Problem Solving We are breezing through notes today

Problem Solving We are breezing through notes today- please make sure that you have done the reading from the text-book

Cognition �Cognition- mental activities associated with thinking, knowing, remembering, and communicating information Concepts- mental groupings of similar objects, events, ideas, and people Prototypes- mental image or best example of a category

Creativity �Creativity- the ability to produce ideas that are both novel and valuable Studies suggest that a certain level of aptitude-a score above 120 on a standard intelligence test- supports creativity Convergent thinking- narrows the available problem solutions to determine the single best solution Divergent thinking- expands the number of possible problem solutions (creative thinking that diverges in different directions)

5 Components of Creativity �Expertise- a well-developed base of knowledge �Imaginative thinking skills- the ability to see things in novel ways, to recognize patterns, and to make connections �A venturesome personality- to seek new experiences, tolerates ambiguity and risk, and perseveres in overcoming obstacles �Intrinsic motivation- being driven by more interest, satisfaction, and challenge than by external pressures �A creative environment- sparks, supports, and refines creative ideas.

Problem Solving: Types of Problems �Greeno (1978) – three basic classes �Problems of inducing structure Series completion and analogy problems �Problems of arrangement String problem and Anagrams ▪ Often solved through insight �Problems of transformation Hobbits and orcs problem Water jar problem

Word Problems Susan gets in her car in Boston and drives toward New York City, averaging 50 mph. Twenty minutes later, Ellen gets in her car in New York City driving towards Boston, averaging 60 miles per hour. Both women take the same route, which extends a total of 220 miles between the 2 cities. Which car is nearer to Boston when they meet?

Simple Word Problems In the Thompson family there are five brothers and each brother has one sister. If you count Mrs. Thompson, how many females are in the Thompson family? Fifteen percent of the people in Topeka have unlisted phone numbers. You select 200 names at random from the Topeka phone book. How many of these people can be expected to have unlisted phone numbers?

Figure 8. 6 Six standard problems used in studies of problem solving

Solution to Water Jar Problem (B-A-2 C)

Mental Set “Insanity is doing the same thing over and expecting different results” tendency to approach a problem the same way as we did before because it was successful in the past – Einstein The first four require the same strategy (B-A-2 C) The 5 th is much simpler (A-C), however people get stuck here

Without lifting your pencil from the paper, draw no more than 4 straight lines that will cross through all nine dots. -no retracing lines

Unnecessary Constraints • Most people will not draw lines outside the imaginary boundary that surrounds the dots • That constraint is imposed by the problem solver, not the prompt. • People also feel compelled to draw 4 lines, but that’s not necessary

The Matchstick Problem Move 2 matches to form 4 (and only 4) equal squares.

Matchstick Solution

Effective Problem Solving �Barriers to effective problem solving: Irrelevant Information Functional Fixedness Mental Set Unnecessary Constraints

Figure 8. 12 The tower of Hanoi problem

Approaches to Problem Solving �Algorithms Systematic trial-and-error Guaranteed solution �Heuristics Shortcuts No guaranteed solution ▪ ▪ Forming subgoals Working backward Searching for analogies Changing the representation of a problem

Insight �Sudden realization of the problem’s solution, contrasts with strategy-based stuff

Confirmation Bias �Tendency to search for information that supports our preconceptions and to ignore or distort contradictory evidence

Heuristics in Judging Probabilities �The availability heuristic ▪ Explains why you are afraid of being attacked by a shark, but you shouldn’t be. �The representativeness heuristic ▪ Judging a book by it’s cover ▪ Use your representative heuristic to make assumptions about this guy

Overconfidence �Tendency to be more confident than correct- to overestimate the accuracy of our beliefs and judgments

Belief Perseverance �Clinging to one’s initial conceptions after the basis on which they were formed has been discredited

Framing �The way an issue is posed; how an issue is framed can significantly affect decisions and judgments

Decision Making: Evaluating Alternatives and Making Choices �Simon (1957) – theory of bounded rationality �Making Choices Additive strategies Elimination by aspects Risky decision making ▪ Expected value ▪ Subjective utility ▪ Subjective probability

Table 8. 3 Application of the additive model to choosing an apartment

Culture, Cognitive Style, and Problem Solving �Field dependence – relying on external frames of reference �Field independence – relying on internal frames of reference Western cultures inspire field independence Cultural influence based in ecological demands �Holistic vs. analytic cognitive styles

Understanding Pitfalls in Reasoning About Decisions � The gambler’s fallacy Assuming something will happen soon because it’s “due” � Overestimating the improbable More likely to die in an airplane or car? � Confirmation bias Seeking information to confirm what you already believe � The overconfidence effect 98% confidence intervals only right 60% of the time � Framing 10 people are drowning, you can either save 5 of them OR let 5 of them die

Language

The Cognitive Revolution � 19 th Century focus on the mind Introspection �Behaviorist focus on overt responses arguments regarding incomplete picture of human functioning �Empirical study of cognition – 1956 conference Simon and Newell – problem solving Chomsky – new model of language Miller – memory

Language: Turning Thoughts into Words �Properties of Language Symbolic Semantic Generative Structured

Language Acquisition �Innateness Hypothesis- humans are hard-wired to acquire language in a way that mammals cannot �Cultural Transmission Language is learned by its speakers Humans are not pre-programmed to speak a specific language Darwin – language ability is “an instinctive tendency to acquire an art”

The Hierarchical Structure of Language �Phonemes = smallest speech units 100 possible, English – about 40 �Morphemes = smallest unit of meaning 50, 000 in English, root words, prefixes, suffixes �Semantics = meaning of words and word combinations Objects and actions to which words refer �Syntax = a system of rules for arranging words into sentences Different rules for different languages

Language Development: Milestones �Initial vocalizations similar across languages Crying, cooing, babbling � 6 months – babbling sounds begin to resemble surrounding language ▪ Twin Talk � 1 year – first word similar cross-culturally – words for parents receptive vs. expressive language

Table 8. 2 Overview of Typical Language Development

Language Development: Milestones Continued � 18 -24 months – vocabulary spurt fast mapping over and underextensions ▪ Overextension = Child calls all things round “ball” ▪ Underextension = Child uses word “puppy” only in reference to their family pet, fails to recognize other puppies �End of second year – combine words Telegraphic speech = “Me have now!” Mean Length of Utterance (MLU) = # of morphemes �End of third year – complex ideas, plural, past tense Overregularization = “I runned over here fast!”

Bilingualism: Learning More Than One Language �Research findings: Smaller vocabularies in one language, combined vocabularies average Higher scores for middle-class bilingual subjects on cognitive flexibility, analytical reasoning, selective attention, and metalinguistic awareness Slight disadvantage in terms of language processing speed 2 nd languages more easily acquired early in life Greater acculturation facilitates acquisition

Figure 8. 4 Age and second language learning

Critical Period �A span/period of time in one’s life which one must acquire a first language �Full proficiency can never be acquired if no language is acquired during the critical period �Exact cut-off age is not certain but is before puberty �Ex. “Genie” and deaf children born to hearing parents �https: //www. youtube. com/watch? v=hmdyc. JQi 4 Q

Theories of Language Acquisition �Behaviorist Skinner (Verbal Behavior 1957) ▪ learning of specific verbal responses �Nativist Chomsky ▪ learning the rules of language ▪ Language Acquisition Device (LAD) �Interactionist Cognitive, social communication, and emergentist theories

B. F. Skinner v. Noam Chomsky Attempts to explain language development have sparked a spirited intellectual controversy. At the heart of this controversy is the nature-nurture debate. Behaviorist B. F. Skinner believed that we can explain how babies acquire language entirely with principles of learning, such as the association of objects with the sounds of words, the imitation of language modeled by others, and the reinforcement of correct use of words and syntax by parents and teachers. Linguist Noam Chomsky, who favors the nature position, believes that much of our language capacity is inborn. According to this perspective, just as "learning" to walk is programmed according to a timetable of biological maturation, so children are prewired to begin to babble and talk. In this exercise, review each of the following examples of language use by children and decide whether it best supports the position of B. F. Skinner or Noam Chomsky. 1. While Marie and her mother are looking at a book together, Marie's mother shows her a picture of an animal and says "cow. " Marie says "cow, " and her mother praises her for her correct utterance. Two pages later, Marie spontaneously points to a picture and correctly identifies it as a cow. 2. When his day care teacher asks 2 -year-old Jack what he did last Saturday, he responds with "We goed to the zoo. " His teacher smiles, marveling at the fact that all children Jack's age make this type of grammatical error. 3. Nicole, who is deaf and was not exposed to sign language until age 3, lacks the manual linguistic skills of deaf children born to deaf-signing parents. 4. Twelve-year-old Malcolm, who emigrated to the United States at age 4, understands English grammar much better than 20 -year-old Maya, who was first exposed to English at age 12.

Can Animals Develop Language? �Dolphins, sea lions, parrots, chimpanzees Vocal apparatus issue American Sign Language �Allen and Beatrice Gardner (1969) Chimpanzee - Washoe 160 word vocabulary �Sue Savage-Rumbaugh Bonobo chimpanzee - Kanzi Symbols Receptive language – 72% of 660 requests

Perspective Taking: Do Animals Have Language? Few controversies have so divided the scientific community as has the controversy about the apes’ capacity for language. Although many scientists have made serious attempts at rearing apes in language-rich environments, the results have not overwhelmingly demonstrated that apes can use language as human beings us it. At the heart of the argument are the criteria we use to determine true capacity for language. Generally, scientists specializing in the study of language impose the following criteria for the debate: • Is the language symbolic: Can it be used to represent absent objects? • Does the language have systematic syntax, or word order? • Can the language be used in a creative or productive manner?

Figure 8. 5 Interactionist theories of language acquisition