Why girls drop math II: Who wants to be alone?

We know that girls are less likely to go into math and “hard science” careers than boys.  There are lots of reactions people have to this news.  Some, like Lawrence Summers (who became the former president of Harvard in large part because this remark in 2005) suggested that women may not have the same innate abilities in math as men.  Others suggest that the school system is somehow failing girls in school.  Still others are concerned about social pressure that girls might feel to shy away from looking smart when there are boys around.

These last two ideas have some traction in popular and political culture.  There has been movement to create all-girls’ schools to give girls an environment to thrive.  Indeed, my home town of Austin Texas has a public all-girls school (named after former Texas governor Ann Richards).  I think there is much to like about the idea about an all-girls school for middle-schoolers.  One question we should ask, though, is whether the mass exodus of girls from math (and to some degree hard sciences) is being caused by a failure of the educational system.

Psychologist Jacquelynne Eccles has studied this question extensively.  One of her more surprising findings is that girls tend to attach less value to math than boys.  There are a few sources of the difference in value that boys and girls place on math.

For one, parents may give their children beliefs about how important math ought to be to them.  Eccles’ evidence suggests that girls are less likely to value math and to take advanced math courses when their parents do not believe that math is as important for girls as it is for boys.  So, girls are internalizing the beliefs of their parents.

For another, there is a pervasive stereotype that mathematicians lead a lonely existence.  When we think about mathematicians, we imagine the lone genius hunched over a desk writing incomprehensible formulas that have lots of Greek letters in them.  On occasion, these lonely figures may emerge from their cramped messy dens to shout Eureka and post the solution to a problem that five people in the world care about on a blackboard in a university hallway. 

Girls find this prospect much less appealing than boys.  Girls are much more likely than boys to state that want a career that has lots of social interaction as a part of it.  When girls start making decisions about the classes they are going to take, they are much more likely to gravitate toward sciences like biology and psychology than toward math, chemistry or physics.  Biology usually leads to pre-medical study in college, and the medical professions are seen as very social.  Likewise, psychology, social work, and other helping professions are seen as social. 

This research suggests that one big reason why girls are less likely to stick with math than boys is a difference in life goals. 

The big question, then, is whether the stereotype about math and the hard sciences is true.  In fact, much of modern science is highly collaborative.  Scientists must find ways to work together to solve difficult problems.  The myth of the lone scientist is just that—a myth.  And that means that science has a public relations job to do.  If we want more girls to go into math and science professions, we are going to need to do more work letting girls know what those careers will really involve. 

I do want to be clear about one thing, though.  There are lots of reasons to think that some girls will be more likely to succeed in a school environment without boys.  So, I am not suggesting that we close all-girl schools.  I am suggesting that the reason to open such schools is not because our current schools are failing to give a good math and science education to girls.  However, we might use venues like all-girl schools to start the process of teaching girls more about what careers are possible with a good math and science education.

Why girls drop math I: Beliefs about Math

Here in Texas, it may be 105 degrees, but marching band practice started, and there have been orientations at my kids’ schools, so it must be time for them to go back.  That got me thinking about a big problem in math and science education.  In elementary school, boys and girls are about even in their performance in math and science.  By middle school, girls start to lag behind, and few women go on to pursue math in college.  What is going on?

There are lots of answers to this question, but I’ll explore a few over the next week.  Think of this as the back-to-school portion of the blog.

One factor that leads girls to drop math is that boys and girls seem to differ in their beliefs about math.  Psychologist Carol Dweck (author of the fantastic book Mindset) argues that people can have two different sets of beliefs (or mindsets) toward academic topics.  

Entity theorists treat academic topics as if they were talents.  You either have them or you don’t.  So, you could be good at math or bad at math.  If you’re good at math, then you’ll learn it.  If you’re bad at math, then at some point, you’ll reach a type of math that goes beyond your abilities.

Incremental theorists treat math as a skill to be acquired.  Stick with math, and eventually you’ll get even the really hard stuff.

Dweck and her colleagues find that people who treat math (or any other academic subject) as a skill will stick with it longer and try harder when it gets difficult than when they treat it as a talent. 

The way this affects boys and girls is that Dweck has collected evidence that boys and girls get different feedback about math from early on in their schooling.  Eventually, everyone hits a topic in math that they struggle with.  When talking to girls, teachers are likely to emphasize that math is hard.  Talking about math as being difficult makes it sound like something that either you can do or you can’t.

Boys tend to get feedback that treats math as a skill to be acquired.  When they hit a hard topic, they are told to try harder and they’ll eventually get it. 

Because girls are more likely than boys to get feedback that treats math as a talent, they are more likely to end up with an entity theory of math.  The truly hard stuff in math comes in middle school, when kids are first exposed to algebra and geometry and later trigonometry and calculus.  Eventually, one of these topics is going to derail everyone, at least for a while.  Because of their beliefs about math, then, girls are more likely than boys to conclude that they have reached the limits of their talent and give up.

That isn’t the whole story, of course, and I’ll pick up on this in my next post.

How do we decide whether you are to blame?

There are lots of situations in which we have to assign blame for an event to a particular person or group of individuals.  Much of the daily newspaper is devoted to deciding who caused events to occur.  Wars may be caused by the actions of a government.  A suspect may be the cause of a series of bank robberies.  A particular player may be given the blame for the loss of a football game.

Assigning blame is particularly important for the legal system.  In order for people to be found guilty of a crime, a jury has to believe that they are responsible for that crime.  And the worst of the crimes are those for which the suspect committed the crime and meant to do it.  For example, the most serious murder cases are those for which the killer meant to kill someone and then carried through the plan.  So, the thoughts of the suspect matter in people’s judgments of guilt.

The role of the perpetrator’s thoughts at the time they committed the crime in assigning blame was examined in paper by Jason Plaks, Nicole McNichols, and Jennifer Fortune in the December, 2009 issue of Personality and Social Psychology Bulletin. 

They examined two kinds of intentions that someone might have to commit a crime that differ in how abstract or specific they are.  Distal intentions are abstract or general commitments to perform an action.  For example, a particular person, J.G. may stand to inherit money from his uncle.  So, he may want to kill his uncle.  That is a distal intention, because killing is a relatively abstract concept.  Proximal intentions are specific commitments to a particular plan.  For example, J.G. may want to run his uncle down with a car.  That is a specific method of trying to kill him.

These researchers were interested in how much a suspect’s thoughts while they committed a crime affected people’s judgments of blame.  They found that in normal situations, both distal intentions and proximal intentions affect people’s judgments of how much someone is to blame for a crime.  To test this idea, they created a series of scenarios and had people decide how strongly a person (J.G.) was to blame for the action.  In all of these scenarios, J.G. wanted to kill his uncle by running him down with his car. 

In the story with both distal and proximal intent, J.G. indeed did run his uncle down with the car and killed him.  In the story with only distal intent, J.G. was thinking about killing his uncle, when his uncle unexpected stepped out in front of the car while J.G. was driving and he killed him.  In the story with only proximal intent, J.G. was trying to keep himself calm by concentrating on the song on the radio, when suddenly he saw his uncle crossing the street and ran him down.  In the story with neither intent, J.G. was concentrating on his favorite song to keep himself calm, and then his uncle stepped unexpectedly into the street and J.G. hit him and killed him. 

People read only one of these four scenarios.  They thought J.G. was most to blame when he had both the distal and proximal and distal intent in mind.  He was least to blame when he had neither to blame when he hit is uncle.  When he had either distal or proximal intent in mind but not both, there was a middle level of blame.

Interestingly, factors that affect how abstractly people think about situations also affected how strongly they weighted proximal or distal intentions.  As one example, lots of research suggests that when we think about events that are far away in time, we tend to think about them more abstractly than when we think about events that are close in time. 

In a second study, people read scenarios like the J.G. story, but were either told that the event had taken place a few weeks before or 75 years before.  The researchers expected that people would think about the situation more abstractly when it took place 75 years ago than when it took place recently.  Consistent with this idea, when the event took place 75 years ago, people thought the distal intent was most important for assigning blame.  For them, the killer was nearly equally to blame when he had the distal intent in mind regardless of whether he also had the proximal intent in mind.  When the event took place a few weeks earlier, though, then the proximal intent mattered most.  The killer was nearly equally to blame when he had the proximal intent in mind regardless of whether he also had the distal intent in mind. 

There are a few interesting conclusions to draw from this work.  First (and not that surprisingly) we think that a person’s intentions matter when they perform an action such as committing a crime.  Second, general factors that affect the way people represent situations have a big effect on the way they assign blame.  In the second study here, increasing the distance in time between the event and the assignment of blame changed the factors people used to assign blame. 

This has interesting implications for the legal system.  A suspect in the United States is supposed to get a speedy trial, though court proceedings can sometimes drag on for years.  If a suspect is tried soon after a crime was committed, then the suspect’s proximal intent may have more influence than the suspect’s distal intent on a jury’s judgment of guilt.  On the other hand, if a suspect is tried a long time after the crime is committed, then the suspect’s distal intent may have more influence than the proximal intent on judgments of guilt. 

Doing good requires hard work. So does feeling good about it.

There is a lot of psychology research suggesting that people prefer objects that are easy to think about than those that are hard to think about.  For example, the classic “mere exposure” effect shows that people generally prefer objects they have seen before to those that they have never seen before.  This preference arises, because it is easier for people to think about an object they have encountered before than an object that is new to them.

One explanation for the mere exposure effect is that ease of thinking causes high preference directly.  That is, there may be a biologically hard-wired connection between liking and ease of thinking. 

An article by Aparna Labroo and Sara Kim in the January, 2009 issue of Psychological Science suggests a different explanation.  Their work suggests that the ease of thinking about something is a piece of information that becomes part of the way an object is evaluated.  Under some circumstances, greater ease of thinking about an object may actually decrease people’s preference for that object.

In particular, when people are trying to satisfy an important goal, they have what Labroo and Kim call an instrumentality heuristic. People believe that a goal worth carrying out is worth working hard at.  Good things require effort.  In these situations, people actually seem to prefer objects that are hard to process.

In one clever experiment, participants were asked to evaluate whether they wanted to give a real donation to the charity Kids in Danger.  This charity promotes safety in children’s products, and was created by psychologist Boaz Keysar and his wife Linda Ginzel after one of their children was killed in a tragic accident involving a portable crib that had a design flaw.  People giving to this charity often feel that they are doing a good deed.

In this study, information about the charity was presented on a computer screen either in a font that was presented clearly on the screen or with a font that was hard to read.  In typical experiments on ease of thinking, products whose descriptions are easy to read are preferred to products whose descriptions are hard to read.  In this experiment, though, because the goal of doing good is associated with effort, people were actually more likely to give to the charity when the description was hard to read than when it was easy to read.  The difficulty of reading the description matched with people’s believes that pursuing an important goal requires effort.

More generally, this finding demonstrates that factors like the ease of thinking about an object can affect preferences for that object, but they do so by providing an additional piece of information about that object.  Whether ease of thinking increases or decreases people’s preferences depends on their goal in making a decision.

Vice, virtue, and the box office.

It is summertime, and the movie studios trot out their summer blockbusters and comedies.  That’s what summer is all about.  In Texas, when it gets to be 102 outside, sitting in an air-conditioned movie theater is not such a bad thing.  But why are people flocking to movies that are clearly so awful.  The poster-child for awful movies this year is Transformers: Dark of the Moon.  The reviews of this movie are uniformly terrible, but the film has already done over $300 million in sales in the United States alone.  What gives?

We could assume that the critics are all just wrong.  But that doesn’t seem to be a complete explanation.  Everyone I know who saw this movie says it was a confused mass of metal.  So the hordes going to the movie must reflect something more basic about the way people make decisions.

The success of summer movies rests on what the behavioral economist George Loewenstein called vices  and virtues.  He’s not talking about the themes of movies here, but about the way people make their choice about the movie they want to see.  The vices in movies are all about the enjoyment.  The virtues are all about the value of the experience of seeing the movie.

Some of the vices in movies are thrills.  Car chases, explosions, and action heroes mowing down endless rows of evildoers are all vices.  Neatly-tied emotional experiences are vices as well.  The standard boy-meets-girl, boy-loses-girl, boy-gets-girl plot of the standard romantic comedy is a vice.  We know by the closing credits the two beautiful stars will be locked in a kiss.  Familiarity is also a vice.  We are far more comfortable with remakes, sequels, and movies that come from familiar TV shows and toys than with things that are new.

Virtues are things that add value to the movie-going experience.  Learning something new is a virtue.  (Documentaries—even well-made documentaries—are chock-full of virtue.)  A complex emotional experience is a virtue.  Grappling with real-world issues is a virtue.  Movies with virtues are satisfying both in the theater and also long afterward.

Loewenstein suggests that people recognize the value of virtues, but when they are actually at the theater ready to buy a ticket, they invariably fall back on vices.  In one study, he gave people a coupon good for a free rental of a movie that they could pick up either that night or the next week.  They had to select the movie they wanted when they selected the coupon. They were given the choice of a virtue movie (Schindler’s List—a movie about the holocaust) or a vice movie (a low-brow comedy).  When people were choosing the movie they would watch next week, they tended to pick the virtue movie.  When they were choosing the movie they would watch that day, however, they would pick the vice movie.  In the moment of choice, people were worried that they would be bored, or sad, or generally not entertained.

Interestingly, movie delivery services like Netflix provide an interesting test of this explanation.  With Netflix, you set up a queue of movies and they get mailed to you.  So, you are choosing movies that you are going to watch some time in the future.  I find that I will put a documentary or a complex heavy “virtue” movie on my queue, and it will get mailed.  But then, it will sit at the house for a few weeks because the time never seems right to watch it.  Eventually we watch it, of course, and typically we really enjoy it and value the experience.  But in the moment of truth, it is hard to actually decide to watch it.

The same thing happens at the movie line over the summer.  In the end, we just want a pleasant experience at the movies.  So, even if the reviews are horrible, we end up valuing the potential thrills, comfort, and familiarity over the virtues of depth, complexity, and knowledge.

Hi ho, hi ho, it’s off to work we go! Synchrony and team-building.

How do you build a team?  In the army, new recruits learn to march in formation.  Camps often teach a camp song that campers sing together at the top of their lungs around campfires.  Religious groups have elaborate group rituals involving singing, chanting, and sometimes moving in unison.  Crowds at sporting events will often cheer together at key moments.  Is there something to this synchronized behavior that creates a sense of a team?

This question was explored by Scott Wiltermuth and Chip Heath in research reported in the January, 2009 issue of Psychological Science.  They had small groups of people perform activities together, and varied whether they performed those activities in unison.  Then, they had people play games in which people could choose to cooperate with each other or compete against each other.

They used a range of different activities.  In one study, small groups walked across a college campus together, but either walked in step with each other, or at their own pace.  In another study, a small group of participants sat in a room and listened to a song over headphones.  Some groups just listened.  Some groups sang the song aloud as it played over the headphones so that the entire group was singing together.  Some groups sang aloud, but the song was played at a different tempo for each person, so that they were all singing, but not together.    

The cooperation games that people played were made to look like they were part of an unrelated study.  Participants were given a few questions after doing the first set of activities, and then a second experimenter came in, and described the new study.  Nonetheless, people were systematically more likely to cooperate with each other in these games if they had moved or sung in unison with their teammates than if they had not.  People singing the song at different tempos acted just like the group that didn’t sing at all.  The synchronized movements also increased people’s sense that they belonged to a common group with the other people in the study.

This finding highlights the importance of our bodily experience in our social interactions.  It is well-known that when people are engaged in a conversation, they tend to match each other in many ways.  For example, people who are conversing tend to match the pitch of their voices, the speed they talk, and even the number of hand gestures they make while communicating.  So, participating in a cooperative task can synchronize people’s bodies. 

Apparently, it goes the other way as well.  Getting people to synchronize their body movements leads to cooperative behavior.  I wonder if I can get my kids to march in step around the house…

When will this streak end?

People have two very different responses to streaks.  For example, when watching a basketball game, we see a player hit two three-point shots in successive trips down the court, and we expect him to make a shot on the next trip down the court.  The idea that a streak is highly likely to continue is a belief in a hot hand. 

However, if you are playing roulette at a casino, and the lands on a red number 4 times in a row, you expect that there is a good chance that it will land on black the next time.  The idea that the odds that a streak will end go up as the streak gets longer is called the gambler’s fallacy.  

Just looking at these two reactions, it is clear that sometimes we expect streaks to continue and other times we expect streaks to end.  What determines which of these reactions we are going to have?

Eugene Caruso, Adam Waytz, and Nicholas Epley looked at this issue in a 2010 paper in the journal Cognition.  They find that you are most likely to assume that a streak will continue (the hot hand) when the cause of the streak is seen to be someone’s intentions.  You believe the basketball player will keep hitting shots, because he intends to make the shots.

When the streak is caused by some kind of mechanical device, then people believe the streak will end (the gambler’s fallacy).  The roulette wheel is a mechanical device that does not intend for the ball to land on either black or red numbers.

These authors tested this idea with a series of clever experiments and studies.  In one experiment, people watched a video of someone flipping a coin.  One group was told to focus on the intentions of the coin flipper to understand “what he is trying to accomplish with his tosses.”  A second group was told to focus on his actions, “the specific movements of his hands and fingers.” 

At various points, the groups made predictions for what the next coin flip would be.  For one prediction, the previous 8 tosses involved a random-looking sequence of 4 heads and 4 tails.  For a second prediction, 6 of the previous 8 tosses had been heads including a streak of 4 heads in a row.  When the sequence was random, people in both groups predicted that the coin would come up heads about half the time.  When the sequence ended with a streak, though, people who focused on the person’s intentions predicted that the coin would come up heads 68% of the time, while those who focused on the person’s actions predicted the coin would come up heads 28% of the time.  That is, thinking about intentions led people to think the streak would continue, while thinking about the mechanism of the flip led people to think it would end.

In another study, people made predictions about stock prices.  They were shown graphs of the performance of some stocks over a two-week period.  The critical items in this study were graphs that had trends in the stock price.  In one graph, the price of the stock went up consistently over the two week period.  Another second graph had a decreasing trend.  Participants were asked to predict the next day’s stock price.  Unsurprisingly, people shown the increasing trend assumed that the stock would keep going up.  People shown the decreasing trend assumed that the stock would keep going down. 

However, the authors had participants complete a questionnaire about an individual difference in anthropomorphism.  That is, some people have a tendency to give human traits and mental characteristics to inanimate objects, while others do not.  Those people who were most likely to think that the stock market has a mind of its own were the ones who were most likely to think that the streak in stock prices would continue.  Those people who were most likely to think that the stock market has no intentions were most likely to think that the streak in stock prices would end.

This last study has important implications.  In daily life, we must often make predictions about what will happen in complex situations.  It is important to recognize those situations in which we have a good causal understanding of the situation and know whether the data we observe are good predictors of future performance and those situations in which the most recent observations are just the outcome of a generally random process.  In these situations, we must take some care not to ascribe intentions to processes that are really random. 

It is more difficult to avoid anthropomorphizing than it looks.  We talk about many institutions using language often associated with the actions of people.  Reports in the business sections of newspapers talk about markets “reacting” to news.  They describe companies “striving” to overcome poor performance.  This language reinforces the idea that organizations may have intentions. 

At times, it may make sense to treat a company like a person.  Companies have managers who make decisions and these decisions may properly be cast as intentions for the strategy that will be followed in the future.  At other times, though, this language may get in the way.  There is a tremendous amount of randomness in the stock market.  When we talk about it in human terms, we gloss over all of that randomness.

In the end, we should try to be a bit more mindful about when we assume that streaks are the results of an agent’s intentions.