2Deductive Reasoning Reasoning from the general to the specific For example, start with a general statement: All cars have tires.You can apply this general statement to specific instances and deduce that a Ford Escort, a Toyota Camry, and a Mercedes Benz must have tires.key words: deductive reasoning
3Common deductive reasoning problems Series problemsSyllogismskey words: deductive reasoning; series problems; syllogisms
4Series problems review series of statements arrive at a conclusion not contained in any single statementFor example:Robin is funnier than BillyBilly is funnier than SinbadWhoopi is funnier than BillyQ: Is Whoopi funnier than Sinbadkey words: deductive reasoning; series problems
5SyllogismsPresent two general premises that must be combined to see if a particular conclusion is truekey words: deductive reasoning; syllogisms
6Syllogism ExampleAll Intro to Psychology students love their instructor.You are all Intro to Psychology students.Must you love your instructor?key words: deductive reasoning; syllogismsThis is one example of a syllogism. The next slide contains an alternate example of a syllogism.
7Syllogism Example All chefs are violinists. Mary is a chef. Is Mary a violinist?key words: deductive reasoning; syllogismsThis is one example of a syllogism. Theprevious slide contains an alternate example of a syllogism.
8Ways to solve syllogisms Mental model theoriesPragmatic reasoning theorieskey words: deductive reasoning; syllogisms; mental model theories; pragmatic reasoning theories
9Mental models theories To solve a syllogism, you might visualize the statementsAll Intro to Psychology students love their instructor.Psych-ologyBi-ologyBi-ologyYou are all Intro to Psychology students.key words: deductive reasoning; syllogisms; mental model theoriesThis slide applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theoryThe first set of drawings illustrates that all Intro to Psychology students must love their instructor.The second set of drawings illustrates that students of other disciplines may love their instructor, but they don't necessarily have to love their instructorMust you love your instructor?YES!YES!YES!
10Mental models theories All Intro to Psychology students love their instructor.Psych-ologyYou are all Biology students.Bi-ologyBi-ologykey words: deductive reasoning; syllogisms; mental model theoriesThis slide applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theoryMust you love your instructor?NO!NO!NO!
11Mental models theories Syllogisms that are easy to visualize are more readily solved than more abstract syllogismsPsych-ologykey words: deductive reasoning; syllogisms; mental model theoriesThis slide adds to the information in Slide 9 and applies the mental model theory to the syllogism encountered in Slide 6. If you used the syllogism on Slide 7 as your example, use Slide 11 to illustrate the mental models theory.Bi-ologyBi-ology
12Mental model theoriesTo solve a syllogism, you might visualize the statementsSyllogisms that are easy to visualize are more readily solved than more abstract syllogismskey words: deductive reasoning; syllogisms; mental model theoriesThis slide applies the mental model theory to the syllogism encountered in Slide # 7. If you used the syllogism encountered in Slide #6, then use Slides 9 & 10 to illustrate the mental model theory
13Pragmatic reasoning theories Solve syllogisms by applying information to pre-existing schemasProblem difficulty related to importance of problem to our lives and survival as a speciesMore relevant = easier to solvekey words: deductive reasoning; syllogisms; pragmatic reasoning theories
14Inductive reasoning Reasoning from the specific to the general key words: inductive reasoning
15Inductive reasoning 18 16 14 ?? ?? 12 10 Rule? Decrease by 2 ?? ??1210Rule? Decrease by 2Q: Why inductive reasoning?Answer: Take SPECIFIC numbers (i.e. 18,16,14) and come up with a GENERAL rule (i.e. decrease by 2)key words: inductive reasoning
16Inductive ReasoningSherlock Holmes is perhaps a better example of INDUCTIVE reasoning than deductive reasoningHe takes specific clues and comes up with a general theorykey words: inductive reasoning
17Inductive reasoning problems ?? ??2526?? ?? ??71411?? ?? ??621key words: inductive reasoningAnswers:Problem #1: The rule is add one, add eight, add one, add eight etc. Instead of 25 and 26, some of your students may have also guessed 34 and 35. That is, they may have beeen going by the rule "add one, multiply by two, add on, multiply by two etc." This would be an ideal time to mention to students that one important idea regarding inductive reasoning is that the more information you have, the more certain you can be that your hypothesis is correct. When you are given limited information (such as only giving you 4 numbers in the sequence with this problem), we are increasing the likelihood that the student would come up with an incorect hypothesis.Problem # 2: The rule is " multiply by two, subtract three, multiply by two, subtract three etc."Problem 3: The rule is " divide by decreasing numbers, starting at 6." That is, divide by six, divide by five, divide by four, divide by two. Although an extra space isn't provided in the slide, before revealing the answer, you can also ask the students what the next number should be. The answer is 1 (since 1 divided by 1 = 1).
18Inductive reasoning problems ?? ?? ?? ?? ?? ?? ?? ??2025303540455055Rule?Increase by fiveWRONG!!!!!key words: inductive reasoning; confirmation biasThis slide is about confirmation bias. To prevent being misleading, the intsructor should be very careful with wording. The intsructor should say something like, " Here is another number problem. I want you to shout out answers and raise your hand when you know what the rule is."This problem, on the surface, seems very easy. Virtually all students will come up with the hypothesis " Increase numbers by 5". Notice that every response they give will be a multiple of 5. That is, students will only give responses that confirm their hypothesis. They fail to recognize that the best way to test their hypothesis is to give an answer that violates their hypothesis. For instance, if they said 68 or 124 or 1,989, they would have been told that these responses were also correct. The correct rule for this problem is "any increasing number." By only sticking to multiples of 5, most students arrived at the wrong rule.What is the correct rule?Any increasing number- the next number could be 87 or 62 or 1,000,006Why did everyone guess the wrong rule?
19Confirmation biasOnly search for information confirming one’s hypothesisExample: reading newspaper columnists who agree with our point of view and avoiding those who don’tkey words: inductive reasoning; confirmation bias
20Chris storyChris is 6’7”, 300 pounds, has 12 tattoos, was a champion pro wrestler, owns nine pit bulls and has been arrested for beating a man with a chain.Is Chris more likely to be a man or a woman?A motorcycle gang member or a priest?How did you make your decision?key words: representativeness heuristicThis slide presents a story problem to demonstrate how people will use a representativeness heuristic. Give the students the problem first and then ask them how they arrived at their conclusion. Students will most likely answer that the traits listed seem more characteristic of a man than a woman and of an outlaw motorcycle gang member than a priest.One problem you might encounter is that students might guess what you're trying to do and might try to give the answer they think you're looking for (i.e. they might say Chris is more likely to be a woman or a priest if they think that's what you want them to say.) Before asking students to give their answer, you might want to tell students to give their gut response, rather than trying to overthink the problem.
21Steve storySteve is meek and tidy, has a passion for detail, is helpful to people, but has little real interest in people or real-world issues.Is Steve more likely to be a librarian or a salesperson?How did you come to your answer?key words: representativeness heuristicThis slide presents a second story problem that demonstrates how people will use a representativeness heuristic. Give the students the problem first and then ask them how they arrived at their conclusion. Students will most likely answer that the traits listed seem more characteristic of a librarian than a salesman.Again, one problem you might encounter is that students might guess what you're trying to do and might try to give the answer they think you're looking for (i.e. they might say Steve is more likely to be a salesman than a librarian if they think that's what you want them to say). Before asking students to give their answer, you might want to tell students to give their gut response, rather than trying to overthink the problem.The next slide contains a second example of a how students might use a representativeness heuristic
22RepresentativenessJudge probability of an event based on how it matches a prototypeCan be goodBut can also lead to errorsMost will overuse representativenessi.e. Steve’s description fits our vision of a librariankey words: representativeness heuristic
23Most will underuse base rates Base rate - probability that an event will occur or fall into a certain categoryDid you stop to consider that there are a lot more salespeople in the world than librarians?By sheer statistics, there is a greatly likelihood that Steve is a salesperson.But very few take this into accountkey words: base rates
24Guess the probabilities How many people die each year from:Heart disease?Floods?Plane crashes?Asthma?Tornados?Stopkey words: availability biasThe purpose of this demo is to show that people will, in general, dramatically overestimate the number of deaths from natural disasters or accidents and underestimate deaths from asthma. Most people will say that more people die each year from floods or tornados or plane crashes than asthma - even though approximately 16 times as many people in the US die from asthma each year than die from floods, tornados and plane crashes combined.Approximate death rates per year in the US for the following:1. Heart disease: 960,5922. Flash floods: 1083. Plane crashes: 1474. Asthma: 5,0005. Tornados: 52Heart Disease:- According to the the American Heart Association, 960,592 people in the US died of heart disease in In 1993, the death rate from heart disease was 954,138.- Heart disease information was obtained at the following websites: 1) )3)Flash Floods:- The 108/year death rate from flash floods represents the average deaths per year in the US during the 1980's. From , a total of 1,083 people died as the result of flash floods.- In the state of Ohio, from , a total of 368 people died during flash flooding.- This data was obtained at the following website:Plane crashes:- The 147/year death rate from plane crashes reflects an average of fatalities from The number of deaths vary year to year (from lows of 0 deaths in 1993 and 1 in 1984 to highs of 319 in 1996 and 486 in 1985).- The 147/year death rate from plane crashes only represents fatalities of the major US air carriers. It does not include fatalities from commuter plane crashes (approximately fatalities per year) or from non-commercial flights of smaller planes.- This data was obtained from the website of the National Transportation safety Board at- An important point ot bring up is that, although 147/year mortality rate may seem high, it accounts for an extremely small percentage of fliers. For instance, in 1997 there were only 2 fatalities out of 625 million passengers ( % of all passengers) who boarded flights of the major US carriers.- This is an interesting statistic to bring up to your class. People who have a fear of flying will often feel flying is more dangerous than driving a car because planes crashes are more heavily reported on national news and in national newspapers and magazines (that is, they are falling prey to an availability bia). However, they will underestimate base rates (that statistically, driving isactually more dangerous than flying)Asthma:- According to the Dec. 8, 1994 issue of the New England Journal of Medicine, in the US, approximately 5,000 people die each year from asthma- This information was obtained at the following websites:1) 2)3)Tornados:The 108/year death rate from tornados represents the average deaths per year in the US during the 1980's. From , a total of 521 people died as the result of tornados.- In the state of Ohio, from , a total of 171 people died during tornados.Although not currently represented on this slide, you might choose to add any of the following:Lightning:- Approximately 73 people per year- The 73/year death rate from lightning represents the average deaths per year in the US during the 1980's. From , a total of 726 people died as the result of lightning.Diabetes: approximately 187,880 deaths per year in the USCancer: approximately 500,000 deaths per year in the USThe diabetes and cancer statistics were obtained from the Center for Disease Control at the following website:
25Availability heuristic Judge probability of an event by how easy you can recall previous occurrences of that event.Most will overestimate deaths from natural disasters because disasters are frequently on TVMost will underestimate deaths from asthma because they don’t make the local newskey words: availability heuristic
26Word probabilitiesIs the letter “k” most likely to occur in the first position of a word or the third position?Answer: “k” is 2-3 times more likely to be in the third positionWhy does this occur?key words: availability heuristicThis is another demonstration of the availability bias at work.
27Class demonstration Name words starting with “k” Name words with the letter “k” in the third positionkey words: availability heuristic
28Availability heuristic Because it is easier to recall words starting with “k” , people overestimate the number of words starting with “k”key words: availability heuristic
29Finish the sequence problems ?? ?? ??126Rule?Decrease by six?? ?? ?? ??3546key words: inductive reasoning; mental sets; problem solvingThis slide gives some more inductive reasoning problems. However, the purpose is not merely to demonstrate inductive reasoning. Rather, the purpose is to set up a demonstration of how mental set can prevent you from solving problems.The two problems on this slide can be solved by applying a mathematical formula to the problems. However, if you try to solve the problem on the next slide by using a mathematical formula, you will never come up with the solution. To solve the problem on the next slide, you have to break out of your mental set and look at the problem from a new angle.Rule?Increase by two, decrease by 1
30Finish the sequence problems ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??1320212229303132392002012993003013023992000Rule?Increasing numbers starting with the letter “t”key words: inductive reasoning; mental sets; problem solving- To solve this problem, you have to break out of the mental set.- Before revealing the true purpose of this slide (i.e. a demo of the megative effects of mental set ) I generally will go through the next 5 slides which give more examples of problems that require a person to break out of a mental set to come up with the correct solution. After going through the slides, I then generally ask people why they weren't able to come up with the solutions. Students will generally give an answer that segues into the discussion of mental set.
31Chess problemTwo grandmasters played five games of chess. Each won the same number of games and lost the same number of games. There were no draws in any of the games. How could this be so?Solution: They didn’t play against each other.key words: mental sets; problem solving
32Bar problemA man walked into a bar and asked for a drink. The man behind the bar pulled out a gun and shot the man. Why should that be so?Solution: The man behind the bar wasn’t a bartender. He was a robber.key words: mental sets; problem solving
33Bar problem # 2A man who wanted a drink walked into a bar. Before he could say a word he was knocked unconscious. Why?Solution: He walked into an iron bar, not a drinking establishment.key words: mental sets; problem solving
34Nine dots problemWithout lifting your pencil or re-tracing any line, draw four straight lines that connect all nine dotskey words: mental sets; problem solving; nine dots problem
35Answer to nine dots problem key words: mental sets; problem solving; nine dots problem
36Metal Set Q: Why couldn’t you solve the previous problems? A: Mental set - a well-established habit of perception or thought
37Strategies for solving problems 1. Break mental setskey words: mental sets; problem solving
38Number problem mental set ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??1320212229303132392002012993003013023992000Most people get stuck in the same rhythmOnly view problems in terms of math formulasNeed to break out of this mental set to solve the problemkey words: mental sets; problem solving
39Nine dots mental setMost people will not draw lines that extend from the square formed by the nine dotsTo solve the problem, you have to break your mental setkey words: mental sets; problem solving; nine dots problem
40Mounting candle problem Using only the objects present on the right, attach the candle to the bulletin board in such a way that the candle can be lit and will burn properlykey words: functional fixedness, mental set; problem solvingAlthough students can work on this problem by simply thinking and visualizing a solution in their heads, this demonstration works better by by bringing the actual materials to class and doing a live demonstration with your students, letting them attemtp to solve the problem through trial and error.To do this task you need the folllowing materials:1. a cork bulletin board2. a book of matches3. a candle4. a BOX of thumbtacks- make sure you keep the thumbtacks in a BOX- also make sure the thumbtacks aren't too big that they can pass through your candle. The smaller the thumb tack, the better
41Answer to candle problem Most people do not think of using the box for anything other than it’s normal use (to hold the tacks)To solve the problem, you have to overcome functional fixednesskey words: functional fixedness; mental sets; problem solving
42Functional fixedness type of mental set inability to see an object as having a function other than its usual onekey words: functional fixedness; mental set; problem solvingSome examples of overcoming functional fixedness include:1. Using a dime to unscrew something when a screwdriver cannot be found.2. Using a book to prop open a door when a doorstop cannot be found.3. Before a baseball game, a rainstorm occurred. They wanted to dry the field a little before beginning play, so they had a helicopter hover above the field, and the rotating helicopter blades acted as a fan and helped dry up the field.
44Find useful analogyCompare unknown problem to a situation you are more familiar withKey words: analogies; problem solvingFor example, let's say you come across someone who has been in an accident and is bleeding badly. You've never had any medical experience at all, but still have to do something to help the person live. You think back to a similar problem at your home when a faucet burst, causing water to go everywhere. The first thing you did at home was to put your thumb up to the faucet to stop the leak. So, you might try to apply direct pressure on the person's wound to stop the bleeding. Unfortunately, just as with the leaking faucte at home, direct pressure does not stop the bleeding. Now, you have to think of what top do next. At home, you realized that you had to turn off the water to the house. Applying this to the current situation, you decide to apply a tourniquet to stop the bloodflow. You find that, just as at home with the lekay faucet, this does the trick and the person is no longer bleeding. Now what do you do with the person? Well, at home, you realized that the water had to be turned on eventually, just as the tourniquet will eventually have to be removed. At home, you called a plumber or other professional to provide a more long-term fix. Applying this to the new situation, you decide to call an ambulance to take care of the accident victim.
45Strategies for solving problems 1. Break mental sets2. Find useful analogy3. Represent information efficiently4. Find shortcuts (use heuristics)key words: functional fixedness; mental sets; problem solving; finding analogies; shortcuts; heuristics
46Two general classes of rules for problem solving 1. Algorithms2. Heuristicskey words: problem solving; finding analogies; shortcuts; heuristics; algorithms
47Two general classes of rules for problem solving Algorithms - things the vice-president might sayAlgorithms - rules that, if followed correctly, will eventually solve the problemkey words: algorithms; problem solvingGive students the chance to write down the definition before reading it aloud to them. The purpose is to see how many students will write down the whole definition before realizing it is a bogus definition. How does this relate to algorithms? Well, assume a student's problem is that they want to do well and get an "A" in their Introduction to Psychology class. Now, if they memorized absolutely everything in the text book and wrote down and memorized each and every single word you said in class, they would most likely get an "A". This is a safe, sure way - an algorithm. However, this can lead to a lot of wasted effort. For instance, you might be writing down a lot of notes (such as the bogus definition) that will not appear on an exam. Also, unlike a computer which can readily process vast quantities of information, a task of this nature in not as feasible in a human.Instead, a student might choose to use a heuristic. For instance, always wait 20 seconds before writing down notes or don't write down the intructor's jokes and amusing anectdotes from the instructor's childhood that have no relevance to the lecture material.
48An algorithm exampleProblem: List all the words in the English language that start with the letter “q”If using an algorithm, would have to go through every single possible letter combination and determine if it were a wordi.e. is “qa” a word; is “qb” a word etc.This would take a very long timeInstead, what rule could you use to eliminate these steps?key words: algorithms; problem solving
49Rules for “q” problem Skip ahead and assume the second letter is a “u” Assume the third letter has to be a vowelThese types of rules are called heuristicskey words: algorithms; problem solving; heuristics
50HeuristicsAny rule that allows one to reduce the number of operations that are tried in problem solvinga.k.a rules of thumb or shortcutsAnother common heuristic:Problem: List all the numbers from 1-100,000 that are evenly divisible by 5Answer: Rather than divide each and every number, you would use the rule: Any number ending in 0 or 5 is evenly divisible by 5.key words: heuristic; problem solving; shortcutsAlso see speaker notes for slide 46 for another example of a heuristic
51Strategies for solving problems 1. Break mental sets2. Find useful analogy3. Represent information efficiently4. Find shortcuts5. Establish subgoals6. Turn ill-defined problems into well-defined problemskey words: functional fixedness; mental sets; problem solving; finding analogies; shortcuts; heuristics; subgoals; ill-defined problems; well-defined problems