# Why does my daughter think she’s bad at math?

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A neat new paper by Alex Eble and Feng Hu helps me to understand why. Eble and Hu set out to tackle the question of how these norms manifest and persist across generations. They are using a pretty cool nationally representative Chinese dataset which has gender bias questions for 7

^{th}and 9

^{th}graders and their parents, as well as test scores and things like aspirations. And, to speed them on their way to identification, China has a law that requires that children are randomly assigned to classes within a given middle school. So, as a result, a child’s peers are random.

So, the bias my daughter expresses is also common in China. 58 percent of boys and 47 percent of girls in Eble and Hu’s sample agree with the statement “boys are better than girls at learning math.” They don’t seem to be actually right: when Eble and Hu look at test scores, girls actually outperform boys by a small margin, but this is a paper about biases and the damage they can do, so let’s look at that.

Given the random variation in peers (and the parents of those peers), does this matter for the bias that individuals hold? Oh yes it does. A one standard devi0ation increase in the bias of peers’ parents increases the likelihood of a child agreeing with the statement that boys are better than girls at math by 4.2 percentage points. Another way to put this is that if you go from a class where 25 percent of the peer parents are biased to one where this 75 percent, your kid is 18.9 percentage points (34%) more likely to agree with the bias. And the effect is equal for boys and girls. (For those of you watching the econometrics on this, Eble and Hu are doing all of these estimates with grade-by-school fixed effects).

Girls internalize this. They are significantly more likely to say that their math class is hard. Boys don’t.

This translates into lower performance. A one standard deviation increase in peer parent bias leads to 0.063 standard deviation decrease in girls’ math test scores. Looking at effects over the distribution, this effect gets steadily worse, the worse the bias among peers’ parents is. (And this is robust to controlling for teacher characteristics)

Eble and Hu then set about understanding the mechanisms that could be at play here. First off, you are probably wondering by now whether the peers’ parents bias is actually picking up some other factor, such as less intelligent peers. Eble and Hu run a set of horse race regressions where they throw in peers’ parents’ education, peers’ performance, peers’ perceived ability and the gender composition of the child’s classroom. The results on bias transmission and math scores are quite stable. So, while there may be other stuff going on, the peers’ parents bias remains a powerful force.

Eble and Hu then tackle different kinds of exposure. Since they observe kids in grade 7 (when they are first assigned to that class) and grade 9 (when they’ve been together for 2 years), they can look at how the duration of exposure matters. It turns out bias is pretty constant over time, but the peers’ parents’ bias effect on girls’ view that math is difficult and their performance on tests get worse over time.

Parents of other girls matter more for girls and boys for boys. Indeed, looking at bias, the effect of girls’ parents’ bias on girls’ own bias (say that 10 times fast!) is 68 percent larger than the effect of boys’ parents, with similar results for test scores.

What about your own parents? This is tricky to estimate because your parents (hopefully) give you a lot more than their biased views. Elbe and Hu interact a girls’ own parent bias with that of the peers’ parents. Boom: own bias and test (significant at 10 percent) outcomes are worse for girls who are exposed to peer parents bias and bias from their own parents at the same time.

Into this darkness comes friends. Friendship is endogenous in all kinds of ways, so this is a more suggestive avenue of investigation (as noted by Eble and Hu). That being said, having close friends in class seems to help offset the impacts of peers’ parents. And, if a girl has five close friends in class, this totally offsets the impacts of peer parent bias.

The final question that Eble and Hu tackle is whether this bias is leading the girls to switch their efforts to other subjects or not. And the results are somewhat depressing. Peers’ parents bias doesn’t increase the girls’ performance in Chinese or English tests. And this result survives controlling for the range of variables they used in their earlier horse race regressions.

Check out the paper if you have a chance. It does a nice job of working through the peer effects econometrics and has a good survey of the literature as well. As for me, I am going back to my daughter. She told me last night that she liked math this year. I told her to stick with her friends.

This is brilliant, Markus. Thanks.

One question - can the data be used to find out if the difference in perceptions comes from boys (and girls) overestimating the ability of boys, or from underestimating the ability of girls? I recall Chris Woodruff's work on female managers in Bangladesh discovered that perceptions were driven by the former effect, which was interesting: women correctly estimated how hard it would be to run a line, while men were overconfident.

Secondly, Woodruff's paper (going by memory again) found that after some time with women running production lines, perceptions adjusted. I wonder if a similar effect could hold in classes: if there's little difference in boys and girls actual scores at first, perhaps making that known could affect how they change over time (and perhaps the evolution of beliefs).

Nice ideas!

Hi Ranil, Alex here (one of the authors). Thanks for the nice ideas! For question one, our gender bias measure is only a relative one: “do you think that boys are better than girls at learning math?” I think this means that we can’t tease apart over/underconfidence by gender, though my casual recollection of what I’ve seen in the relevant literature is in line with what you lay out - girls are about on the mark and boys are overconfident.

For question two, this is a great idea. I don’t think we can test it directly, but I can say that one of the findings of this and our other gender bias paper (https://cdep.sipa.columbia.edu/sites/default/files/cdep/WP43Ebleupdated…) is that exposure to the bias causes differences in effort and enthusiasm, which then appear to contribute to the formation of future human capital. This means it’s a bit of a moving target; as time progresses, girls’ relative performance positions decline and this then works against the “revelation” mechanism you describe. Perhaps a ripe setting for a structural model of belief updating and changing (relative) ability?

thanks for the response, Alex, and for the great papers. The moving target part is interesting - really reinforces the need to act early (or prevent).

Always love keeping up with your blogs, Markus. I thought I was quite good at math until I moved to a new town and didn't have friends in class supporting me. I never fully recovered my confidence in my math skills. Peer support is so important.