Girls and Boys and Math Anxiety

When you wander around college campuses, you see the effects of strong gender differences in preferences for majors.  At many schools, there are far more women than men majoring in psychology and biology, but far more men than women majoring in math and engineering.   

This observation has led researchers to explore reasons why men and women differ in the fields they choose.  One of the factors that has been explored is math anxiety—the amount of anxiety that people anticipate or experience when thinking about or doing math.  A common observation across many studies is that when women are asked about their anxiety about math in general they exhibit a higher level of math anxiety than men.

An interesting study by Thomas Goetz, Madeleine Bieg, Oliver Ludtke, Reinhard Pekrun, and Nathan Hall in the October, 2013 issue of Psychological Science examined three questions. First, they wanted to replicate the finding that women exhibit higher levels of math anxiety then men.  Then, they asked whether women who are currently taking a math class or a math exam are actually experiencing more anxiety than men.  Finally, they explored reasons for the differences in math anxiety.

Across two studies, they got measurements from about 700 German students in grades 5-11.  In one study, students were asked for their general level of math anxiety and then were asked to assess their anxiety twice while taking a math exam.  In the other study, students were asked about their general math anxiety and also their specific anxiety in the middle of a math class.  Students were also asked questions about how good they thought they were at math and information was gathered about their math grades.

Both studies found that the girls were more anxious about math in general than the boys.  Interestingly, when the questions were asked during an exam or during a class, the girls and boys were equal in their level of anxiety (and both boys and girls had very little anxiety in the moment).  

What is going on here?

It isn’t math performance.  The girls and boys in both studies were doing equally well in their math classes.

Instead, it seems to be related to differences between boys and girls in how good they think they are at math.  The boys’ ratings of their competence at math were consistently higher than those of the girls.  Statistical tests show these differences in ratings were related to differences in general math anxiety.

These findings suggest that it would be valuable to help all children get better calibrated about how well they are doing in math classes.  Knowing their level of performance could help them to reduce their anxiety about math in general.  In addition, it might be useful to take children who have general math anxiety and to help them to realize that they do not experience that much anxiety when they are actually doing math.  

Clearly, math anxiety is not the only factor that leads to differences in the majors that people pursue in college and the careers that they establish.  But, anything we can do to reduce the influence of general anxiety on career choices is a good thing.

Fables May Fail to Help Children

Stories are a central way that we pass information to people.  The beauty of stories is that they embed real cultural wisdom in a specific context.  They are easy to remember.  They capture people’s attention.  For all of these reasons, we often use stories to help people learn new strategies for dealing with life.

When we tell stories to young children, though, we often make them even more interesting by introducing fantasy elements.  Aesop’s fables were about animals rather than people.  Picture books are filled with stories of fairies, witches, unicorns, and princesses from faraway lands. 

There are lots of goals for telling stories to children, but there is often at least some attempt to teach kids something about life.  When we hope to educate, does it matter whether the stories are about the real world or about fantasy?

This question was explored in a series of studies published in 2009 in the Journal of Cognition and Development by Alison Shawber, Ruth Hoffman, and Marjorie Taylor.  In these studies, children were told stories about people or fantasy characters who had to solve a problem.  For example, a character might carry a number of apples by wrapping them up in a blanket.  Later, the children would be exposed to a problem like having to carry a lot of marbles.  They were given many objects to solve this problem including a towel.  The correct answer was to wrap the marbles up in the towel, just as the character in the story wrapped up the apples.

In one study, younger children (about 4-years old) and older children (about 5-years old) were told one story about a real child and a second story about a fairy that solved a different problem.  The solutions associated with the real child and the fairy were varied across children, so that the influence of the character was not related to the specific solution presented in the story. 

After hearing the stories, children were given a chance to solve a problem similar to the one described in the story.  If they could not solve it on their own, they were given a hint to use the story.  At the end of the experiment, the children were asked which story they would like to hear again as a measure of whether they preferred the story about the child or the story about the fairy.

Overall, children were more likely to solve the problem when it was told about a real child than when it was told about a fantasy character.  About 75% of the children in the study solved the problem with or without a hint when it was about a real child, but only about 50% solved it with or without a hint when it was about a fairy.

Another interesting result was that the younger children who preferred the story about the fairy to the story about the child had much more difficulty solving the problem than the older children who preferred the story about the fairy.  So, there seems to be a trend where children gradually learn to extract the solution from fantasy setting.

Putting all of this together, it suggests that young children find may find fantasy characters interesting, but they have a hard time learning the point of the story when it is embedded in a fantasy situation.  They find it easier to understand the point of the story when it is about real people.  The older children who liked fantasy stories tended to get better at solving the problem, but even they were much worse overall than the ones who heard the story about the real child. 

This work suggests that when stories are being told to teach children rather than just to entertain them, it might be best to focus those stories on realistic settings rather than fantastic ones. 

What Does Nostalgia Do?

When people get nostalgic, they are living in the past.  In those moments, the past seems rosy, and often as more positive than the present.  Nostalgia can be induced by thinking about past events, by going to places you have experienced before, or even by hearing a song that brings back memories of things that happened.  

Is nostalgia a good thing or a bad thing for people?  It clearly seems to make people feel better in the moment. Any time you focus on a positive memory, you tend to get a boost of positive feeling.  But, are there any other positive benefits of nostalgia?

This issue was explored in a paper in the November, 2013 issue of Personality and Social Psychology Bulletin by Wing-Yee Cheung, Tim Wildschut, Constantine Sedikides, Erica Hepper, Jamie Arndt, and Ad Vingerhoets.  They suggested that nostalgia may actually make people more optimistic about the future.

In one study, the researchers simply had college students write a short essay about a past event that made them feel nostalgic or a past event that seemed ordinary.  Ratings suggested that making people write about a nostalgic event made people feel more nostalgic and also slightly more positive than writing about an ordinary event.  Using a program called the Linguistic Inquiry and Word Count (LIWC) software developed by my colleague Jamie Pennebaker and his colleagues, the researchers analyzed the words used in the essays.  LIWC counts different kinds of words that appear in text including words relating to optimism.  People writing about nostalgic events contained more words relating to optimism than people writing about ordinary events.  

In another study, participants instructed to think about a past event that made them feel nostalgic rated themselves as feeling more optimistic than those instructed to think about an ordinary event.  Optimism increased above and beyond any influence that thinking about a nostalgic event had on people’s positive feelings in general.

The remaining studies in this paper examined why nostalgia makes people feel more optimistic.  These studies used internet surveys in order to have a broader age range of participants.  They induced nostalgia in some participants by having them listen to songs or read song lyrics that were associated with nostalgic feelings (for those participants).  

As in the other studies, participants who were induced to feel nostalgic also expressed more optimism of the future.  This optimism is related to two other factors.  First, nostalgia makes people feel more socially connected to others.  This social connection boosts people’s positive feelings about themselves.  That increase in self-esteem then increases feelings of optimism. 

This set of studies suggests that nostalgia can play a beneficial role in people’s lives.  When times are tough, it may seem as though things may never get better.  By focusing on positive times from the past, though, people may help themselves to be more connected to others, which can give them the resources to be more optimistic about the future.

A limitation of this study is that these effects were all statistically reliable, but they were rather small overall.  People got more optimistic, but not by a lot.  It remains to be seen how much of a practical impact nostalgia may have on people’s day-to-day behavior.

Some Odd Numbers are Odder Than Others

The ability to classify objects is crucial to thinking. When you place an object into a category, you are able to predict things about it.  When you see a small furry four-legged animal in someone’s back yard, and you categorize it as a dog, then you can predict that it will probably bark and might want to chase a ball or gnaw on a stick.  In this way, your categories allow you to use your past knowledge to help you understand new situations.  

Often, an object is placed into a category because it is similar to other members of the same category.  So, you decide that the furry four-legged animal is a dog, because it looks like other dogs you have seen in the past.  You categorize the tall, woody plants in the yard near the dog as trees, because they are similar to other trees you have seen.

Sometimes, of course, an object belongs in a category because the category has a strict definition that determines who is and who is not a part of it.  In math, an odd number is any number whose final digit is not divisible by 2.  A triangle is any three-sided closed figure. 

An interesting observation over the years is that even when people are faced with categories that have strict definitions, they treat them in a similar way to categories whose membership seems more based on similarity.  In 1983, Sharon Armstrong, Lila Gleitman and Henry Gleitman found that people believed that some members of categories like even and odd numbers are better than others.  So, a number like 400 is judged to be a better example of an even number than a number like 798, even though—technically speaking—both are perfectly good even numbers.

A 2013 paper in the journal Cognition by Gary Lupyan looked at this effect more carefully.  In one study, he gave people one second to classify numbers as odd or even.  The numbers had between 1 and 4 digits.  He manipulated how many of the other digits in the number were of the same parity as the judgment to be made or of opposite parity.  That is, if a four-digit number to be classified was even (because its right-most digit was even), then on some trials all of the other digits were even, on some trials one, two, or three of the other digits were odd.

Unsurprisingly, people were highly accurate at this task.  However, the more of the digits of a number that were the opposite parity to the judgment to be made, the slower and less accurate people got.  In another study, participants were shown numbers and given as much time as they wanted to make judgments, and they made more errors when the numbers had some digits that were opposite to the parity of the correct response.  This effect was also observed when the numbers were spelled out (Three hundred and fifty two) rather than written as Arabic numerals (352).  

Other studies in this paper found a similar effect for triangles.  People got slower and less accurate to classify triangles as they differed more from a typical equilateral triangle.  A third set of studies demonstrated a similar effect for grandmothers.  A woman is a grandmother if her offspring has a child of his or her own.  Yet, the typical grandmother is also older and retired.  The less that particular women resembled a typical grandmother (despite being grandmothers), the less chance that participants judged they had to win a contest in which every grandmother entered had an equal chance to win.  

What does all of this mean?

The human mind is ill-suited to carry out rules.  We need to be able to recognize new items quickly and to figure out what they are likely to do in order to understand how to interact with them.  

It is rare in nature that there is a specific rule that defines a category that does not come along with lots of other features that help to identify the item.  A dog may be an animal that has dog DNA, but dogs also have lots of characteristic features that help us to understand what they are.  (Trees are another matter entirely, though, many things we classify as trees are less related to each other than they are to other plants that we could consider bushes or flowers.)

So, the human mind evolved to focus on classifying items based on their observable properties.  Humans have invented lots of rule-based categories like even numbers, triangles, and even bachelors and grandmothers.  But, we do not have mechanisms that allow us to simply use rules.

You might think that is a problem.  It would be great to adapt to rule-based categories so that we would not make mistakes classifying them.

However, even many categories that seem rule-based are not.  Consider what seems to be a simple concept like murder.  It should seem obvious that killing another person is a crime.  But, what about someone who kills another person in self-defense?  How about an elderly man assisting the suicide of his long-suffering wife to spare her additional years of pain?  It is hard to determine whether these examples are actually murder.  Our ability to use other factors besides rules to classify items allows us to figure out how rule-based categories apply in the real world. 

Children Can Adopt a Sharing Mindset

We tend to think of children as selfish creatures.  Parents talk about the importance of teaching their kids to share and to play well with others.  Yet, the human species needs to be cooperative to survive. Individually, humans are rather weak creatures, but because of our collective ability to share our experiences and to teach each other, we have come to dominate the planet. 

So, is sharing and cooperation something that needs to be taught? 

This question has been explored by many researchers.  For example, Mike Tomasello and his colleagues demonstrate that even young children tend to share, to cooperate in pursuing shared goals, and to want to punish people who harm others.  

A fascinating paper by Nadia Chernyak and Tamar Kushnir in the October, 2013 issue of Psychological Science explores a related question:  can children adopt a mindset to share with others?  They suggest that if children are given the choice to share with someone else, then that can create a more lasting state of mind that leads them to continue sharing.

In one study, 3- and 4-year-old children were introduced to a puppet dog and were told that the dog was sad.  One group was told to give the dog a sticker to make him feel better.  A second group was given a choice to either give the dog a sticker or to put the sticker in the trash.  For this group, the choice was not personally costly.  A third group made a costly choice. They could either give the sticker to the dog to make it happy or keep it for themselves.  Kids of this age love stickers, so giving up the sticker would come at a personal cost.  After making this choice, the children were introduced to a puppet elephant who was also sad and were given some more stickers.  They could either keep the stickers or give them to the elephant to make her happy.    The key question was whether children would keep the last set of stickers or give them away. 

In all conditions, there was a tendency for the children to give the sticker to the dog.  Even the children who had to make the costly choice between keeping the sticker or giving it to the dog tended to give the sticker away to make the dog happy.  

The children who had no choice and those who chose to give the sticker to the dog rather than throwing it away were not that generous to the elephant.  Only about 20% of these children tended to give the stickers to the sad elephant rather than keeping them.  In contrast, about 70% of the children who had to make the difficult choice in the first part of the study also gave the stickers away to the sad elephant.  This finding suggests that children adopted a mindset of sharing when they had to make a difficult choice.

A few other studies in this paper helped to clarify this effect.

In one study, children were either given the chance to play with a sticker immediately or to make the difficult choice to save the sticker until a later time.  Children find it hard to delay gratification, though most children in this study did put the sticker away to play with later.  Afterward, the children were given the chance to give stickers to a sad elephant or keep the stickers.  Most children in this condition chose to keep the stickers, suggesting that just making a difficult choice is not enough to create a sharing mindset.

One final study had two groups.  Each group had an opportunity to keep an item or give it to the puppet dog to make it happy.  One group had an easy choice.  They either kept or gave away a small scrap of paper.  The other group had a difficult choice, they either kept or gave away a toy frog.  Afterward, both groups had the chance to give stickers to a sad elephant.

Again, most children chose to make the dog happy by giving up the object.  The children who made the hard choice, though, were much more likely to give their stickers to the sad elephant than those who made the easy choice.

Putting all of this together, children do have a tendency to want to keep things for themselves rather than to give them away.  Most of the children in this study kept the stickers for themselves rather than giving them away to make a puppet happy.  However, getting children to make a hard choice promoted a sharing mindset.  When children actively chose to give something valuable to someone else, they continued that behavior later in the study.

This finding is consistent with work on adults suggesting that giving things away tends to make people happy.  For example, a study published in Science by Elizabeth Dunn, Lara Aknin, and Michael Norton suggests that when people give money to others, it increases their happiness.  One possibility is that by giving stickers away in this study, children are also learning that giving things to others has its own rewards.  Future work will have to explore what children learn from these difficult choices that promotes sharing.

Social Competence and Anger

Life is full of frustrating people and situations.  Driving in a car, you may get cut off by a driver on a cell phone.  A colleague at work may fail to complete an important task that makes it harder for you to do your job.  A friend may leave you out of a social event, which makes you feel excluded.  

Your long-term relationships are affected by how you deal with these frustrations.  You may never see the bad driver again, but your driving habits after being cut off may affect the drivers around you.  Getting angry with a friend or colleague can cause tension in that relationship.  Talking with people who have let you down or hurt your feelings can help to repair the damage their actions caused.

An interesting paper in the October, 2013 issue of Personality and Social Psychology Bulletin by Michael Robinson, Adam Fetterman, Kay Hopkins, and Sukumarakurup Krishnakumar examined the role of social competence in dealing with these kinds of everyday frustrations. 

The idea behind social competence is that there are many ways to react to situations, and some of them are more constructive than others.  People who are better at identifying the most constructive ways to deal with situations may also do a better job of dealing with life’s frustrations.

As a measure of social competence, the authors identified many work-related scenarios that were dilemmas, but were not obviously frustrating.  For example, an executive at work may find out that one of her employees is struggling with an alcohol problem.  People are presented with four possible actions (such as forgiving the employee, asking about personal problems, and ignoring the situation) and are asked to rate the effectiveness of these responses.  Their ratings are compared against the ratings of experts.  Previous work suggested that this measure was a good predictor of behavior in a work environment.

In one study, the researchers compared people’s scores on this test of social competence to their score on a scale that measures how often they react aggressively when they get angry.  The higher the scores on the test of social competence, the lower was people’s tendency react aggressively when angry.  This relationship held, even after considering other core personality traits like agreeableness (which measures how much people want to get along with others) and emotional stability.

In another study, a group of people who had taken the test of social competence filled out a daily diary for 14 days.  In this diary, they noted any frustrating events that happened during the day and then rated whether they engaged in aggressive behaviors like insulting someone, criticizing them, or arguing.  They also noted any mental lapses like forgetting an appointment or having difficulty making a decision.  Previous work shows that when people get frustrated, they experience more cognitive problems during the day.

Overall, people with low scores on the test of social competence were more aggressive and had more mental lapses than those with high scores on the test of social competence.  This effect was particularly strong on days that had many frustrations in them in which people had interpersonal conflicts or did not get things that they wanted. 

Why Do People Gamble Too Much?

I grew up in Central New Jersey.  When I was about 10, the state legalized casino gambling in Atlantic City, making it the only place on the East Coast of the US at that time where people could gamble legally.  I have some relatives who live near Atlantic City.  There are lots of cheap buses to get there from all over the New York and New Jersey area, and so I would hop on with all of the gamblers to go visit family.  The ride down was always tense with anticipation, but the ride back had lots of tired and dejected gamblers.  I always felt like many of those people on the bus with me had real gambling problems.

What exactly is it that drives people to gamble too much? 

Intuitively, it seems like there are two possibilities.  One is that people with gambling problems are focused on the thrill of gambling.  When you walk through a casino, there are lights and bells and the sounds of people winning money.  There must be a real jolt when your number comes up on a roulette table, or the bars all align on a slot machine. 

Of course, another possibility is that gamblers are just focused on the money.  They want to win money and gambling seems like a way to do it.

An interesting paper by Cheryl Hahn, Tim Wilson, Kaichen McRae, and Dan Gilbert in the October, 2013 issue of Personality and Social Psychology Bulletin explored these two possibilities. 

As a measure of the vulnerability to problem gambling, they asked participants to fill out the Gambling Attitudes and Beliefs Survey, which has been used in past research.  This scale asks people to rate their agreement with statements like “I know when I’m on a streak” and “If I lose, it is important to stick with it until I get even.” 

In one study, participants were given the gambling survey.  Later, they were given a chance to play what seems like a strange gambling game.  Two decks of cards were placed in front of them.  One deck had 9 red cards and 1 black card.  The other deck had 5 red cards and 5 black cards.  At the start of each trial, the decks were shuffled and placed face-down on the desk.  Participants could choose which deck they wanted a card drawn from.  If the card was red, they would get 10 cents.  If the card was black, they would get nothing.  The game was repeated for 20 trials.  A second group was shown the experimental situation, but they just predicted how may cards they would want to take from each deck over the course of the study.

Economically, it seems clear that participants should always choose from the deck with 9 red cards, because they have the best chance of winning when they draw from that deck.  If they choose often from the deck with only 5 red cards, then they must value the suspense of whether they will win and the thrill of winning despite lower odds. 

People who scored highly on the gambling survey predicted that they would choose somewhat more cards from the risky deck (with 5 red cards) than people who scored low on the gambling survey.  In actuality, though, people who scored high on the gambling survey actually chose fewer cards from the risky deck on average than those who scored low on the survey. 

That is, these results suggest that people who scored highly on the gambling survey were more interested in the money than in the potential thrill of beating the odds.  The researchers obtained a similar result in a second study.

In one final study, participants who had filled out the gambling survey were given 3 minutes to do a series of math problems.  Some people were told that they would be paid 5 cents for each problem they got correct.  Others were given no monetary incentive.  The people who got a low score on the gambling survey answered about the same number of items correctly regardless of whether they were being paid.  Those who got a high score on the gambling survey answered more questions correctly on average when they were being paid than when they were not. 

Putting these results together, it suggests that people who are vulnerable to problem gambling are more strongly motivated by obtaining money than by the suspense of gambling or the thrill of winning.

Of course, this finding was obtained with college students, and there may have been few real problem gamblers in this sample.  As the researchers point out, the stakes in this situation were also low.  More work still needs to be done to see whether this focus on winnings over the thrill of gambling holds up in further studies.