2 Can you solve the following 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 telephone numbers. You select 200 names at random from the Topeka phone book. How many of these can you expect to have unlisted phone numbers?
3 Answers to the Questions #1 There are 2 females ~ Mrs. Thompson & her one daughter, who is the sister to each of her brothers.#2 None ~ you won’t find any unlisted phone numbers in the phone book.
4 Types of Problems Problems of Inducing Structure Require people to discover the relations betweennumbers, words, symbols or ideasAnalogy problemsSeries completion problemsProblems of ArrangementRequire people to arrange the parts of a problem in a way that satisfies some criterion – usually there are many ways, but only a few form a solutionProblems of TransformationRequire people to carry out a sequence of transformations in order to reach a specific goal
5 Problems of Inducing Structure What word completes the analogy?Merchant: Sell :: Customer : ________Lawyer : Client :: Doctor : __________What number or letter completes each series?__A B M C D M __
6 Problems of Arrangement The String ProblemTwo strings have from the ceiling but are too far apart to allow a person to hold one and walk to the other. On the table are a book of matches, a screwdriver, a few pieces of cotton. How could the strings be tied together?InsightSudden discovery of the correct solution following incorrect attempts based primarily on trial & errorOften helps to solve Arrangement Problems
9 Barriers to Effective Problem Solving Irrelevant InformationMany problems include information that is irrelevant to solving the problemLeads people astrayFunctional FixednessThe tendency to perceive an item only in terms of its most common useEx. In the string problem, people see a screwdriver in terms of its most common use, not as a possible weight.Mental SetExists when people persist in using problem-solving strategies that have worked in the pastUnnecessary Constraints
10 Approaches to Problem Solving Working BackwardSearch for AnalogiesForming Sub-goalsUse intermediate stepsChange Representation of the ProblemChange how you see the problemAlgorithmsMethodical, step-by-step procedure for trying all possible alternatives in searching for a solutionEx. Anagram IHCRA – you would list out all the possible arrangements of the lettersHeuristicsA guiding principle or “rule of thumb” used in solving problems or making decisions
11 Try some more problems The Tower of Hanoi – move rings from peg A to peg C. You can only move the top ring on a peg and you can’t place a larger ring above a smaller one
12 Try some more problemsThe water lilies on the surface of a small pond double in area every 24 hours. From the time the first water lily appears until the pond is completely covered takes 60 days. On what day is half of the pond covered with lilies?A teacher had 23 pupils in his class. All but 7 went on a museum trip and thus were away for the day. How many students remained in class that day?
13 Decision MakingEvaluating alternatives & making choices among those alternativesHerbert SimonTheory of Bounded RationalityPeople tend to use simple strategies & focus only on a few facets of available options resulting in “irrational” decisions
14 Selecting an Alternative Elimination by AspectsGradually eliminate less attractive alternativesWhen any alternative fails to satisfy criterion, it is eliminatedAdditive StrategyList personally important attributes then rate choices based on each
15 Which Strategy Do We Use? John Payne (1976)When there are few options with few attributes to evaluate by additive strategiesMore options & more factors elimination by aspectsWe adapt out approach to the demands of the taskTversky & Shafir (1992)We delay our decisions when alternatives are not dramatically differentWe struggle with conflict & so seek out additional info
16 Risky Decision Making Making choices under conditions of uncertainty StrategiesExpected value – extrinsic rewardSubjective utility- intrinsic worthSubjective probability – personal estimates of worth
17 Heuristics in Judgements of Probability Amos Tversky & Daniel KahnemanAvailability HeuristicEstimated probability based on the ease with which relevant instances come to mindEX. Divorce Rate based off of how many of your friends are divorcedRepresentativeness HeuristicEstimated probability based on how similar the event is to the typical prototype of that eventEX. Flipping a coin 6 times1. T T T T T T2. H T T H T H
19 Pitfalls in Reasoning about Decisions Law of Small NumbersMisleading results tend to happen in smaller samples – small samples lead to flukesMisplaced faith in small numbers explains why people are often willing to draw general conclusions based on a few individual casesChance of getting all “heads” flipping a coin 5 times is much better than 100 timesGamblers FallacyOdds of a chance event increase if an event has not happened recently
20 Pitfalls in Reasoning about Decisions Overestimating the ImprobableOverestimation of the dramatic, vivid – but infrequent eventsConfirmation BiasSeeking info that supports your decisions while ignoring disconfirming infoBelief PerseveranceHanging onto beliefs in the face of contradictory evidenceActual Mortality Rates for Causes of DeathAsthma2,000Accidental Falls6,021Tuberculosis400Suicide11,300Tornados25