Helping girls like math is not the same as helping them to do well.

In Education circles, there has been a lot of concern about women and math.  On the positive side, there are no clear differences in the performance of boys and girls in math classes up through the end of high school.  On the negative side, once women get to college, they tend to take fewer math classes and fewer classes in the math-heavy sciences than men.

There is also evidence that women sometimes perform more poorly on important tests of math achievement than they should given their ability.  That is, their scores on these tests do not reflect their true ability, because of a phenomenon called stereotype threat.  Stereotype threat was first described by Claude Steele and Joshua Aronson in a 1995 paper in the Journal of Personality and Social Psychology.  The basic idea is that if you are a member of a group that is the subject of a negative stereotype, then your concern about showing that stereotype to be valid can harm your performance.  So, women who know that there is a stereotype that women are worse than math at men may do poorly on tests of math achievement just because they are aware of the stereotype.

Stereotype threat has been an important area of research, and I have written about it before in this blog.  One stream of work relating to stereotype threat tries to find ways to eliminate it.  An interesting set of studies in that vein was presented by Chad Forbes and Toni Schmader in the November, 2010 issue of the Journal of Personality and Social Psychology.  They were particularly interested in the difference between women’s attitudes about math and their beliefs in stereotypes about math performance.  This issue is important, because it is possible that women are less likely than men to pursue math because they don’t like it.  It is also possible that they don’t pursue math because they are concerned they might do poorly.

Forbes and Schmader designed procedures to change women’s attitudes and beliefs about math (at least temporarily).  To influence attitudes, they had people do a task in which they had to classify words.  Some of the words were related to either math (like addition) or language (like paragraph).  Participants had to press a button to classify the words.  Other words were either positive or negative.  Some participants had to press the same button to respond both to the math words and the positive words and to use a second button to respond to the language and negative words.  A second group did it the opposite way (math and bad on one button and language and good on the other).  Other research suggests that doing this task can give people a more positive attitude about the concept paired with good words. 

Later in the experiment, participants were given the opportunity to work on different kinds of problems, and some of them were math problems.  Participants could choose which problems to work on.  Women in this study were more likely to choose to work on math problems when they were given the training that math is good than when given the training that math is bad.  However, this training did not influence their performance on the problems.  That is, they did not solve a higher percentage of the problems when trained to have a more positive attitude about math.

In another study, participants got training related to the stereotype about math.  In this case, they classified items either as math-related or language-related or things that women are good at or that men are good at.  The group that was trained to discount the stereotype used one button to respond both to things that women are good at and to math words and to use the other button to respond to things that men are good at and language words.  A second group did the task the opposite way (women are good at and language words; men are good at and math words). 

Later, the participants did math problems.  In this case, women who were given training to help them discount the stereotype actually performed better on the later math test than those who got training that was consistent with the stereotype.  The researchers also gave participants a test of their working memory capacity.  Working memory is the kind of memory you need to use when you are solving problems.  It refers to the amount of information you can keep in mind at once.  In general, having more working memory is better than having less when solving math problems.  Previous research has found that stereotype threat situations decrease people’s working memory capacity.  Forbes and Schmader found that the training to discount the stereotype increased women’s working memory capacity.    

There was a lot of detail here, so let me try to summarize.  Improving women’s attitude about math made them more likely to choose to do math problems, but not more likely to do better on those problems.  In contrast, changing women’s belief about the stereotype affected their performance on math problems, but not their willingness to do math.

These results suggest that if we want to increase the number of women who participate in math and science careers, it will be important to influence both attitudes about math and beliefs about stereotypes.  The results of this study suggest that both are possible.

It is easier to ask for forgiveness than for permission

I remember driving in my car several years ago and hearing a song by Rodney Crowell on the radio called Earthbound.  It has a lyric in it that says, “Fifty years of livin’ and your worst mistakes forgiven, it just takes time time time.” The sentiment is that as things recede into the past, people are often willing to forgive you for things you have done.

I was reminded of this song while reading a paper by Eugene Caruso in the November, 2010 issue of the Journal of Experimental Psychology: General.  This paper presented a number of studies demonstrating that people view a moral lapse as worse if it is going to happen in the future than if it has happened in the past.

In one study, people were told about a fictitious scenario in which Amazon.com would charge its most loyal customers more money for products than new customers.  Most people would see this as unfair.  One group was told that Amazon tried this policy for a week a month ago.  A second group was told that they were planning to try this policy a month from now.  People rated themselves as more upset when the test was in the future than in the past.  They also rated the policy as more unfair when it was going to happen in the future than when it had already happened. 

The amount of time matters as well, though.  When the test either happened a year ago or was going to happen a year in the future, then there were no differences between past and present. 

This effect is not limited to negative events.  In another study, people were told about a generous cash donation.  When people were told that the man was going to make this donation next month, they felt better about him and thought the donation was more generous than when they were told that he made the donation last month.

Finally, while people treated the past and future differently, they don’t think that they should treat it differently.  In a study looking at this question, people made judgments about another unfair scenario.  This one involved a story about Coca-Cola trying to change the price it charged for a drink depending on the temperature outside.  In this study, though, people made judgments both about the past and the future.  When the time frame shifted from past to future, people did not change their judgments.  Still, the basic effect from the previous studies was obtained.  Those participants who made judgments about the future first rated Coca Cola’s policy as more unfair than those who made the judgments about the past.

Why does this happen?  We generally view the future as changeable and the past as fixed.  By treating a moral lapse in the future as very negative, we are putting pressure on ourselves and others to act properly.  Once the lapse has happened, though, there isn’t anything we can do about it.  The further it recedes into the past, the more that we feel as though we need to get on with our lives.  And so we ultimately end up forgiving others.

Given this set of results, you might be tempted to just ignore moral restrictions and do whatever you want.  Before you do this, though, Caruso points out an additional factor that affects people’s judgments.  While we are often willing to forgive people for their lapses in the past, we are much less willing to forgive when we find out that they planned ahead for their lapse.  He points to studies exploring the penalties people want to give to others when there is evidence that they broke the law.  When there is also evidence that they planned ahead to break the law, the punishments are more severe than when it does not seem that people planned ahead to break the law.

Your future happiness depends less on the present than you might think

You make a lot of decisions based on how you think they will make you feel in the future.  Car dealers ask you to think about how happy you’ll be driving a beautiful new car.  Ads for cruises ask you to think about how great you’ll feel after a relaxing vacation.  On the flip side, people work hard for a new promotion believing that if they don’t advance in their career, they will be devastated.

The evidence is pretty clear, though, that big positive and negative events don’t have an enormous impact on people’s happiness.  In a 1998 paper in the Journal of Personality and Social Psychology Dan Gilbert, Tim Wilson, and their colleagues found that college faculty being evaluated for tenure believed they would be quite unhappy if they were denied tenure.  Several months after their tenure decision, though, college faculty who had been denied tenure were no less happy than those who had gotten tenure. 

This finding that we believe that future positive and negative events have a bigger impact on our future happiness than they do is called an affective forecasting error.  One thing about these errors that is not well understood is why they don’t go away over time.  We all have experience with these errors.  As a kid, I remember toys that I really wanted to get because I had seen them in a catalog.  When I actually got one of those toys, though, it was never quite the life-changing experience I expected.  So, why didn’t examples like this get rid of these affective forecasting errors?

This question was explored in a November 2010 paper in the Journal of Experimental Psychology: General paper by Tom Meyvis, Rebecca Ratner, and Jonathan Levav. 

These researchers find that people have difficulty remembering their initial prediction for how they would feel after a positive or negative event.  In one study, they asked voters in the 2008 election how they would feel a week after the election if Barack Obama won.  Supporters of John McCain rated that they would be quite unhappy.  A week after the election, these same voters were contacted again and asked how happy they were.  They were also asked to recall how happy they said they would be when they predicted it before the election.  These voters were significantly happier than they predicted they would be (that is the affective forecasting error).  They also remembered their prediction as being less extreme than it was.  That is, they did not remember predicting that they would be very unhappy.

The researchers demonstrated that this poor memory for previous predictions makes it hard for people to learn to predict better in the future.  In this study, some people were reminded of their initial prediction, and those people who were reminded of what they actually predicted showed smaller affective forecasting errors in the future.

In the first session of the experiment, people ranked their preference for flavors of jellybeans, and then were asked how much they would enjoy eating jellybeans that they liked moderately well after eating either a jellybean that they really like or one that they don’t like much at all.  People usually predicted that they would like a moderate jellybean less after eating one they really like than after eating one they don’t like at all.  (This is called a contrast effect.)

People came back for a second session, and actually ate sequences of jellybeans and rated their enjoyment.  As it turns out, preference for jellybeans isn’t affected at all by the one you just ate, and so there was an affected forecasting error.  The participants were able to look at their ratings and see that they enjoyed the jellybean equally well regardless of what else they ate.  One group of participants was then shown their original prediction (which showed that they expected a difference in enjoyment).  The other group was not reminded of their original prediction.

Then, everyone did a similar task.  They ranked a series of ice cream flavors.  Then, they were asked how much they would enjoy eating a flavor they like moderately well either after having a spoonful of an ice cream they really enjoy or after having a spoonful they do not like at all.  Obviously, this judgment is quite similar to the one about the jellybeans.

Those people who were reminded of their original judgment with the jellybeans correctly predicted that their enjoyment of ice cream would not be affected much by what they had eaten before.  Those who were not reminded of their earlier judgment predicted that their enjoyment of the ice cream would be influenced by the flavor they ate before.  So, those people who were not given a reminder still showed an affective forecasting error.

Overall, then, it seems like we continue to mis-predict how events will affect our future happiness because we have difficulty remembering the predictions we make.

Do these affective forecasting errors really matter?  In fact, these errors may be both a blessing and a curse.

On the positive side, it can be motivating to be very concerned about a future event.  College faculty approaching tenure are often quite productive in the years before their evaluation, because they believe that the outcome of this decision will have a huge influence on their career.  Even though the actual tenure decision won’t influence their future happiness much, this hard work may still lay important groundwork for their research in years to come.

On the negative side, though, these affective forecasting errors can also lead to bad decisions.  If you really believe that a sports car will make you happier, you may overpay to own it.  That means that you will spend a lot of money on a purchase that ultimately won’t affect your happiness that much. 

On balance, then, it is probably best to remember that there are lots of factors that affect how happy you will be in the future, and that no single event will have that big an influence on that happiness.

The structure of our goals affects how we plan for the future

Lots of the things we hope to do in life—our goals—can be accomplished in many ways.  If you want to go into business for yourself, you might first train at a company that does similar work and then find a business partner, and then start your own firm.  Alternatively, you might go to school to get some additional skills.  While you are in school, you might also try to make contacts with potential business partners.  After completing school and finding a partner, you can then start your business.  The plans you create to achieve your goals are an important determinant in whether you succeed.

So, it is useful to know something about how you generate plans.

An interesting paper in the October, 2010 issue of Psychological Science by Kachina Allen, Steven Ibara, Amy Seymour, Natalia Cordova, and Matthew Botvinick looks at one influence on our plans.  They suggest that people may have very abstract plan structures that can be used to suggest how people may achieve many different kinds of goals.  Activating one of those abstract structures may make it easier to use that same structure again in the future.

One structure that people may use is a goal chain.  First you perform action A, then action B, and then action C, which allows you to achieve your goal.  The first plan I suggested above has this structure.  First you train, then you look for a business partner, finally you start your own business. 

Another structure involves carrying out independent actions at the same time in order to ultimately achieve your goal.  That is, you perform action A and action B at the same time, and then use those actions to do action C, which allows you to achieve your goal.  The example where you go to school and look for business partners at the same time and then start a company is an example of this structure.

The authors of this paper did two studies to demonstrate that people have these abstract structures for thinking about plans.  In the first, they had people read sentences that described sequences of actions.  The sequences of actions could have either of the two structures I just discussed.  For example, the sentence “John purchased a carousel ticket, gave it to the attendant, and went for a ride” has a goal chain structure.  The sentence “John sliced up some tomatoes, rinsed off some lettuce, and tossed together a salad” has the structure of doing two independent events and then putting those together to do a third.

Some people saw 40 sentences (half of each type) randomly intermixed.  A second group saw the sentences blocked, so that they saw 20 sentences of one type followed by 20 sentences of the other type.  The group that read the sentences in a blocked order read and comprehended the sentences faster than the group that read them intermixed.  This result suggests that people were able to reuse the same goal structure over and over when a whole batch of sentences all used the same abstract plan structure.

Another explanation for the results of this first study is that there is something about the way we structure and comprehend language that is affecting reading speed.  That is, the sentences used to describe plans may have a similar structure in a way that benefits reading about similar plans. 

To test this possibility, the authors did a clever study.  They had people read the same kinds of sentences randomly intermixed.  Before each sentence, people saw an arrangement of three blocks.  The blocks could be arranged in a tower or an arch.  The tower is similar to a goal chain, because creating a tower requires stacking one block on a second and then putting a third on top.  The arch is similar to the independent events, because two blocks are placed on the ground and a third is placed on top of it.

If people saw a tower first, they were faster to read sentences describing a goal chain than a plan with independent events.  If people saw an arch, the plan with independent events was read faster than the goal chain.  So, the results of the first experiment were not just a reflection of the way people understand language.

This set of findings suggests that we are able to represent our plans at an abstract level that focuses just on the structure of the events in the plan.  Activating the general structure of a plan makes it easier to think about other plans with the same structure in the future.  One factor that affects how we try to achieve our goals is the general structure of the plans we have used in the past.  When evaluating a new plan, then, it is worthwhile thinking about whether there are other ways to achieve the same goal to make sure that we have not missed another plan structure that might be better-suited to the goal we are trying to achieve.

Birth Order and Baseball

Siblings are both similar and different.  When you look at your friends, you may notice family resemblances.  Friends may look like their siblings, or sound like them, or even have similar interests.  At the same time, they are unique individuals.

 One particularly interesting aspect of the differences among siblings is that their position in the family may affect who they are.  There has been a lot of interest in the ways that birth order may affect personality, achievement, and behavior.  Research suggests that there are some systematic influences of whether you are a first-born or later-born sibling on aspects of your behavior.

 In a 2001 paper in American Psychologist, Robert Zajonc reviewed a number of studies on effects of the order of birth on performance on tests of intelligence and academic ability.  He focuses on data suggesting that both birth order and the size of a family affect academic performance.  That is, first born children tend to do better on intelligence tests and tests of academic performance than later-born children.  But, the larger the family, the worse that everyone in the family does overall.

 There are lots of reasons why birth order might affect academic performance.  Zajonc argues that when families have fewer kids, they can spend more time with each child, which tends to help them academically.  In addition, older children help to teach younger ones, which tends to help them as well.  If you have ever tried to teach someone, you know that you have to learn it well yourself in order to be helpful.  So, older siblings end up learning material better just because they have to help their younger siblings.

 Birth order also affects risky behavior.  Frank Sulloway and Richard Zweigenhaft discuss this issue in a paper in a November, 2010 paper in Personality and Social Psychology Review.  They looked at birth order and sports.  First, they reviewed a number of studies looking at the kinds of sports that people end up engaging in.  They found that older siblings are generally less likely to participate in risky contact sports than younger siblings.

 Then, the authors analyzed major league baseball players.  Over the years, there have been many sets of siblings who have both made it to the majors as baseball players.  Overall, there was a tendency for younger siblings to be more successful overall than older siblings.  Younger siblings tended to have longer careers and to play more games overall. 

 The biggest differences between older and younger siblings, though, were in risky behaviors.  For example, one of the riskiest behaviors in baseball is the stolen base.  Players try to move ahead on the base paths by running from one base to another while the pitch makes its way from the pitcher to the catcher.  Once they were on base, younger siblings were far more likely to attempt to steal bases than their older siblings.  Interestingly, younger siblings were also more likely to be hit by a pitch than their older siblings. 

 It wasn’t that younger siblings were just better athletes, though.  Older siblings tended to be better pitchers than younger siblings.  They struck out more batters and walked fewer.  These differences were small and not statistically reliable.  They do demonstrate that the other differences are not just a matter of athletic ability.

 Why do older and younger siblings differ?  Psychologists have given many explanations for these differences, and chances are there are a lot of factors that contribute to the differences.  One prominent explanation has to do with differences in family dynamics for older and younger siblings.  Older siblings get a lot of their parents’ attention.  First children have a few years alone with their parents.  After the first child, each child after that has to do something to get some attention from the rest of the family.  The argument is that later children have to be more extroverted and more likely to take risks to get attention.  And these sibling rivalries may continue into adulthood.  The behaviors that people use to get the attention of their families as kids may continue to affect the way they act long after they leave home.

That package made me overeat

Snacking can be hard to control.  It is common for people to sit down with a box of crackers or a box of pretzels and eat mindlessly until they discover that they have finished them all.  Overeating is a huge part of the problem that people have losing weight.  It is hard to exercise enough to overcome a food binge.

 There are lots of factors that affect the amount that people eat.  It is now well-known that large plates will lead people at a buffet to fill them with more food than small plates and so they end up eating more.  Large portion sizes at restaurants cause people to eat more than they would if the portions were smaller.  These aspects of the environment are interesting, because people are often unaware that they are being affected by them.

 A paper in the October, 2010 issue of the Journal of Consumer Psychology by Adriana Madzharov and Lauren Block adds something else to this list:  the number of items shown on the packaging. 

 Many snack foods show a picture of what the product looks like.  A box of chocolate chip cookies will show sample cookies on the front.  A bag of pretzels will show pictures of the pretzels.  A box of crackers will show the crackers.

 The studies in this paper make three main points.

 First, the number of items on the front of the package affects people’s judgments of how much food is inside the package.  In studies with packages of cookies and animal crackers, people judged that a package had more in it when the package pictured many items on the front than when it had few.  So, a package with four cookies on the front was judged to have fewer cookies in it than a package with seven cookies on it.  People also judged the portion size to be bigger when there were many items pictured on the package than when there were few.

 Second, when given the chance to actually eat, people ate more food from packages with many items pictured on it than from packages with few items pictured on it.  That is, the beliefs that the package has more in it and that the portion size is larger led people to consumer more food.

 Third, this effect was strongest for people who say that they like to think visually.  People often display preferences for the way they like to learn new things.  In a final set of studies in this paper, the authors had people rate how much they like to think visually.  Those people who were high visual thinkers were much more likely to overeat from packages depicting many food items than people who do not characterize themselves as visual thinkers.

 What can you do about this?  If you are trying to avoid overeating, you really need to use your environment to help you eat smart.  Here are two suggestions.  First, you should minimize the number of snacks you keep at home.  If there is no snack food in the house, you can’t eat it.  Second, when you do decide to snack, don’t rely on the package to guide you in the amount you eat.  Instead, take out a small bowl and put the snack food in it.  Put the package away and only eat what is in the portion you set out. 

Huh, my mind was wandering. Maybe I’m bored.

How do you know when you’re bored?  There are probably lots of ways.  If you are sitting in a class, lecture, or talk, you might find yourself feeling frustrated that the speaker is talking in a monotone.  Or, you might not like the topic.  Another possibility, though, is that you might find your mind wandering to thoughts that have nothing to do with the class or talk or lecture.  Do you use mind wandering to help you decide whether you are bored?

This question was examined in a paper by Clayton Critcher and Tom Gilovich in the September, 2010 issue of Personality and Social Psychology Bulletin. 

How might mind wandering make you think that you are bored?  Perhaps it depends on what you are thinking about.  For example, if you start thinking about positive things, then you might think that you are daydreaming about pleasant things because the task you are supposed to be doing is boring.  Often, when your mind wanders to negative things, it is because those negative things are bothering you, and you can’t help thinking about them.  So you might assume that negative thoughts come to you whether you want them to or not, and so daydreaming about negative things might not be caused by boredom.

Another possibility, though, is that you are most likely to think that daydreaming is a signal that a task is boring when you think about the kinds of things you could be doing rather than that task.  So, when you are sitting in a class or lecture, you might be most likely to interpret your mind wandering as a symptom of boredom if you start thinking about other things you could be doing rather than sitting in that class. 

To explore this issue, the authors first found a clever way to affect people’s mind wandering.  They started the experiment by having people write about other things they could be doing.  Some groups wrote about fun things they could do.  Other groups wrote about responsibilities they could be taking care of.  Later, the group that wrote about fun things they could be doing daydreamed about more pleasant things than the group that thought about responsibilities. 

Similarly, if people wrote about things they could be doing instead of being in an experiment, their daydreams tended to be about things they could be doing at that moment.  If people wrote about things they had done in the past, then their daydreams tended to be about things in the past.

After doing this writing, people were asked to do something moderately interesting like doing a jigsaw puzzle or a crossword puzzle.  Later, they were asked how much they enjoyed doing the puzzle.

The results suggest that people use what they daydream about to help decide whether they are bored.  They said they found the puzzle least interesting when they daydreamed about positive things they could be doing at that moment.  So, if they did the puzzle and their mind wandered to other fun things they could be doing instead, then they assumed that they must be bored with the puzzle. 

Another interesting aspect of these experiments is that in one study people were asked to focus on the relationship between what they wrote about at the beginning of the study and their thoughts later.  These people were more likely to realize that what they daydreamed about was affected by what they wrote about.  For these people, daydreaming about positive things they could be doing did not make them think they were bored by the puzzle. 

In the end, you should remember that your mind wanders all the time.  It can be difficult to focus attention on one task for a long period of time.  And there are many factors that can affect what you think about when you daydream.  That means that you should not always assume that daydreams are a sign that you are bored.  They might just be a sign that you have a lot on your mind.