4. A man used a key that allowed him to enter but could not be used to open any locks. What kind of key was it?

5. Figure 7.3 shows a classic problem called the nine-dot problem. Your task is to draw no more than four lines that connect all the dots without lifting your pen or pencil from the paper (solutions to the nine-dot problem are shown on page 260).

Two Interlocking Squares?

Figure 7.3The Nine-Dot Problem

Problem solving

• a cognitive process in which we employ mental strategies to solve problems.

  • Edward Thorndike observed that animals placed in his puzzle box used trial and error to solve the problem of escaping from the enclosed compartment.

    • The animals would try one response after another until they stumbled on the action that activated the escape mechanism. Solving a problem by trial and error is a “hit-or-miss” approach of trying one solution after another until finding the correct one.

• two problem-solving strategies

  • algorithms

    • step-by-step set of rules for solving a problem

    • ex> math

  • heuristic

    • A rule of thumb used to solve problems or make judgments or decisions

      • Using the means–end heuristic, we evaluate our current situation and compare it with the end result we want to achieve. We then develop a plan to reduce the distance between the two, step by step.

      • using a backward-working heuristic, for instance, we start with a possible solution and then work backward to see if the data support the solution.

      • using creating subgoals, we break a larger problem down into smaller, more manageable problems.

        • ex> In AIDS research, one team might work on how HIV penetrates the cell, another on how it reproduces, and so on.

Mental Roadblocks to Problem Solving

• mental set: The tendency to rely on strategies that worked well in similar situations in the past

  • ex> climbing over to driver seat to push breaks rather than pull emergency break

• functional fixedness: the inability to see how familiar objects can be used in new ways

  • ex> not using cup as paper weight when wind blows papers down

• decision making

  • often influenced by underlying cognitive biases that hamper our ability to make rational or sound choices

  • confirmation bias

  • representativeness heuristic: We apply this heuristic whenever we assume that a given sample of behaviors is representative of a larger population

    • ex> can lead us to reject attending a particular college because we were unimpressed with the one or two students we happened to meet on a campus tour

  • availability heuristic: the tendency to base decisions on examples that readily come to mind

    • ex> we might buy a particular brand because we recall having seen it advertised on TV

creativity

• Divergent thinking: ability to conceive of new ways of viewing situations and new uses for familiar objects

• convergent thinking: the attempt to find the one correct answer to a problem

• analogy : a comparison between two things based on their similar features or properties

  • ex> the actions of the heart to those of a pump

• conceptual combination: combining two or more concepts into one can result in novel ideas or applications that reflect more than the sum of the parts

  • ex> “veggie burger”, “home page”

• conceptual expansion: one way of developing novel ideas is to expand familiar concepts.

  • ex> a chef’s variation of a traditional dish

language

• phonemes: The basic units of sound in a language.

  • English has about 40 phonemes to sound out the 500,000 or so words found in modern unabridged English dictionaries

    • ex> “dog” “d” “au” “g”

• morphemes: The smallest units of meaning in a language.

  • The word pretested consists of three morphemes: “pre,” “test,” and “ed.”

• syntax: determine how words are ordered within sentences or phrases to form meaningful expressions.

  • ex> “buy milk I” doesn’t make sense

  • “Don’t trip going down the stairs” means something very different from “Have a good trip.”

• semantics: The set of rules governing the meaning of words.

• language acquisition device: Chomsky’s concept of an innate, prewired mechanism in the brain that allows children to acquire language naturally

  • We acquire the ability to speak, much as we do the ability to walk and jump, because we have an inborn propensity to develop it

• linguistic relativity hypothesis: The proposition that the language we use determines how we think and how we perceive the world

  • ex> French Canadians, Chinese, and Africans see the world differently because of the vocabulary and syntax of their native languages

    • ex> English has 11 words for basic colors: black, white, red, green, yellow, blue, brown, purple, pink, orange, and gray

    • Navajo language, which has no separate words for blue and green.

intelligence

“Intelligence is the global capacity of the individual to act purposefully, to think rationally, and to deal effectively with the environment.”

• mental age: A representation of a person’s intelligence based on the age of people who are capable of performing at the same level of ability.

(1904) Binet and Simon calculated intelligence by subtracting the child’s mental age from his or her chronological (actual) age

In 1912, a German psychologist, William Stern divided mental age by chronological age, yielding a “mental quotient.”

It soon was labeled the intelligence quotient (IQ). I

Q is given by the following formula, in which MA is mental age and CA is chronological age:

ex> if a child has a mental age of 10 and a chronological age of 8, the child’s IQ would be 125

• tests of intelligence must be standardized, reliable, and valid

  • Standardization is the process of establishing norms for a test by administering it to large numbers of people.

  • Reliability refers to the consistency of test scores over time.

  • Validity is the degree to which a test measures what it purports to measure

Intelligence tests may be biased against children who are not part of the White majority culture.

Low IQ scores alone are not sufficient to determine intellectual disability

The causes of intellectual disability include both biological and environmental factors

Biological causes include genetic or chromosomal disorders, brain damage, and exposure to lead.

The most common environmental cause is a deprived family environment, one lacking in verbal interactions between the child and the parents and lacking in intellectually stimulating play activities.

Psychologist Louis L. Thurstone (1887–1955)

primary mental abilities: Seven basic mental abilities that Thurstone believed constitute intelligence.

1. verbal comprehension,

2. numerical ability,

3. memory,

4. inductive reasoning,

5. perceptual speed,

6. verbal fluency,

7. spatial relations

Psychologist Howard Gardner (b. 1943)

multiple intelligences: Gardner’s term for the distinct types of intelligence that characterize different forms of intelligent behavior.

Gardner identified eight different intelligences:

1. linguistic,

2. logical-mathematical,

3. musical,

4. spatial,

5. bodily-kinesthetic,

6. interpersonal,

7. intrapersonal,

8. naturalist

Robert Sternberg (b. 1949)

triarchic theory of intelligence: Sternberg’s theory of intelligence that posits three aspects of intelligence:

1. analytic,

   • traditional IQ

2. creative,

   • allows us to invent new ways of solving unfamiliar problems.

3. practical

   • ability to apply what we know to everyday life—the common sense, or “street smarts,”

sternberg believes we need all three types of intelligence to succeed in life