Saturday, February 13, 2010

Math Anxiety, Math Education and Gender Expectations

A recent study has shown that young girls in the United States who are taught by teachers with math anxiety are more likely themselves to develop anxiety of about math. The study is by psychologist Sian Beilock et al. at the University of Chicago. Her research looked at second graders’ anxiety levels in mathematics. She found that, with her sample, there was no correlation between gender and attitude towards math at the beginning of the school year. However, by the end of the school year, girls were much more likely to develop math anxiety. Moreover, girls were much more likely to develop such anxiety if their female teachers had math anxiety. Rather than summarize all of the more interesting details in the study, what follows first is a large quote from the study followed by my comments:

If it is simply the case that highly math-anxious teachers are worse math teachers, one would expect to see a relation between teacher anxiety and the math achievement of both boys and girls. Instead, teachers with high math anxiety seem to be specifically affecting girls’ math achievement—and doing so by influencing girls’ gender-related beliefs about who is good at math.

This study explores the relation between female teachers’ math anxieties and their students’ math achievement. Thus, it is an open question as to whether there would be a relation between teacher math anxiety and student math achievement if we had focused on male instead of female teachers. In one sense, the lack of male elementary school teachers in the United States makes this a hard question to answer. Yet, it is an important question, given research suggesting that girls are more socially sensitive than boys in early elementary school (16). Thus, it is possible that even with male teachers, a relation between teacher anxiety and female student achievement might occur. Nevertheless, the literature on math anxiety, gender modeling, and the impact of negative stereotypes on achievement lead us to speculate that any relation between male teacher anxiety and girls’ math achievement would be obtained through a different route than the one proposed here. Moreover, in the current work, the relation between female teachers’ math anxieties and girls’ math achievement was mediated (or accounted for) by girls’ beliefs that boys are better at math. Hence, it seems unlikely that a male teacher’s math anxiety would affect girls’ math achievement by pushing girls to confirm that boys are good at math.

In addition, children do not blindly imitate adults of the same gender. Instead, they model behaviors they believe to be gendertypical and appropriate (9). Thus, it may be that first- and secondgrade girls are more likely to be influenced by their teachers’ anxieties than their male classmates, because most early elementary school teachers are female and the high levels of math anxiety in this teacher population confirm a societal stereotype about girls’ math ability (2). This match between teacher math anxiety and societal norms would not hold for male teachers exhibiting math anxiety. However, if such a correspondence is important in influencing student achievement, we would expect that for school subjects for which girls are stereotyped to excel (e.g., language arts), male teachers’ anxieties would have an impact on male more than female students’ achievement.

It is important to note that the effects reported in the current work, although significant, are small. There are likely many influences on girls’ math achievement and gender ability beliefs overand above their current teachers’ anxieties. For instance, previous teachers, parents, peers, and siblings who either do or do notmodel traditional academic gender roles may play an important part in shaping girls’ gender ability beliefs and their math achievement more generally. Exploring these relationships—in addition to the influence of both male and female teachers—will help to elucidate the full range of social influences on student achievement.

In conclusion, we show that female teachers’ math anxiety has consequences for the math achievement of girls in early elementary school grades. Given that this relation is mediated by girls’ gender ability beliefs, we speculate that female teachers model commonly held gender stereotypes to their female students through their math anxieties. These findings open a window into gender differences in math achievement and attitudes that emerge over the course of schooling.

Interestingly, math anxiety can be reduced through math training and education (17 –19). This suggests that the minimal mathematics requirements for obtaining an elementary education degree at most US universities need to be rethought. If the next generation of teachers—especially elementary school teachers—is going to teach their students effectively, more care needs to be taken to develop both strong math skills and positive math attitudes in these educators.

How should we respond to this study? As with all initial scientific studies, the data is by its nature tentative, but in this case it looks very robust.Consequently I will for the remainder of this post assume that the phenomenon as described in Beilock et al. is accurate.

We currently focus most of our resources aimed at getting young women to be confident in math at the middle school and high school level. Moreover, prominent celebrities who have tried to deal with this problem have focused almost exclusively on this older age cohort. Danica McKellar for example has focused on encouraging mathematical confidence and learning in middle school girls. This new study suggests that much of the damage done to girls’ mathematical confidence occurs at a very young age. Thus, we may need to rethink where resources are being allocated. Unfortunately, this study does not as of yet include any long-term follow-up. So how much of this early math anxiety is correctable later is not clear. Aside from this sort of vague generality about resource allocation, here are four concrete proposals that need discussion.

First, let’s get the most controversial possibility out of the way: We may want to consider more direct encouragement of males to engage in elementary school teaching. Put less politely, we should consider affirmative action and other incentives to encourage males to go into elementary school teaching, at least for math. While this study showed that young girls picked up on the math anxiety of their female teachers, it is clear that young males did not gain math anxiety from female teachers. Moreover, math anxiety is simply less common among males. Thus, male students will be unlikely to pick up math anxiety, and female students will not pick it up from male teachers until they are older. This proposal has a number of problems. Foremost among them is that it assumes that male teachers will not act in an overly sexist fashion, either explicitly or implicitly denigrating female mathematical ability. Unfortunately, it is clear from anecdotal evidence that many teachers of both genders do explicitly disparage young girls’ mathematical ability. See for example this thread at SkepChick . Moreover, the exact impact of male teachers is far from clear: The study looked only at female teachers. Without more data about how students of both genders interact with male teachers both with and without math anxiety, this proposal must by nature be extremely tentative. The argument can be made that this will send a bad message to young children, i.e., that only males can teach or do math. However, that’s erroneous. Currently, around 90% of elementary school teachers are female. If we replace the females with math anxiety with males without math anxiety or even males with mild math anxiety, the fraction of teachers who are male will still be well below half. So this step also helps correct for a pre-existing gender disparity in elementary sc hool teaching.

Second, and almost as controversial as the first proposal, we can encourage teachers, especially females, to not go into elementary school teaching if they have math anxiety or simply aren’t very good at math. Unfortunately, we already suffer serious problems in the United States getting qualified people to teach elementary school. So directly altering who we encourage to become teachers is non-optimal. Similarly, increasing the required level of math background for elementary school teachers is not a good response. Moreover, as Beilock discusses, proper education can remove or reduce math anxiety. This leads directly to the third possible response.

Third, we must take more steps to directly reduce math anxiety in teachers and people planning on becoming teachers. This should likely focus on female teachers or teacher-candidates who have shown to have serious math anxiety issues. We can introduce them to additional areas of math, where the math is easy to understand and fun. Very elementary number theory and graph theory may be relevant areas. More broadly, we can also have them play mathematical games that get them more comfortable with the idea that math can be fun. Zendo for example would be an excellent potential confidence builder.

Fourth, we can take direct steps to expose young females to mathematically confident females. One method of doing so is to have the math sections of elementary education taught by separate teachers who are more mathematically confident. Even in schools with high percentages of teachers with math anxiety, some teachers will still likely be mathematically confident. Having those teachers handle the math teaching for other teachers (or possibly specializing to only teach math) is an option. Also, we can encourage young girls by having them directly interact with female mathematicians. Part of the problem is that mathematically confident females generally go into industry, sciences or upper tiers of academia, not elementary school teaching. So, mathematicians and scientists should visit local elementary schools. If schools can regularly sponsor visits by firefighters, police officers and members of other vocations and professions, there’s no reason that mathematicians and scientists can’t do the same thing. It doesn’t take much to show up and say “Hey! Look! I’m a lady who does math. And I enjoy it!”

Fortunately, resources which are spent encouraging the general public and children of all ages to be more mathematically confident can potentially work in general to help the situation with female students. Thus, work like Steven Strogatz’s new regular column in the New York Times to help make math more accessible to the general audience can be helpful.
No matter what happens we need to look at this data dispassionately at the same time as we try to gather more information about the transmittable nature of math anxiety. As a society we are short-changing many bright young females. Because those students then do not go into math-intensive areas of study,the society suffers. These problems need to be addressed. We are not doing enough now to address them.


Etienne Vouga said...

Interesting study. I haven't been able to find a full-text copy of Alexander and Martray 1989, but from the example sMARS questions given in the results section it appears that here math anxiety was equated with anxiety performing arithmetic, particularly mental arithmetic. That makes sense given the ages of the students.

But in the age of Mathematica, Matlab, etc, being "good at math," and consequently a successful scientist or engineer, has nothing at all to do with arithmetic, but rather with competence at
- Calculus & Vector Calculus
- Basic Algebra & Linear Algebra (by which I mean *abstract* linear algebra; taking determinants or matrix inverses by hand, as sometimes taught in high schools, is a supremely pointless exercise.)

These advanced topics require a kind of abstract thinking very different from the rote execution of algorithms that is arithmetic. It's not obvious to me that the two are correlated at all, and in fact I'd venture that the stereotype is inverse correlation ;)

That the students in the study performed worse when the teacher is incompetent is thus only relevant to the extent that
- being bad at arithmetic handicaps the learning of higher math (my take is that it doesn't much),
- the student's belief that she is bad at math, having been reinforced by the incompetent teacher, persists into high school and poisons her enthusiasm for algebra, calculus, etc.
I don't have trouble believing that the latter is a widespread, serious problem. As you point out though, no data yet exists on this long-term effect. Without it, it's still far from obvious to me that allocating resources towards better elementary school teachers (instead of, say, better calculus teachers) would increase the quantity (or quality) of women in science.

Joshua said...


Some valid points. However two things to note: First, one way they tested for math anxiety in the latest Beilock study was to also have kids draw pictures of students who were good at math and then asked them if the pictures were of boys or girls. So there's also an expectation issue.

Also, while it may be true that once kids advance to a certain point arithmetic skill isn't what matters as much, they need a decent command of some very basic arithmetic in order to do things like calculus. Not necessarily adding or multiplying large numbers, but being able to consistently do small enough arithmetic and also to recognize when answers are likely wrong. It is true that people probably don't need to be arithmetic whizzes, but if they can't add 0 to a number or multiply by 1 without thinking then they aren't going to get very far.