Introduction to psychology/Psy102/Tutorials/Cognitive processes and intelligence/Full problems
Bat and ball: Limits of intuition
Frederick (cited by Kahneman, 2003) suggests a simple puzzle to demonstrate the limits of everyday intuition:
- Question: “A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?”
- Most people report an initial tendency to answer “10 cents” because the sum $1.10 separates easily into $1 and 10 cents and because 10 cents is about the right magnitude.
- Frederick reported that 50 percent of Princeton students and 56 percent of University of Michigan students gave this wrong answer.
- Simple subtraction convinces students of their error: $1.00 for the bat – $0.10 for the ball = $0.90, not $1.00. The correct answer is $1.05 for the bat, $0.05 for the ball.
- What's going on? Why?
Train stations: Mental set
This exercise illustrates the limitations of having a mental set. A mental set refers to an approach to problem solving which you have learnt from past experience. If we are presented with a different kind of problem, our mental set is likely to be used and we have difficulty finding an answer.
Ask students to get out a pen and paper which they will need in order to solve a problem. Then read the following narrative slowly, pausing between numbers and sentences:
After reading the story, ask students to write down answers to the following questions:
- How old is the engineer of the train?
- How many stations were there?
- How many passengers are left on the train?
- Altogether, how many passengers have disembarked the train since the first station?
- Altogether, how many passengers have boarded the train along its route.
- 1st question might startle a lot of students who might claim it is unanswerable, but just repeat the first sentence and they will groan.
- 2nd question will be difficult unless they have heard the problem before. We are so busy attending to changes in the number of passengers that we don’t attend to the stop themselves (mental set).
- 3rd question - most will get correct as their mental set had them continually processing passenger total.
- 4th and 5th questions - will probably be missed because the students will have kept to one “set” ie keeping track of the revelant quantities.
- It is almost impossible to process all the information needed to answer the questions because we have a limited capacity to store and process new material. Keeping track of more than one or two of the relevant figures creates information overload, so we tend to use specific strategies that have worked in the past.
- Consider that this mental sets and our limited information processing capacity relates to many other aspects of psychology, e.g., eyewitness testimony and intelligence testing.
Linda: Representativeness heuristic
Read the following to students:
|“||Linda is 31, single, outspoken, and very bright. She majored in philosophy at university. As a student, she was deeply concerned with discrimination and other social issues, and she participated in antinuclear demonstrations.||”|
Then ask them to indicate whether they think statement 1 or statement 2 is more likely.
- Linda is a bank teller.
- Linda is a bank teller and active in the feminist movement.
Did the majority choose statement 2? Ask them why and get them to discuss it.
We tend to judge the likelihood of things in terms of how well they seem to represent or match a particular prototype. While “representativeness” works much of the time, it leads to errors when its conclusion runs counter to the laws of chance. You can explain that the probability of any two uncertain events occurring together (i.e., being a bank teller and being active in the feminist movement) is always less than the odds of either happening alone.
Buddhist monk problem
Read the following problem to students and encourage them to discuss how they might solve it.
|“||One morning at sunrise a Buddhist monk began to climb a mountain on a narrow path that wound around it. He climbed at a steady 3 miles per hour. After 12 hours he reached the top where there was a temple and remained there to meditate for several days. Then, at sunrise he started down the same path, walking at a steady 5 miles an hour. Prove that there must be a spot along the same path which he occupied on both trips at exactly the same time of day.||”|
|— Duncker, 1945|
The Buddhist monk problem demonstrates how some problems are most easily solved by representing them graphically or visually rather than trying to work it out mathematically.
Graphically, try drawing this as one monk climbing and one monk descending (from side-on - altitude is the Y axis and time is the X axis). At same point, the lines (paths) must cross. Visually we can't tell at exactly what time, but the question simply asks to prove that there must be a spot he occupied at the same time on both trips. Regardless of the two monks' walking rates, the two paths would have to have cross at some point. Now simply pretend these two trips happened on two separate days – the monk was at a same spot on the path at precisely the same time of day for both trips. To view a graph, see Slide 8 of this powerpoint file
Source: Figure from Cognition (4th ed.), by Margaret Matlin, p. 352.
- Distribute the truth/lie handout to students and explain you are going to test their ability to distinguish truth from lies.
- Explain that you have put 10 slips of paper in an envelope, 5 of which say “tell the truth” and 5 of which say “tell a lie”.
- Get 10 volunteers to take a slip each and not to let other students know which they have.
- For each topic, select a volunteer from one of the 10 with the slips of paper, and get that student to stand up and tell his/her truth or lie. The remainder of the students write down whether they thought it was the truth or a lie and how confident they are (0 – 100%). When all the stories are told, the volunteers reveal which statements were truthful and which were lies.
- Then get students to compute the number they got correct out of 10, and their average confidence level (you might have to explain how to do this).
- Then ask how many were more correct than confident (should only be a few) and then how many were more confident than correct (should be the majority). If students just guessed the answers, they should be right 50% of the time because half were telling the truth and half were lying.
- This demonstrates our tendency to overestimate the accuracy of our current knowledge.
- Milojkovic and Ross reported their Stanford students were 52% correct and 73% confident – similar to the levels achieved using these materials. Milojkovic and Ross also report that when people were 90 to 100% confident, they were no more correct than when they were only 50 to 65% confident.
- See also overconfidence effect (Wikipedia)
What is intelligence?
- Invite the class to define intelligence (this should be difficult - try to elicit different types of definitions, looking for common themes). Some ideas which may come up:
- Knowledge? (Debatable - although this was commonly tested esp. in earlier IQ tests)
- What IQ tests measures (A somewhat cynical, circular definition)
- Mental speed, accuracy, efficiency, and underlying capacity to solve problems
- One intelligence - or many?
- Intelligence is a subset of cognition - i.e., those cognitive processes which combine to form mental ability to solve different kinds of problems
- Intelligence is the single most tested/measured psychological quality (with personality not far behind) - study and testing of intelligence it has also played an important role in psychology becoming a science
- But intelligence testing is fraught with potential dangers, problems, and controversies - more about this in the lecture next week...
Clear desks and tables to the side, then ask the class to line-up in order of how much they believe each of the following (ask some people for each line-up where they sit and why):
- Intelligence is due to nature vs. nurture
- Intelligence is single vs. plural (single, general underlying ability (g) vs. multiple, distinct abilities (multiple intelligences))
- Intelligence is speed of processing vs. knowledge you have
- Intelligence is related to whether one was breast-fed or not
- Intelligence is increased by school attendance school vs. not related to school attendance
- IQ is stable vs. rising
- Intelligence predicts or doesn't predict income.
- Intelligence can vs. cannot be artificially created (artificial intelligence).
- IQ is affected by diet vs. is not affected
- IQ is associated with some simple abilities. No one with measurable IQ has difficulty deciding which of two lines is longer or whether two pairs of letters are identical. However, in order to perform these simple tasks, a person with an IQ below 70 may need up to five times longer than an individual with a higher IQ. The nervous systems of those with low IQs are simply less efficient.
- School attendance correlates with IQ. Staying in school can elevate IQ or, more accurately, keep it from slipping. Evidence for this dates back to the turn of the twentieth century when the London Board of Education found that the IQs of children in the same family decreased from the youngest to the oldest. The older children progressively missed more school. Toward the end of the Vietnam War, a lottery determined draft priority. Those men born on July 9, 1951, were picked first so they tended to stay in school longer in order to avoid the draft. Those men born July 7 were last in the lottery and thus had no incentive to stay in school. Men born on July 9 had higher IQs and also earned 7 percent more money. Summer vacations also seem to affect IQ. With each passing month, children’s end-of-year scores decline.
- IQ is not influenced by birth order. The idea that birth order influences personality and intelligence has not stood up under recent scrutiny. Moreover, the claim that large families make low-IQ children may be unfounded because researchers have found that low-IQ parents make large families. Smart people tend to have small families, but it is not small families per se that make people smart.
- IQ is related to breast-feeding. Even when researchers control for factors such as the sense of closeness mother and child experience through nursing, breast-fed children appear to have an IQ of 3 to 8 points higher by age 3.
- IQ varies by birth date. State policies mandate the age of students entering school as well the age they may leave, typically 16 or 17. Those born in the final three months of the year are more likely to enter school a year later; thus, when they leave school, they have been attending one year less. For each year of school completed, there is an IQ gain of approximately 3.5 points. Unsurprisingly, as a group, those born later in the year show a lower IQ score.
- IQ evens out with age. Imagine, suggests Ceci, two biological siblings adopted by two different middle class families, at age 5 and again in early adulthood. Are their IQs more alike when younger and living in the homes of their adoptive parents or when they are older and living on their own? Contrary to expectation, as the siblings go out on their own, their IQ scores become more similar. The probable reason is that once they are away from the dictates of their adoptive parents, they are free to let their genotypes express themselves. Because they share about 50 percent of their genes, they will become more alike because they are likely to seek similar sorts of environments.
- Intelligence is plural, not singular. Regardless of their views of so-called general intelligence, researchers agree that there are statistically independent mental abilities such as spatial, verbal, analytical, and practical intelligence. Howard Gardner is, of course, a primary proponent of multiple intelligences theory.
- IQ is correlated with head size. Modern neuroimaging techniques demonstrate that cranial volume is correlated with IQ. Evidence also comes from studies of the helmet sizes of members of the Armed Forces whose IQs were measured during basic training. Correlations are quite small.
- Intelligence scores are predictive of real-world outcomes. Even among those with comparable levels of schooling, the greater a person’s intellectual ability, the higher the person’s weekly earnings. Those with the lowest levels of intellectual ability earn only two-thirds the amount workers at the highest level earn.
- Intelligence depends on context. In visiting racetracks, researchers found that some men were excellent handicappers while others were not. A complex mental algorithm that was used to convert racing data from the racing programs sold at the track distinguished experts from nonexperts. However, the use of the algorithm was unrelated to the men’s IQ scores. Some experts were dockworkers with IQs in the 80s, but they reasoned far more complexly at the track than all nonexperts, even those with IQs above 120. At the same time, the experts performed very poorly at reasoning outside the track.
- IQ is going up. IQ has risen about 20 points with every generation, an increase called the "Flynn effect," after New Zealand political scientist James Flynn. The rise in IQ has been attributed to better nutrition, more schooling, and better-educated parents.
- IQ may be influenced by the school cafeteria menu. In one large study, 1 million students enrolled in the New York City school system were examined before and after preservatives, dyes, colorings, and artificial flavors were removed from lunch offerings. The investigators found a 14 percent improvement in IQ after the removal. Improvement was greatest for the weakest students.
World War I IQ Test
- WWI Army Intelligence Test - Answers
- Note that an intelligence test does not measure drive, persistence, creativity or any of the myriad other skills that often count for more in achieving success out of school.
- A low score on an IQ test does not mean probable failure in life. All it means is that the person taking the test did poorly on that particular test. If the score is a valid reflection of cognitive ability, then the person will probably find particularly complex cognitive tasks harder than "normal".
- However, most of us do not spend our lives in situations that can be easily measured by paper-and-pencil tests. Thus, scores obtained on such tests should be viewed with some restraint and skepticism, particular if they are high or low.
- IQ tests measure only one aspect of overall "life skill".
Chitling test of intelligence
- Handout out the The Chitling Test of Intelligence - ask students to complete and then score according to this answers.
- Formally the Dove Counterbalance General Intelligence Test, the Chitling Test of Intelligence was designed by Adrian Dove, an African-American sociologist, as a half-serious attempt to show that IQ tests are culturally biased in part due to American children are just not all speaking the same language.
- Ceci, S. J. (2001). Intelligence: The surprising truth. Psychology Today, July-August, 46-53.
- Dove, A. 'The "Chitling" Test. From Lewis R. Aiken, Jr. (1971). Psychological and educational testings. Boston: Allyn and Bacon.