Adding Up Peer Beliefs: Experimental and Field Evidence on the Effect of Peer Influence on Math Performance

We studied how gendered beliefs about intellectual abilities transmit through peers and differentially impact girls’ academic performance relative to boys’. Study 1 (N = 8,029; 208 classrooms) exploited randomly assigned variation in the proportion of a child’s middle school classmates who believe that boys are innately better than girls at learning math. An increase in exposure to peers who report this belief generated losses for girls and gains for boys in math performance. This peer exposure also increased children’s likelihood of believing the gender–math stereotype, increased the perceived difficulty of math, and reduced aspirations among girls. Study 2 (N = 547) provided proof of concept that activating a gender–math performance gap among college students reduces women’s math performance but not verbal performance. Men’s task performance was not affected. Our findings highlight how the prevalence of stereotypical beliefs in one’s ambient and peer environment, even when readily contradictable, can shape children’s beliefs and academic ability.


Wu, Cai
better at learning math than girls may be transmitted in children's peer environment and change their math ability and psychological outcomes. We used a natural experiment among middle-school children who were randomly assigned to different classrooms. We found that the prevalence of gendered belief in math ability in a child's peer environment influences their subsequent performance in midterm math exams as well as noncognitive outcomes. Next, we conducted a preregistered laboratory experiment to provide proof of concept that the saliency of a gender-math performance gap can pose an immediate effect on women's math performance. The combination of the field and lab data provides rigorous evidence that the level of gendermath stereotype in the ambient environment can have both immediate and cumulative effects on students' math achievement.
We focus on the influence of peer beliefs in children's and young adults' ambient environment because the roots of gender inequality in STEM aspiration and attainment stem further back. Research shows that gender stereotypes about intelligence emerge early and affect children's interests (Bian et al., 2017). Common stereotypes associate math and high-level intellectual ability with men more than women, and stereotypical beliefs such as boys are innately better at math than girls may discourage girls from pursuing math and other STEM-related domains. In particular, educational and occupational aspirations begin to crystallize in early adolescence, coinciding with the development of increasingly salient gender identity and gender roles (Bandura et al., 2001;Eccles & Roeser, 2011). Young people are subject to a multitude of messages from the ambient environment regarding what is appropriate and expected from their own gender group. It is also during adolescence when young people begin to move away from parental influence and become increasingly susceptible to peer influence (Riegle-Crumb & Morton, 2017;Wentzel, 2012). The peer influence might be even more pronounced for girls than boys because girls are socialized to be more aware of and sensitive to others' opinions (Beutel & Marini, 1995;Gilligan, 1982).
Research on the stereotype threat investigates how gender stereotypes and bias can function within local environments to deter women's STEM interest and achievement (Shih et al., 1999;Steele, 1997Steele, , 2010. It is hypothesized that the gender-math gap persists in part because widely known negative stereotypes about women's math abilities put female students in situations that put pressure on them about how they would be evaluated by other people (Lewis & Michalak, 2019). These situations are thought to be threatening enough as to hamper academic performance (Steele & Aronson, 1995). Given the prominent contribution of stereotype threat, or social identity threat more generally, to the gender disparity in STEM, a large number of replication studies have been conducted to refine the theory and calibrate the magnitude of the effects. According to metaanalyses (Flore & Wicherts, 2015;Nguyen & Ryan, 2008), large and significant findings were concentrated among earlier and small-sample studies, whereas recent reanalysis and replication attempts failed to replicate earlier findings (e.g., Finnigan & Corker, 2016;Ganley et al., 2013;Shewach et al., 2019;Stoet & Geary, 2012;Zigerell, 2017). Notably, many replication attempts do not cast doubt on the existence of the effect per se but provided clarification on the robustness of the phenomenon in different contexts. In addition, most studies focus on the experience of the individuals targeted with negative stereotypes. Less is known about how these stereotypes may transmit through social environment and group interactions and subsequently impact academic performance.
In this research, we focused on the transmission of stereotypical beliefs in children's peer environment and tested the impact of the gender-math stereotype on students' academic and psychological outcomes in a context where the widely held belief is readily contradictable. We predict a causal relationship between the prevalence of gender-math stereotypes in one's peer environment and girls' effort and math performance. The theoretical intuition is that the stereotypical

Statement of Relevance
Gender disparities in science, technology, engineering, and math (STEM) occupations and interest persist in many societies and coincide with the stereotypical belief that men are inherently better at learning math than women. We tested the hypothesis that belief in the gender-math stereotype may be transmitted through peers, affecting one's belief formation and aspirations and, further, affecting one's math abilities. In a large-scale natural experiment on middle-school children and in a preregistered laboratory experiment in China, we found that gendered beliefs in intellectual abilities had both immediate and prolonged effects on female students' academic performance and belief formation. These effects were potentially transmitted through one's peer groups, where same-gender peers had a less pronounced impact than different-gender peers. These findings highlight the importance of one's ambient and peer environment on the propagation of gendered beliefs and their cumulative impact on intellectual abilities and psychological outcomes.
belief-boys are better at math than girls-can transmit in one's ambient environment through peer interactions. Girls must manage sporadic comments from peers about the innately inferior math-learning ability of their gender, make sense of what they are expected to study, and juggle doubts about their own capabilities. At the moment, the saliency of negative messages can be threatening, and preoccupations with these negative stereotypes can be distracting. Over time, girls in a high-stereotype environment can be less motivated and less able to exert effort in math study and subsequently fare worse in math tests.
We tested these theoretical intuitions using two different but complementary designs. Studying the peer influence of the gender-math stereotype is challenging because it is ethically unjustifiable to randomly expose some children to a greater level of stereotype and bias for the purpose of studying them. Our first experiment sidestepped this concern and exploited the random assignment of children to the classroom to generate quasi-experimental evidence of peer influence on children's academic performance. We focused on a mechanism that is understudied: the peer influence of gender-math stereotypes over time. Because the natural experiment does not offer direct momentary causal evidence of a stereotypical belief, we bolstered the causal mechanism by testing the immediate effect of exposure to gender-math stereotypes in a laboratory. Thus, the two studies in this article are highly complementary. The natural experiment demonstrates the phenomenon in the real world and provides us with an estimate of the long-term effect of classroom-level gender-math stereotypes on girls' versus boys' academic performance, whereas the laboratory experiment provides proof of concept that activating gender-math stereotypes can cause immediate impact on female students' math performance.

Open Practices Statement
The laboratory experiment was preregistered (https:// osf.io/9wfsr/); the natural experiment was not. Data and materials for the laboratory experiment have been made publicly available via OSF and can be accessed at https://osf.io/9wfsr/. For the natural experiment, we analyzed archival data; requests to access these data should be directed to the relevant archive (http://ceps .ruc.edu.cn/).

Study 1: Natural Experiment
Method Participants and procedure. The first experiment used a sample of schools in the China Education Panel Survey (CEPS), a large-scale and nationally representative sample of middle school students in mainland China. 1 The CEPS uses a stratified, multistage sample design covering 19,487 students from 438 middle schools in 112 counties (districts). In each sampled county (district), four middle schools with Grades 7 and 9 were chosen, and four classes were surveyed from each middle school, including two Grade 7 classes and two Grade 9 classes. To identify the causal impact, we limited the sample to schools where students are randomly assigned to classrooms. Our sample contained 67 middle schools, 208 classrooms, and 8,029 students covering 26 counties (49.3% female; average age = 13 years; 10.7% ethnic minorities). In the Supplemental Material available online, we present additional statistical evidence to show that schools in our sample do assign students randomly, as reflected by predetermined student performance and academic performance characteristics.
In this natural experiment, we did not experimentally induce the salience of the gender gap in math performance, but we used the quasi-experimental variation in actual classroom-level belief that boys are innately better than girls at learning math. This research design allowed us to study the impact of being assigned to a peer environment (i.e., a class) with different peer characteristics (Eble & Hu, 2022;Feld & Zölitz, 2017;Hu, 2015;Sacerdote, 2011). At the beginning of middle school in China, students are assigned to classes and remain in the same class for the next 3 years. In the same class, students interact extensively both academically and outside of class. Every lecture is delivered according to the same schedule as the class. Additionally, students participate in self-study sessions as well as outdoor activities together. We predicted that the classroomlevel gender-math stereotype would affect various academic and nonacademic social interactions and subsequently impact girls' math performance in an accumulative way.
In the CEPS sample, middle school students in the seventh and ninth grades completed a questionnaire about their beliefs and aspirations at the beginning of their academic year, before any formal tests took place. Specifically, we obtained students' gender-math beliefs from their responses to the following question, "Do you agree that boys' natural ability in studying math is greater than that of girls?" The wording of this question refers to the innate math ability of each gender, not just the relative performance of boys and girls in the child's current school or classroom. This question enabled us to generate a classroom-level variable summarizing the beliefs of the child's peers in their randomly assigned classroom. We quantified the gender-math stereotype, the key independent variable, as the proportion of students' peers in their classroom who believe that boys' innate math ability is superior to girls' innate math Wu, Cai ability. There were a lot of naturally occurring variations in the aggregate level of stereotypical belief: in some classrooms, only 13.33%; in others, up to 91.89% (Fig. S1 in the Supplemental Material shows the peer gendermath stereotype between classes). These variations are not related to gender compositions of a classroom.
All middle schools in our sample administer midterm exams in the fall semester. The CEPS data include administrative data on the child's test scores in three core subjects: Chinese, English, and mathematics. In each school, all students in the same grade take the same midterm exam in each subject, which is graded centrally at the school level. Accordingly, student test scores across classes within a particular grade are comparable at each school. In addition to administrative data on academic performance, we also used measures on students' extracurricular participation and students' self-reports of confidence, aspirations, and perception of teachers' behaviors.
Analysis strategy. In our empirical analysis, we estimated the effect of the proportion of peers who believe the gender-math stereotype-that boys are innately better at learning math than girls-on a child's academic and psychological outcomes and how the effect varied with the child's gender. Our identification strategy exploited the random variation between classrooms in a given grade within a school in the proportion of peers who hold this stereotypical belief. The random classroom assignment allowed us to control for other external variables that might affect the children's academic performance. To examine the impact of peer beliefs regarding the gender-math stereotype on students' academic outcomes, we used the following fixed-effect linear model: where Y icgs is the outcome variable for student i in class c in grade g in school s. PB icgs is the gender-math stereotype in a child's classroom, defined as the proportion of student i's peers in their classroom who believe that boys have innately greater math ability than girlsstandardized to be mean 0 and standard deviation 1. Female icgs indicates whether or not student i is female.
To increase the accuracy of our estimations, we also controlled for student characteristics X icgs 2 and teacher characteristics W cgs 3 that are not affected by class assignment. λ s is the school fixed effect, λ g is the grade fixed effect, and ε icgs is the error term. We clustered the standard errors at the class level, accounting for correlations in outcomes among students in the same class. See the Supplemental Material for detailed demographic descriptions and balance tests.
The coefficient we were most interested in was b 1 , which measured how a 1-standard-deviation increase in the proportion of peers who believe that boys have innately superior math ability than girls differentially impacted girls' and boys' outcomes. In other words, it represents the impact of peer beliefs in the class on the gender gap (cf. Muralidharan & Sheth, 2016). The coefficient b 2 measured how boys' outcomes were affected by a 1-standard-deviation increase in the proportion of peers who believe that boys have innately superior math skills. Because the classrooms are randomly assigned, b 1 and b 2 represented unbiased estimates of the effect from peers' gender-math stereotypes (see the Supplemental Material for robustness checks for causal identification).

Results
Academic performance. We first examined the effect of peer gender-math stereotypes on test scores of three core subjects-Chinese, mathematics, and English (see Table 1 for main results; see Table S4 in the Supplemental Material for results on simple effects). In this nationally representative sample, girls outperformed boys on average in all three core subjects, consistent with prior empirical findings in China (Akabayashi et al., 2020;Gu & Jean Yeung, 2021). However, even in this setting-where girls' test scores were significantly higher than boys'-a considerable proportion of students still believed that boys were innately better at math than girls (M = 53.3%, SD = 0.499; see Table S1 in the Supplemental Material).
It is estimated that girls' test scores in math, relative to boys', worsened by 0.894 standard deviations after being exposed to peers who believed that boys had innately superior abilities in math. On the other hand, a 1-standard-deviation increase in the stereotypicalpeer-belief measure led to an increase of 0.439 standard deviations in boys' standardized math scores (see Table  1; for simple effects on boys and girls separately, refer to Table S4 and Fig. S2 in the Supplemental Material). Interestingly, the coefficient of PB icgs icgs × Female , indicating the effect of peers' stereotypical gender-math beliefs, was statistically significant for math but nonsignificant for Chinese and English. The results indicated that girls' math performance would decline because more of their peers believed that boys had innately superior abilities in math, and the gender gap would widen. However, we did not observe this gender difference in Chinese or English test scores (see Models 1 to 3 in Table 1).
We next explored how these patterns are differentially impacted by peers of different genders. Specifically, we calculated two class-specific measures of the proportion of peers who believe that boys have innately superior abilities in math, one for girl peers and one for boy peers. As children with the same gender identity are more likely to interact in this age group, peers of the same gender should be more influential in transmitting beliefs than peers of different gender (Currarini et al., 2009;Eble & Hu, 2022). According to Models 4 and 5 in Table 1, same-gender peers' beliefs had a smaller impact on math performance than beliefs of peers of a different gender. Table S5 in the Supplemental Material shows these estimates using raw test scores as outcomes.
Extracurricular course enrollment. Next, we examined whether children's participation in extracurricular activities was affected by the proportion of peers who hold the gender-math stereotypical belief. We found that having a greater proportion of peers who hold the gendermath stereotypical belief lowered girls' participation only in extracurricular mathematics courses (b = −0.016, SE = 0.010, p < .1). However, we did not observe this type of gender disparity in participation in other extracurricular courses, such as Chinese, English, and painting (see Fig.  1a; see also Table S6 in the Supplemental Material).
Psychological outcomes. Furthermore, we evaluated the relationship between the proportion of peers who hold the gender-math stereotypical belief and three variables relating to students' beliefs: the likelihood that students will hold the same stereotypical belief, their perception of their parents' stereotypical beliefs, and their perception of peers' stereotypical beliefs. Figure 1b presents the results of estimating Equation 1 with these three belief outcome variables as the dependent variable. We found that peer beliefs influenced the beliefs of boys and girls differently. Our findings suggest that a 1-standarddeviation increase in the proportion of peers who hold the stereotypical belief increased girls' likelihood of holding this belief themselves, girls' likelihood of perceiving that their parents hold this belief, and girls' likelihood of perceiving that their peers hold this belief by 0.034, 0.026, and 0.031 standard deviations, respectively (ps < .1; see Table S7 in the Supplemental Material).
We next examined whether the proportion of peers who believe that boys are better at learning mathematics than girls affected boys' and girls' perceptions of attention and praise from teachers in different ways. We found that having a greater proportion of peers who hold the gender-math stereotypical belief resulted in a significant decrease in girls' perception of attention (b = −0.056, SE = 0.018, p < .01) and praise from their math teachers (b = −0.044, SE = 0.023, p < .1), compared with boys' (see Fig. 1). However, the proportion of peers who held gender-math stereotypes did not similarly influence boys' and girls' perceived attention and praise from English and Chinese teachers, although girls were somewhat less likely to perceive attention and praise from Chinese teachers (see Table S8 in the Supplemental Material).
It is possible that girls exposed to more peers with the gender-math stereotypical belief may lower selfconfidence and/or expectations for studying mathematics, which, in turn, will diminish their performance in math. Moreover, because math is one of the three core subjects in middle school, the degree of confidence a student has about studying math might also affect their perception of career choice in their future. It is also common for parents' expectations to be influenced by their children's academic performance. If exposure to peers who hold the gender-math stereotypical belief significantly influences students' academic performance, this may affect the degree of stress that students feel in relation to their parents' expectations about their academic achievement. Here, we examined how gendermath stereotypical beliefs affect self-confidence and stress outcomes. Results suggest that boys and girls have diverging estimates (see Table S9 in the Supplemental Material). We found that exposure to more peers who believe the gender-math stereotype-that boys' innate math ability is superior to girls' innate math abilityincreased girls' likelihood of believing that math is difficult (b = −0.074, SE = 0.020, p < .01) and decreased their agreement that math relates to their future career advancement (b = −0.054, SE = 0.021, p < .01), compared with boys' (see Fig. 1d). However, we did not find differential influence for boys and girls with respect to their perceptions of Chinese and English (see Table S10 in the Supplemental Material). This peer-environment effect also contributed to higher levels of stress among girls about their parents' expectations regarding their academic achievement in comparison with stress levels of their male counterparts (b = 0.075, SE = 0.028, p < .01).

Study 2: Laboratory Experiment
The natural experiment confirmed that a peer environment with high levels of the gender-math stereotype could hurt girls' math performance and reduce their pursuit in math-related extracurricular activities. Such a peer environment also increases a child's likelihood of believing the gender-math stereotype, increases the perceived difficulty of math, and reduces aspirations among girls. However, the natural experiment did not directly test the mechanism underlying these factors. We assumed that a peer environment high in stereotypical peer beliefs hurts girls' math performance because of the detrimental effect of the gender-math stereotype transmitted through peers. To establish a direct causal attribution of the effect to the stereotypical belief, we need to experimentally manipulate the activation of such beliefs and observe the immediate impact on female versus male students. Next, we conducted a laboratory experiment to explicitly activate gender-math stereotypes, followed by an assessment of test performance.

Method
The experiment was preregistered on OSF (https://osf .io/9wfsr/) and approved by the University of California, Los Angeles Institutional Review Board. This experiment included a cross-sectional sample of undergraduate and graduate students in a large university in Southern China. A total of 547 undergraduate and graduate students were recruited through the behavioral economics laboratory on campus (167 men, 380 women; age: M = 20.67 years, SD = 2.43, range = 18-36). The majority of the students majored in economics and had taken advanced college-level mathematics classes. Participation in the experiment was voluntary. All participants were compensated 30 renminbi (RMB; $6.3 U.S.) as a standard participation fee and 3 RMB in cash for each question correctly answered. 4 This compensation rate was seen as attractive to an average student in China. Students were motivated to get high scores: The more correct answers they got, the more real bonus they would earn. Thus, better performance in the lab was rewarded, just as better performance in the real world is rewarded.
In the experiment, 547 college students reported to the laboratory in mixed male and female groups of 19. Each participant had their own cubicle in the laboratory with minimal distraction. Participants were presented with a 5-min video clip and answered questions regarding the content of the video. Each participant was randomly assigned either to a stereotype-activation condition, in which the video portrayed observable gender gaps in math performance in the United States and China, or to a control condition without gender or math-related information. The video in the stereotypeactivation condition contained statistics from several representative surveys (e.g., China Family Panel Studies 5 ) that suggest that (a) men outperform women in mathematics on average and (b) more men than women score in the top percentiles in standardized math tests. The stereotype-activation video is meant to trigger thoughts on gender-based differences in math performance. It is intended to bring to the forefront any easyto-activate stereotypical beliefs on gender-math stereotypes. The video in the control condition talked about human memory and introduced strategies to facilitate memory encoding and strengthening without mentioning gender differences. We expected the control video to evoke no gender or math-related thoughts for either women or men. In contrast, we hypothesized that the gender gap in the stereotype-activation condition would evoke negative stereotypes and hamper math performance for female college students but not for male college students.
After viewing the video and answering factual questions about the video content, participants performed a series of computer-based academic tests used to measure either math or verbal performance. They were informed that they would have 20 min to complete different types of test questions and that they would receive their scores at the end of the experiment. The 20 min were divided into four 5-min test sessions. 6 Each of these test sessions was composed of five advanced college-level math questions or five advanced collegelevel Chinese verbal questions. The order of the test sessions was counterbalanced. Math performance was calculated by the number of questions participants got correct out of all math questions (all students attempted all test questions). Similarly, verbal performance was calculated by the number of questions participants got correct out of all verbal questions. After completion of these test sessions, participants were offered a bonus test session in which they could choose to complete either five more math questions or five more verbal questions. This choice task was intended to measure their domain preference. We also collected participants' self-reported psychological outcomes, including test anxiety, domain identification, stereotype threat, confidence, and effort, as well as general demographic information at the end of the experiment but before they received test feedback on the number of correct answers and their compensation.

Results
Math and verbal performance across genders in the laboratory experiment is plotted in Figure 2. In the control condition, we found an existing gender gap in math test scores between male and female students, which is consistent with the baseline gender-math gap in Chinese universities (we provide statistics regarding this realized gender gap in math in Chinese colleges by university rank using data from the 2010 to 2016 Chinese College Students Survey in the Supplemental Material). Male college students performed similarly well in math and verbal tasks across both the control condition and the stereotype-activation condition-math: t(164) = −0.31, p = .75; verbal: t(164) = 0.12, p = .90. In contrast, in the stereotype-activation condition, designed to trigger thoughts on gender-based differences in math, the female college students performed significantly worse in math tests compared with the female students in the control condition-math: t(343) = 3.28, p = .0011, Cohen's d = 0.34. No difference was found in verbal tests, t(343) = 1.20, p = .23. A two-way analysis of variance revealed a significant interaction between gender and condition on math performance, F(1, 543) = 4.47, p = .035. In other words, for both math and verbal tasks, the male college students were uninfluenced by condition, whereas the female college students performed significantly worse in math when the gender gap in math was made salient. Women in the stereotypeactivation condition scored 0.9 point lower on average (M = 4.19, SD = 2.70) than women in the control condition (M = 5.10, SD = 2.58; p = .001), which represents an 18% drop in math performance. We conducted additional robustness checks (e.g., controlling for participant demographics and/or session fixed effects; see the Supplemental Material) and found consistently significant results (see Table S11 in the Supplemental Material). Contrary to the preregistered hypothesis, our results did not reveal a significant difference in students' domain preference-female and male college students were equally likely to choose to complete either a math bonus session or a verbal bonus session in the treatment and control conditions (p > .05).
We hypothesized that the activation of the gendermath gap could potentially induce distracting thoughts among female students, who would be less able to exert effort in math tests and subsequently fare worse. Using the self-reported outcomes measured at the end of the experiment, we found a significant interaction effect between gender and condition on the ability to focus and exert effort in the tests. Female college students in the stereotype-activation condition reported having more distracting thoughts and exerting significantly less effort in the tests (M = 4.48, SD = 1.17) compared with male students (M = 4.88, SD = 1.15, p = .003) or women in the control condition (M = 4.78, SD = 1.11, p = .013). We did not find a similar interaction effect on the other psychological outcomes measured, including academic domain identification, sense of threat, and test anxiety (ps > .05).
In sum, we found a robust effect of the activation of gender-math gaps on female college students' math performance. Female students in the stereotype-activation condition exerted less effort and had more distracting thoughts during the experiment. The stereotype activation did not affect male college students and did not affect male or female students' verbal performance. However, these findings have limitations. The causal attribution of a laboratory experiment comes at the expense of some external validity. For example, we explicitly activated gender-math stereotypes in a laboratory environment. Such explicit priming may not mirror naturally occurring circumstances. In a natural environment, comments about gender-math stereotypes may come less explicitly and co-occur with social group interactions. The behavioral impact might follow much later after a series of encounters with such stereotypes rather than observed immediately after one single encounter. It is possible that the gender-math gap puts pressure on boys to perform consistently well in math, creating a cognitive load comparable with that experienced by girls. It is also possible-though less plausible-that the girls structure their lives to avoid these concerns. The findings from the earlier natural experiment help address these issues, and thus the two experiments are complementary.

Discussion
Across two experiments, the results advanced an important channel through which gendered beliefs in math ability are transmitted in one's ambient environment and affect female students' academic performance. We used data from a natural experiment and a wellpowered preregistered laboratory experiment to demonstrate that gender-math stereotyping has both a cumulative and immediate influence on girls' and women's performance in mathematics. The age at which stereotyping influences math performance starts much earlier before adulthood. A potential route of influence is through peer environment: The more girls are exposed to peers who hold erroneous stereotypical beliefs on the innately superior math ability of boys, the worse they fare in math tests. We overcame the practical and ethical barriers to estimating this relationship experimentally by applying a quasi-experimental research design in a natural setting with substantial random variations in the proportion of a child's peers who hold the gendered belief in math ability.
Several aspects of the current research make it likely to have underestimated the full impact of the influence of peer beliefs. First, we studied one cohort of outcomes in middle schools (Study 1) and the momentary effect from a laboratory (Study 2), whereas the overall career effects of decades of cumulative exposure to these stereotypical beliefs are likely to be larger if they compound over time. Second, we conducted our study in contexts where female students are already strong in mathematics-in Study 1, middle school girls on average outperformed boys, and in Study 2, the majority of participants were college economics majors. Even in contexts where the stereotype runs counter to reality, we still find harm in exposure to peers who hold such beliefs.
Although some researchers suggest that the role of negative stereotype is "overcooked" and its influence on behavior is overexaggerated ( Jussim, 2015;Stoet & Geary, 2012), our research suggests the harm from gender-math stereotyping is still alive and perpetuating itself through the peer environment. The prior research on gender inequality focused almost exclusively on changing girls' attitudes and choices, with relatively less attention to the messages from peers with whom they share classrooms and schools on a daily basis (Riegle-Crumb & Morton, 2017). It may be more fruitful to * Results from Study 2: mean score on the math and verbal tasks in the stereotype-activation and control conditions, separately for female and male college students. Error bars reflect 95% confidence intervals. The asterisk indicates a significant (p < .05) two-way interaction between gender (female vs. male) and condition (stereotype activation vs. control).
change the ambient social environment that children and young adults are embedded in. We call attention to the importance of examining sources of peer influence within local contexts, as well as highlighting the need for more research that focuses on peer influence on stereotypical belief formation during the formative stages of adolescence in particular. Our work may also provide a new perspective on the debate on stereotype threat. According to the stereotype-threat theory, the possibility of confirming a negative stereotype for a target group provokes anxiety and threat, which leads group members to underperform on the task domain they are stereotyped on. Consistent with the main prediction, our laboratory experiment and field data support that negative stereotyping causally reduced female students' math performance. However, contrary to the increased anxiety or effort as proposed by classic stereotype-threat theory, our results showed no evidence of changed levels of anxiety or threat. Instead, our data suggest that girls and young women reported significantly reduced effort (consistent with past studies such as Jamieson & Harkins, 2007Mrazek et al., 2011;Seitchik & Harkins, 2015), possibly from lowered self-confidence and selfexpectations and increased distracting concerns (though our design cannot distinguish between a direct effect and a conditional effect). The prior theory also noted that targets of negative stereotypes must identify with the domain in which the threat occurs in order to be affected by a threat cue (Aronson et al., 1999;Deaux et al., 2007;Shih et al., 1999). The rationale is if targets do not care about the domain in which they are negatively stereotyped, then there should be no threat to the self to be concerned about and thus no stereotypethreat effect. However, we did not find a moderating effect of domain identification or perceived importance of mathematics-women and girls across the board seem to be affected by the negative stereotyping.
Although our study addresses some of the limitations of prior research, it is subject to limitations. Although we demonstrated the peer environmental influence on academic and psychological outcomes, we know less about the process of change from the belief transmission. Although we captured the actual beliefs of the children and their peers, we do not have measures on what the children believe that their peers think as well as the actual classroom interactions and experiences. We speculate that the denser the gender-math stereotype is in a child's ambient peer environment, the more likely disparaging messages from peers will be transmitted through social interactions, leading to the observed gender inequality in aspiration and attainment. Future research could focus on the actual interactions that happen within peer groups, as well as continuously investigate the generalizability across different contexts and populations.
These findings bear theoretical and practical implications. Social beliefs about differential abilities of gender groups contribute to individual belief formation (Bian et al., 2017;Jayachandran, 2015;Nollenberger et al., 2016). We show that exposing a child to a greater number of peers who hold a stereotypical (but objectively inaccurate) belief causes a child to be more likely to hold the belief themselves. Moreover, the peer influence impacts not only belief formation but also demonstrated academic performance. Understanding the underlying mechanisms was critical for developing interventions that reduce stereotype threat and the group-based disparities that inspired this line of research. How can we curb the peer transmission of gendered beliefs in ability? How can we change these objectively inaccurate and proven harmful beliefs? Future research should aim to attend to theoretically driven interventions that mitigate and reverse the harm from beliefs in differential group-based ability.

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