Introduction

While gender disparity in science, technology, engineering, and math (STEM) fields has been studied extensively during the last decade [1–4], attempts to increase the representation of females in STEM disciplines through classroom interventions have led to mixed results [5]. Therefore, it is critical to evaluate the mechanisms contributing to these disparities in order to achieve persistent change [6]. There are multiple possible mechanisms for these gender disparities at the undergraduate level, including general societal perceptions and stereotypes, and local factors such as perceived classroom and departmental norms and practices [7]. The latter often reflect social cognitive factors such as implicit bias, stereotype threat, and others [8–15]. Implicit gender bias has been clearly demonstrated in the evaluation of the competence of musicians [16], and it is plausible that similar effects would be present in other male-majority fields. Such implicit bias in college classrooms can have a significant impact on the chilly climate [17] for women in male-majority fields such as physical sciences and engineering [18].

Grunspan et al. examined students' gender bias in their perception of their peers’ competence (“peer perception bias”) in an undergraduate biology course [19]. They found that male students preferentially selected their male classmates as more knowledgeable compared to female classmates, while female students showed no such bias. Even if a female and a male student had the same grade, the male student was more likely to be nominated as knowledgeable by other male students. Furthermore, they found that “celebrities”, students who were chosen by the most students as being particularly knowledgeable, were overwhelmingly male.

Such gender bias in peer perception, if found consistently across institutions and STEM fields, would have important implications for understanding gender disparities in STEM. Biased perceptions would contribute to the chilly climate of STEM courses for female students, make women less likely to pursue these fields, and make it significantly harder for them to thrive if they do pursue these fields [20, 21]. Furthermore, perceptions of one’s peers plays a major role in hiring and progression in a field [21, 22], arguably a greater role than any objective measure of knowledge or ability.

The Grunspan et al. result was particularly worrisome, because the study was conducted in undergraduate biology courses. Unlike many other STEM fields, biology courses (and the discipline in general) have slightly more female students than male students [23]. We shared the view of Grunspan et al. (p. 12) that STEM fields with lower female representation might exhibit even larger peer perception biases compared to biology, as previous work has shown that female enrollment in science courses is negatively correlated with implicit and explicit science-gender-biases [24]. The lower presence of women in a STEM field can be particularly consequential for implicit gender biases in that field according to the associative-propositional evaluation model [25, 26]. According to this model, implicit biases are the results of associative processes in memory. Therefore, a lack of repeated exposure to women in a field (that is, few female role models, instructors, or peers) can lead to a weaker association between women and that field, and thus more implicit biases toward women. On the other hand, it is possible that women in engineering may be perceived as particularly exceptional because they have persisted in the male-majority discipline [27, 28], which may counter gender biases.

To test the hypothesis that peer perception bias would be more pronounced in male-majority fields, we conducted a similar study to that of Grunspan et al., but in an introductory mechanical engineering course. We chose this course because it was the largest engineering course at our institution in a strongly male-majority engineering discipline. Of course, such biases in STEM are not isolated to female students and also exist for many other minority groups. However, in the present study, we only looked at gender because of the small number of students in the class from other minority groups.

Grunspan et al.’s study also presented the possibility that classroom environment or instructional practices might mitigate the effects of gender on students’ perceptions of their peers. They found that the network of nominations and the strength of the peer perception bias differed between courses with an all-male instructional team and a course that used random call and included a female instructor. Random call has been found to eliminate gender gaps in class volunteers [29], and female instructors can reduce the science-gender-biases of female students [30]. It is possible that these aspects of the classroom impact how comfortable students are with speaking up in class, which in turn might impact their nominations. This raises broader questions about how classroom environments or instructional practices affect students’ peer perceptions. Another variable to consider would be how familiar students are with their peers in general, which could be very different in courses that use lecture-based instruction versus active learning [31].

We collected our data in two sequential offerings of the same introductory mechanical engineering course at Stanford University. Although these offerings covered the same content, they had different instructors (both tenured faculty members) who used very different instructional practices. One offering used traditional lecture-based instruction and was taught by a male instructor. The second offering had extensive use of active learning, including interactive lectures and group activities [32], and was taught by a female instructor. The variations in the offerings were not experimentally designed by the authors, but rather predetermined by the departmental constraints of these two offerings. That said, these variations allowed us to not only examine the generalizability of potential peer perception bias in mechanical engineering courses, but also to examine variations in students’ perception of their peers in different classroom environments, as hypothesized by Grunspan et al. We also examined students’ perception of the classroom environment itself across these two offerings to probe the impact of the classroom environment or context on the biases and nomination networks.

Materials and methods

Course offerings and participants

The study was conducted in the fall and spring quarter offerings of the introductory mechanical engineering course. This course is a requirement for mechanical engineering majors as well as six smaller (but still male-majority) engineering majors: aeronautics and astronautics, biomechanical engineering, civil engineering, product design, environmental systems engineering, and architectural design. It was also an elective course for other engineering majors. The percentage of bachelor’s degrees awarded to women in the respective disciplines in 2015–2016 in the US were: mechanical engineering 13.8%; aerospace: 14.3%; biomedical: 41.4; civil engineering 24.0%; environmental systems engineering 28.3%; and architectural design 32.7% [33]. At Stanford university, for the year of data collection for this study (2015–2016), the percentages of women declaring their major in the engineering disciplines for which we have data are: mechanical engineering 36%; bioengineering 43%; civil engineering 43%; and environmental system engineering 81% (13 out of 16 students) [34].

The spring quarter offering of the course (“traditional”) was taught by a male instructor in a stadium-seating lecture hall. The typical class session involved lecture from the instructor along with multiple questions posed to students for individual answers. The fall quarter offering was taught by a female instructor in a classroom with moveable chairs and tables that could be rearranged for group work (“interactive”). Students were divided into four fixed groups to work on group activities in class. Students also had two group projects carried out over the course, with different groups for each project. The typical class session involved some lecture from the instructor with multiple questions to students, but almost all the class sessions included in-class lab and group activities, which required students to interact with each other. Student grades for the Traditional offering were based only on homework and exams, while for the interactive offering, the group projects and class discussion counted for 25% of the grade, with homework and exams making up the remaining 75%. The number of students enrolled in each offering by gender and grade level is given in Table 1. Because of prerequisites, freshmen students could not enroll in the fall offering.

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Table 1. Student characteristics for the two course offerings.

https://doi.org/10.1371/journal.pone.0212477.t001

The data were collected through a survey given in class. Students participating in the study, therefore, were ones who attended class and completed the survey on the day the survey was conducted. The student characteristics for each offering are summarized in Table 1. While both offerings had about the same number of enrolled students (approximately 80), the probability of students attending the class on the data collection date was significantly higher for the interactive offering (p = 0.0001), and this was not different across genders (p = 0.330). The female-male ratio was also higher in the interactive offering, suggesting some selection bias in the offering in which students chose to enroll. This selection may have been influenced by the gender of the instructor and/or the different teaching practices, both of which were known to most students before they enrolled.

For both offerings, the survey was administered in a paper format during the first 10 minutes of the class session, in week nine of the ten-week quarter. Grunspan et al. administered the survey multiple times throughout the course, but the largest bias was consistently observed at the end of the course. To comply with instructors’ desire to minimize the disruption, we only conducted the survey once and did so at the end of the course to maximize the signal. The first page of the survey included a written consent form for students to read and sign. Before starting the survey, the researcher summarized the content of the consent form including participants’ rights and privacy, instructed students to read the form carefully, and, if willing to participate in the study, sign it. For both offerings, the survey included the following parts:

1. A list of students enrolled in the class, along with a prompt to nominate the students from the list who they thought were “particularly strong in the course material.” The class list was in alphabetic order by last name for half of the surveys and in reverse alphabetic order for the other half to reduce the impact of the list sequence on the nomination pattern. We decided not to use a random list, as it would have made finding a particular name on the list much more difficult and time consuming for students. We did not say whether students could nominate themselves.
2. Two multiple-choice questions asking students about their familiarity with their classmates:
   1. "What percentage of the names on page 2 did you recognize?"
   2. "How many other students in the class have you discussed course material with (in or out of class)?"
3. Demographic questions, which asked for students’ name, ID number, gender, age, and their declared/intended major. Gender and age were multiple-choice questions, and the rest were open-response.
4. Four questions about students’ perception of the course learning environment taken in their entirety from a validated survey [35]. These questions asked the student to rate the following statements about the course environment from strongly disagree (1) to strongly agree (5), with question d) used to check for possible overall differences between the two offerings with regard to the students’ perceptions about diversity issues in general:
   1. Students in the class try to help one another understand course material (e.g. sharing lecture notes when absent).
   2. Students in the class consider themselves as part of a community.
   3. I am comfortable making a comment or asking a question during class discussions.
   4. Stanford University demonstrates a strong institutional commitment to diversity.

In the interactive offering, we also asked students to name the classmates with whom they interacted the most and to name their team members for the two class projects. For both offerings, the instructors provided the research team with all students’ course grades at the end of the quarter. The course grades were compared across genders and across participating and non-participating students (that is, those who attended and did not attend class on the data collection date). The Institutional Review Board of Stanford University approved this study under IRB protocol number 37719.

Results

We first present an overall summary of the nomination patterns and student grades in the two course offerings. Then we present our findings regarding our two research questions: RQ1) peer perception bias in another institution and field, and RQ2) understanding factors affecting peer perception.

Basic nomination patterns across the two offerings

The breakdown of nominations between genders and offerings is shown in Fig 1. Students in the interactive offering, on average, made 3.92 nominations and received 3.54 nominations. Students in the traditional offering, on average, made 2.43 nominations and received 1.26 nominations. Linear multivariable regression analysis of the number of nominations made and received, controlling for students’ grade and gender, shows that the average number of nominations made and received by students in the interactive offering was significantly higher than in the traditional offering (difference between offerings in nominations made: t(113) = 2.70, p = 0.008; difference between offerings in nominations received: t(159) = 6.06, p < 0.0001). The details of these regression analyses are included in Tables A and B in S1 File. In this and the subsequent analysis, we have excluded self-nominations as in [19]. The pattern of self-nominations is discussed below separately.

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Fig 1. Average number of nominations made and received by each student across genders and course offerings.

The error bars represent the 95% confidence intervals. The average number of nominations made and received is not the same for each category because the students who did not submit the survey could receive a nomination but could not make a nomination.

https://doi.org/10.1371/journal.pone.0212477.g001

The graphs for the nomination networks for the two offerings are shown in Fig 2. This illustrates the differences in the nomination patterns in the two offerings, with more overall nominations made and received in the interactive offering. It also shows that, in the interactive offering, the network of nominations was more interconnected compared to the traditional offering, and fewer students made no nominations or received none.

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Fig 2. Network of students’ nominations for both offerings.

Nodes represent students; links going out of each node represent nominations made by that student, and links going in to each node represent nominations received by the student. The size of each node represents the number of nominations received by that student.

https://doi.org/10.1371/journal.pone.0212477.g002

RQ1: Peer perception bias in a different institution and field

ERGM network model for peer perception.

Table 2 shows the summary of the ERGM models for each offering. For both offerings, the gender of the nominator did not affect the probability of a student receiving a nomination (traditional: p_gender = 0.639; interactive: p_gender = 0.857); however, the grade of the nominee had a small but statistically significant effect on the probability of a student receiving a nomination (traditional: p_grade = 0.002; interactive: p_grade = 0.009). In looking at the dependence of nominations on the gender of the nominee, there was no significant male-male bias (traditional: p = 0.524, interactive: p = 0.223) or female-female bias (traditional: p = 0.161; interactive: p = 0.823) in the nominations received in either offering. This means that, controlling for the grade of the nominee, network structure, and student familiarity, neither female nor male students showed any gender preference in their nominations. This was true for both course offerings. These results are different from Grunspan et al.’s findings that male students were more likely to nominate their male peers than female peers.

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Table 2. Coefficients from exponential random graph modeling (ERGM) for both offerings, with standard errors in parentheses.

https://doi.org/10.1371/journal.pone.0212477.t002

To address limitations of ERGM, we checked the findings of the ERGM analysis three ways. First, by using logistic regression to predict the probability of a student being nominated. Second and third, by using multivariable linear and Poisson regressions to predict the number of nominations received by each student. In these three regression models, the predictors were: gender of nominee, gender of nominator, and course grade of nominee (Tables C, D and in S1 File). The addition of an interaction between gender of nominee and nominator in either of these models did not improve the model fit significantly, and when included, was either insignificant or marginally significant. Therefore, in these results we also did not find evidence for significant male-male bias in peer perception. Although the sample size in this study is much smaller than in Grunspan et al., an analysis of our statistical power, as shown in Table F in S1 File, indicates that if there was a bias in either course offering of the size observed in Grunspan et al.’s study, we could have rejected the null hypothesis that there is no bias with a p-value of 0.02 or smaller.

Celebrity status and course performance.

Grunspan et al. also looked at the gender composition of students receiving exceptional numbers of nominations (“celebrities”). They found that the celebrities were predominantly male, the student with the most nominations in a class was always male, the highest rank for female celebrities was fourth, and, given the same grade, female students had lower celebrity rankings than their male peers. In our study, as shown in Fig 3, the most nominated student in the traditional offering was male and the second was female with only one fewer nomination (5 vs. 4). In the interactive offering, the most nominated student was female. Overall, there is no obvious pattern of gender preference in celebrity status. Also, as can be seen in Fig 3, in both offerings, the student with the highest grade was ranked third. We conclude that the prerequisite for becoming a celebrity in these courses was neither the highest grade nor being a male, in clear contrast with Grunspan et al.’s findings.

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Fig 3. Students receiving the most nominations in the two offerings, by number of received nominations and course grades.

Green students are male and blue are female. Recall the ratio of the number of male to female students was 1.8 for the traditional offering and 0.9 for the interactive offering.

https://doi.org/10.1371/journal.pone.0212477.g003

Self-nomination.

An unforeseen finding in our data was that of self-nomination. As discussed above, we (and Grunspan et al.) excluded self-nominations from the analyses above because we were interested in students’ perceptions of their peers. We found, however, that male students nominated themselves with marginally higher probability regardless of the course offering (p = 0.092). This result is consistent with previous reports of male students having higher self-concept [40] and male scholars being more likely to cite themselves [41]. Approximately a third of participating male students (8 out of 27 in the traditional offering and 12 out of 35 in the interactive offering) nominated themselves as being highly knowledgeable. However, for female students, these percentages were 6% (1 out of 15) and 18% (7 out of 40), for the traditional and interactive offerings, respectively. In the interactive offering, students of both genders nominated themselves with higher probability, but the difference between offerings was much larger for female students. Due to the small number of self-nominations, particularly for female students, these differences were not statistically significant (p = 0.467), however. Nonetheless, this result suggests that looking at self-nominations of competence might be a novel way to explore how female and male students’ self-confidence is influenced by instructional practices.

RQ2: Understanding factors affecting peer perception

To better understand the distinctions in the impact of the different offerings, we examined differences between the offerings in the students’ familiarity with their peers and, to a lesser extent, their perceptions of the class environment.

Students’ familiarity with their peers.

In the interactive offering, we asked students to name the peers they worked with most often, as well as their project team members. The majority of students’ nominations (64%, SE = 4%) were from these proximity circles, and this percentage was not different across students’ gender (U = 554, p = 0.86; Mdn_female = 0.33, Mdn_male = 0.39). This result is consistent with the ERGM result that mutuality was the strongest factor influencing the probability of students’ nominating a peer.

We determined students’ overall familiarity with their peers through their responses to two questions on the paper survey that probed: 1) What percentage of the names on the class list they recognized, and 2) How many other students in the class they discussed the material with (in or out of class). The responses to these two items, shown in the Tables 3 and 4, indicate that, not surprisingly, students in the interactive offering knew significantly more of their classmates (Fisher’s exact test: p < 0.0001), and interacted with significantly more of them (Fisher’s exact test: p = 0.003). In the traditional offering, 32.5% of the participants replied that they recognized 0% of their classmates’ names. In the interactive offering, in contrast, there was no student who did not recognize any of their classmates’ names. In the traditional offering, only 24.4% of students reported that they had discussed the course material with more than 5 of their classmates, while, in the interactive offering, this fraction was 45.3%. The difference in the students’ familiarity and interactions with their classmates can explain the higher number of nominations made in the interactive offering compared to the traditional offering.

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Table 3. Percentage of students’ names participants recognized across the two offerings.

https://doi.org/10.1371/journal.pone.0212477.t003

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Table 4. Number of classmates with whom students discussed course material.

https://doi.org/10.1371/journal.pone.0212477.t004

Students’ perception of the learning environment.

Grunspan et al. observed a suggestive pattern that the course learning environment might have influenced students’ peer perception bias. To explore this issue, we asked students about their perception of the course learning environment explicitly [32]. We saw a difference in students’ perception of the learning environments as shown in Fig 4, with students of both genders indicating more positive perceptions of the interactive class environment. They found it to be a more supportive environment (U = 2237, p < 0.0001, Hodges-Lehmann estimator Effect size = 0.42), with a higher sense of community (U = 2526.5, p < 0.0001, Hodges-Lehmann estimator Effect size = 0.56), and were more comfortable asking questions (U = 2064, p = 0.001, Hodges-Lehmann estimator Effect size = 0.30). Also, female students were significantly less comfortable asking questions in the traditional offering than male students (U = 104, p = 0.009, Hodges-Lehmann estimator Effect size = 0.29), while this difference was marginal in the interactive offering (U = 530, p = 0.059, Hodges-Lehmann estimator Effect size = 0.22). Students in the two offerings did not differ in their perception of the university’s commitment to diversity (U = 1764.5, p = 0.160), suggesting that their responses to the other questions were determined by the specific class environment, rather than general perceptions about the institution and their fellow Stanford students as a whole.

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Fig 4.

A. Average responses to the perception questions. B. Responses to “Comfortable asking questions” item broken down by gender and course offering. This was the only item that showed a significant gender difference. The error bars represent standard errors.

https://doi.org/10.1371/journal.pone.0212477.g004

Future work should evaluate whether these patterns reproduce and how they moderate students’ peer perception in courses, while controlling for students’ selection biases and effects of instructor gender. This will clarify whether interactive instructional practices lead to classroom environments that encourage a greater sense of belonging and a supportive community. Other work [32] has shown indication of such effects.

Discussion

To study a potential mechanism for gender disparity in STEM, we examined whether students in a mechanical engineering course showed gender bias in peer perceptions as observed by Grunspan et al. [19] in biology classes. Grunspan et al. observed a bias against female students by their male classmates in perceived knowledge of the subject. We conducted the study in two offerings of an introductory mechanical engineering course to test the generalizability of these results in another institution and a more male-majority field.

In contrast to the previous study in introductory biology, and our own hypothesis, we saw no bias against female students. These findings suggest that the gender bias reported by Grunspan et al. is not necessarily generalizable to different STEM fields and/or different institutions. The different findings across the two studies calls for further investigation to understand potential differences in gender biases in student perceptions of their peers across different STEM fields and different institutions.

In both the interactive and traditional course offerings, we saw that the probability of receiving a nomination was mainly associated with students’ familiarity with their peers and, to a lesser extent, the grade of the potential nominee. In the interactive offering, we also asked students to list friends and project members. We observed that more than 60% of nominations made by each nominator were from their listed friends and project members. Students were more familiar with each other in the interactive offering, made more nominations, and correspondingly had a more interconnected network.

The different instructional approaches used in the two offerings of the course probably impacted the different levels of familiarity and associated number of nominations. We noted a number of other intriguing differences between the two offerings of the course, which we speculate might be associated with the differences in the instructional practices. Students perceived the interactive course to be a more comfortable and supportive community. Our study does not allow us to draw conclusions as to the connection between these perceptions and the teaching methods used because of the likely presence of selection bias between the two offerings, as well as the difference in instructor gender. However, these initial observations can inform future studies to investigate the effects of instructional practices on students’ perception of the learning environments and possible impacts on peer perceptions.

A limitation of our study is that a number of students did not attend the class on the date of data collection, and so did not nominate their peers. This number was larger in the traditional offering. However, as mentioned in the results section, male and female students were equally likely to not participate in the study, so these missing students are unlikely to affect the determination of gender bias.

Our study differs from that of Grunspan et al. in a number of ways that may have contributed to the differing results. One factor is class size. The Grunspan et al.’s study used three courses, each with hundreds of students. We had 81 and 83 students in the two offerings studied. As discussed in the power analysis in S1 File, we had sufficient statistical power to observe bias of the reported size, but there could be other factors that depend on class size. For example, class size could also have contributed to the results through the impact on students’ familiarity with their classmates. It is plausible that this could result in different nomination patterns between large and small classes. In a small class, it is relatively easy to get to know a larger fraction of fellow students in the classroom setting, and hence have better knowledge of their competence compared to what is possible in a large class. This will mean that the nomination patterns of students in large classes will be more sensitive to any gender imbalances to their familiarity circles.

Another difference between the two studies is the level of students. In our study, the students were more advanced, spanning all four years, and it is possible this influenced the extent of the peer perception bias. We cannot rule out the possibility that as the students advance in STEM fields, biases are reduced because students are more integrated into the culture [21, 22]. The two different institutions are also rather different, one being relatively small and highly selective, while the other is a much larger public institution, and this may result in differences in the student populations.

The other major difference between the two studies was the academic fields under study: biology compared to mechanical engineering. Biology as a field has stronger representation of women than mechanical engineering. We, as well as Grunspan et al. (p. 12), initially hypothesized that low female representation in male-majority STEM fields might lead to a larger peer perception bias in these fields compared to biology. However, cultural norms, characteristics of the institution, instructional practices, and role models in the field or in the institution might have stronger effects on gender biases in a specific discipline than the mere gender ratio. The possible impacts of these local issues and how they interact with the broader image of the field to influence gender bias warrant further study.

Understanding factors that contribute to gender biases and resulting variations in gender biases across different STEM fields or institutions is critically important, as both overestimation and underestimation of gender biases across fields are harmful. Overestimation of gender biases can send discouraging but untrue messages to female students considering entering those fields, while underestimation can inhibit the efforts needed to address such biases where they exist. In addition, the more nuanced understanding of gender biases can inform more targeted efforts for each field to overcome these biases. Grunspan et al. concluded that “our work implies that the chilly environment for women may not be going away any time soon” (p. 13 of [19]). Our study suggests that the environment may not be as chilly as they concluded.

Supporting information

Acknowledgments

We thank Sheri Sheppard, Peter Pinsky, and Jeany Wang for their help and support in conducting this study. We also like to thank Benjamin Keep, Cissy Ballen, and Wieman group members for their valuable feedback. We would also like to thank anonymous reviewers who provided us with valuable feedback on the earlier drafts of this paper.