Strengthening the STEM Pipeline for Women: An Interdisciplinary Model for Improving Math Identity

Abstract

Drawing on a social identity framework of mathematical development, the authors present a model, Improving Girls' Math Identity (IGMI), designed to address two key “leaks” in the female STEM pipeline: undergraduate and middle school. IGMI involves a supportive professional development network for undergraduate women preparing to transition into mathematics-related careers, and a mentorship program connecting middle school girls with these undergraduates to develop metacognition, problem-solving, and spatial skills. Preliminary evidence demonstrates that the model successfully strengthens undergraduates' problem-solving abilities, improves resilience and persistence in pursuing STEM fields, and increases investment in supporting future cohorts of women in mathematics and science.

Keywords:

• Gender
• STEM pipeline
• problem-based learning
• metacognition
• spatial reasoning

1. INTRODUCTION

Research attributes the gender gap in STEM to many causes, including societal beliefs and stereotypes, lack of female role models, workplace culture, lack of interest, gender differences in beliefs about achievement and performance, and gender differences in performance on spatial reasoning tasks [41]. Boys and girls are equally prepared, skilled, and interested in mathematics and science through primary and secondary school [57]. However, around adolescence, girls begin to report lower interest in mathematics and science, and lower aspirations for pursuing these fields relative to boys, particularly among certain ethno-racial groups [61]. There is a clear shift in girls' social identity relative to mathematics during middle school that impacts their willingness to pursue and engage in STEM fields beyond these formative years. This is evidenced in high school as girls enroll in fewer science and mathematics courses, and in college as fewer women go on to major in STEM disciplines: for instance, although over 57% of bachelors degrees were awarded to women in 2018, they only earned 39% of STEM degrees [53].

Self-confidence in mathematics, in particular, can directly affect women's interest in and exposure to the wide range of STEM majors and careers [19]. Although people in science and engineering careers in the U.S. are not necessarily those who performed at the highest levels in their mathematics courses, there is still a perception that success in STEM majors requires very strong performances in mathematics classes [77].

As an interdisciplinary group of researchers and STEM practitioners, the authors designed an intervention entitled Improving Girls' Math Identity (IGMI), which addresses two of the major “leaks” in the so-called STEM pipeline: the college period and the middle school period. Integrating a social identity framework with three core skills (metacognition, problem-based learning, and spatial reasoning), the program aims to address societal, psychological, and intellectual factors that contribute to the gender gap in mathematics and subsequent STEM outcomes. IGMI recruits and trains a cohort of undergraduate women majoring in STEM fields to become mentors who lead workshops (GEM – Girls Exploring Math) for local middle school girls.¹ These mentors represented a range of majors, including mathematics, genetics, neuroscience, biology, engineering, and computer science, among others. Some undergraduate team members intended to pursue careers in education, and many planned to pursue STEM industry jobs and/or advanced STEM degrees. Preliminary evidence from this intervention indicates that it has been successful in creating a network of supportive female STEM majors who might not have otherwise interacted. The program has also improved mathematical self-efficacy and confidence among both college students and middle schoolers in problem-solving, presenting mathematical work, and approaching new problems. Finally, IGMI has strengthened participants' ability to navigate a future STEM career as women and has created an investment in nurturing future generations of underrepresented groups through the STEM pipeline. Further details about outcomes are given in Section 4.

2. BACKGROUND

IGMI was designed with the goal of improving math identity among undergraduate women and middle school girls. A math (or STEM) identity comprises the beliefs and attitudes a person holds about mathematics (or STEM) along with the degree to which they see themselves as members of the corresponding community [3,35,44]. The authors argue that an interdisciplinary program that addresses both mathematical skills and social identity development can have positive outcomes on confidence in mathematics and consequently more broadly in STEM fields, for women and girls.

2.1. Social Identity Framework for Improving Math Identity

A social identity framework that is conducive to the pursuit of mathematics, and, more generally, STEM, includes three relevant components:

1. A belief that the student is capable of completing training and tasks expected of a mathematician or science professional. Research indicates that widespread beliefs about mathematics and science capability influence women's confidence, self-concept, and self-efficacy [1,5]. In the U.S., male students are more likely to overestimate their STEM abilities, and female students are more likely to underestimate their STEM abilities [19]. Furthermore, cultural stereotypes can exacerbate a fixed mindset about mathematics and science. Psychologists define a fixed mindset as the belief that people are born with an innate or natural ability to succeed in a given area [27]. A growth mindset, by contrast, can act as a protective factor against widespread cultural stereotypes about STEM competence: if a student adopts a growth mindset or believes that she can develop and improve her mathematical abilities over time with practice, then she is more willing to persist in the face of early challenges [56]. In fact, a belief in neuroplasticity, or that one can improve their mathematical and spatial reasoning skills with practice, has been shown to result in improved academic performance and increased likelihood of enrollment in more advanced mathematics courses [58]. Researchers have shown that adopting a growth mindset is especially vital for increasing persistence in mathematics for women [23].

2. A belief that a career in a mathematics-related field is personally relevant and meaningful to the student's broader life goals. Social factors, like gender (as well as race and socioeconomic background), shape which values take priority for a given person. Relative to boys and men, girls and women tend to value careers in which they can help others and improve society [17]. Although many STEM careers involve a “helping” component, girls and women may self-select out of these due to a misperception that these careers lack altruistic aspects [41]. Research on comparative advantage demonstrates that girls who score comparably high in both mathematics and literature or English are much more likely than boys to pursue a humanities-related field [10,76]. Better awareness about the degree to which mathematics-related fields involve societal impact, i.e., helping others and espousing altruistic values, could inspire, enable, and nurture a STEM-compatible identity for girls and women. Additionally, a gained awareness of the actual use of what is learned in the mathematics classroom in the context of a future career or field of study can inspire a student to better identify as a mathematics or STEM learner [3].

3. A belief that an educational and professional career in mathematics or other STEM fields will be welcoming to the student. Many studies have confirmed that women experience a “chilly climate” in mathematics-related fields in the form of microaggressions, sexual harassment, and persistent doubts about their ability from peers and colleagues [11]. If a student believes that she will face an unwelcoming environment throughout her educational training and eventual career, she may be less likely to pursue that field [36,38]. Furthermore, the nature of the STEM pipeline results in fewer women in senior, experienced positions, yielding fewer female mentors and role models for women early in their careers. Same-gender role models are an important resource known to promote the persistence of women in these fields [67]. Finally, both women and men tend to believe that physical sciences, engineering, and mathematics fields in particular are less conducive to work/family balance. Since women continue to shoulder the majority of housework, childcare, and emotional labor in American families, this is a known concern for girls and women as they consider their future careers [74]. This is an unfortunate misperception given that STEM professions offer some of the highest autonomy, pay, and benefits relative to other jobs; for example, the median annual salary for a person with a B.S. degree in Mathematics, Science, or Engineering is currently around $90,000 as of 2021 [53].

Interventions targeting these components of the social identity framework are crucial for promoting a math-compatible identity for girls and women at the critical stages of adolescence when they begin to lose interest in STEM [44], and college, when students are making critical career decisions. By addressing each of these beliefs, STEM-capable girls and women may be more likely to choose, pursue, and persist in mathematical and scientific career opportunities [26].

2.2. Mathematical Skills Building

In addition to promoting a positive math identity in girls and women, IGMI is also designed to develop three sets of mathematics-related skills: metacognition, problem-based learning, and spatial reasoning.

1. Metacognition, the practice of thinking about one's thinking, empowers students to identify as independent and resourceful problem-solvers [33,50]. During and after work on a problem or other cognitive activity, metacognition involves monitoring and reflecting upon methods used, which methods were effective, and the quality of learning. The GEM workshops include metacognitive wrap-up discussions in which participants answer questions like, “What are the big takeaways from today?” and “What challenged you?” This type of immediate reflection has been shown to improve student planning and self-regulation during future cognitive challenges and experiences, gradually enabling students to become their own teachers [50]. Students develop as metacognitive learners through practice, typically by asking themselves questions about the planning, monitoring, and evaluation of a learning experience like a class meeting, homework session, or assessment [70].

2. Education research suggests that a flexible, problem-based approach improves learning outcomes, knowledge retention, self-efficacy, attitude, and motivation [73]. Key features of problem-based learning include a learner-centered environment, rich questions, and opportunities for learning by doing [42]. This allows all learners to share and build on their existing expertise, creating a more engaged learning environment where learners can acquire new knowledge incrementally, bridging from their prior knowledge to form lasting connections [9]. Specific to mathematics, a problem-based approach allows for multiple points of entry, offers several paths to a solution and welcomes a variety of learner levels. Students at the same stage typically use different strategies to approach the same problem. Tactics vary in their precision, time required, and knowledge required. Thus, exposure to multiple strategies provides a broader problem-solving toolkit [9]. For example, at one GEM workshop, participants were challenged to find the shortest path that a spider could take between two points in a room. The participants could use painters tape or string to experiment with various routes through the actual room, build a 3D model of the room with construction paper, or work out possible solutions with a 2D model of the room. Problem-based learning has been shown to be effective in mathematics and science classrooms [34]. Giving students the opportunity to pose problems, discuss misconceptions, develop models, and propose solutions encourages higher-level thinking. Additionally, fostering an environment in which creative problem-solving and discussion are valued over quick answers can improve students' math identity [3]. Problem-based learning is one way to nurture active learning, which research supports enhances learning in STEM fields [34].

3. Spatial ability plays a critical role in the development of quantitative reasoning skills [75]. There are documented sex differences in spatial reasoning performance, though the relative contributions of biological, social and cultural factors are still under active debate [39]. A gender gap in cognitive spatial reasoning skills may be one barrier to female participation in STEM careers in adulthood. There is considerable evidence that spatial ability is not an immutable skill; even brief interventions can improve performance [72]. Work by engineering professor Sheryl Sorby has shown that targeted workshops can significantly improve spatial reasoning skills [65,66]. GEM workshops include spatial training in the form of visualizing and representing three-dimensional objects in two dimensions. With training, engineering students, undergraduate students outside engineering, high school students, and even middle school students show large and consistent improvement in tests of spatial skills. Similar training with a classroom-based spatial reasoning intervention also improved middle school children's spatial reasoning performance [47]. Following training in spatial reasoning, gains in mathematical ability on real-world problems as well as visual and spatial problems have also been observed [12]. Intervention with spatial training can improve the spatial abilities of girls and women, leading to long-term gains and increased interest in, and pursuit of, STEM careers.

3. PROGRAM OVERVIEW: IMPROVING GIRLS' MATH IDENTITY (IGMI)

The intervention developed by the authors, Improving Girls' Math Identity (IGMI), can serve as a viable, scalable model for addressing two key “leaks” in the STEM pipeline. As a two-tiered program, it includes (1) a mutual support and professional development network for current STEM undergraduate women preparing to transition into mathematics, engineering and science careers, and (2) a mentorship program connecting middle school girls with these STEM undergraduate women to engage in mathematical skills training and promote the development of a positive math identity.

The model centers on female STEM undergraduate students who participate in a two-semester course sequence. In the first semester course (“Undergraduate Training Course”), students investigate the current state of gender in STEM through readings and discussions, consider the cognitive and social development of adolescents, practice working through challenging mathematics problems, and use the content as well as their experiences to prepare to lead workshops for local middle school girls. In the second semester course (“Experiential Learning Course”), students serve as formal mentors and role models to the middle schoolers as part of the GEM (Girls Exploring Math) program, a workshop series for local sixth-eighth graders held on weekends during the academic year and weekdays during the summer. The undergraduate students develop and lead these workshops, which involve a mathematical training component coupled with a discussion of topics related to gender in STEM, i.e., STEM careers and trajectories, the challenges and rewards of being a woman in STEM, and tours of labs/clinics of female STEM researchers, engineers, doctors, and surgeons.

Undergraduate students join the IGMI team through an application process completed during the Spring semester preceding Semester 1. The program is advertised widely across campus, inviting any interested students to apply. Once a short written application has been submitted about general interest and skills related to the project, team leaders select those whose application meets a minimum baseline of quality and conduct interviews and reference checks of the remaining applicants. After the interviews, a target group of 10–15 students are admitted to the course.

3.1. Semester 1: Undergraduate Training Course

The first semester course includes community building, weekly readings with written reflections, in-class discussions, mathematical problem solving, and workshop-leading practice. Both the mathematics problems and the gender in STEM readings completed during the training course are rich and appropriate for college-level students. The course materials are adapted and used as inspiration for activities that are engaging and age-appropriate for middle school students.

The primary recommended text for the fall course is the American Association of University Women (AAUW) report, Why So Few? Women in Science, Technology, Engineering, and Mathematics, covering the foundational material needed for explaining and understanding the gender gap in mathematics and STEM [41]. With that foundation in place, IGMI team members can start to generate ideas for building resilience and retaining women in STEM. The course also includes a variety of additional readings, short videos, and interactive assignments. Assignments include academic articles, news articles and even controversial op-eds, podcasts, TED Talks, and interactive web applets. For each assignment, undergraduate students complete a written reflection. This exercise requires students to relate the assignment to their own experiences and/or the imagined experience of a middle school girl participating in a GEM workshop. See Appendix 1 for a first-semester syllabus.

Class time is spent on community building, whole-group discussions, mathematical problem-solving, guest lectures, and practice workshops. Team leaders (faculty members) and undergraduate students begin each class by answering an ice-breaker question. In some cases, these questions are silly (“what kind of sauce would you like to be able to shoot out of your fingers?”) and in some cases, they are more serious (“whom do you admire?”). Beginning with an ice-breaker sets the expectation that everyone will have the opportunity to speak during class and gives the team members a chance to learn about each other [52].

During whole-group discussions, students share their reflections with the class. There are two different models for these discussions: (1) faculty team leaders direct the conversation or (2) pairs of undergraduates are assigned to prepare and lead each discussion. In both models, students have an opportunity not only to discuss the reading but to reveal to the other members of the class their own experiences related to these topics. While discussions provide a chance to solidify concepts and sometimes challenge ideas, they also build and reinforce connections between students.

During the training course, students also complete several problem sets and spend class time working in groups on mathematics puzzles. Puzzles are adapted from a variety of sources including Sorby's Developing Spatial Thinking [64], American Mathematics Competitions, Math Circles of Chicago, and fivethirtyeight.com riddlers. Classic problems like the Tower of Hanoi and some areas of open mathematical questions are also introduced and explored. Problems are selected and presented so that they are both accessible and complex enough to challenge many learner levels. Undergraduate mentors together with faculty team leaders design mathematics puzzles for GEM workshops based on the problems completed by the undergraduates during the training course.

Curriculum problems are challenging for college students and can be adapted or scaffolded to be appropriate for middle school students. While a college student may have a wider variety of mathematical tools available for solving the problems, the puzzles can be approached in many different ways. For example, the Tower of Hanoi problem can be solved using mathematical induction, but it can also be understood through experimentation and pattern-finding. Similarly, an undergraduate student familiar with conditional probability could use that concept to solve the Monty Hall problem, while middle school students might look for the answer by playing a hands-on version of the game, Let's Make a Deal, using cups and candy, for example, repeatedly and recording the results. Some problems are engaging and challenging for many skill levels without adaptation. For example, both undergraduates and middle school students alike can puzzle over how to make an origami shape without any instructions. Often, the undergraduate mentors find the assigned problem sets difficult, and team leaders encourage them to have fun and persevere through perceived struggle. At-home problem sets include a written metacognitive exercise in which students comment on their own experience with the problems (what was difficult, what wasn't, etc.) and imagine the experience a middle school student might have with the material.

After completing the problem sets and reflections, undergraduate students discuss their work during class. They share their strategies with each other, identify common difficulties, suggest changes or adaptations that would help engage middle school students, and anticipate the ways in which a middle school student might tackle the problems. Students also spend time in class working on new puzzles that they have not already seen for homework. Groups work together to make progress on in-class puzzles while faculty team leaders facilitate. Then, the full class reflects together on the problem-solving process. The reflections offer an opportunity for undergraduates to consider their own mindsets regarding mathematics problems and to think metacognitively about facilitating group work for middle schoolers.

In lieu of mid-term and final exams, undergraduates work in pairs to design and lead mock workshops. Each of these is an abbreviated version of a typical GEM workshop, including both mathematical problem-solving and an activity to build age-appropriate social and emotional skills that promote persistence in mathematics. Pairs take turns leading activities while the remaining group members act as workshop participants. Mock workshop assignments are an opportunity for undergraduates, with the help of faculty members, to troubleshoot any potential issues before working with middle schoolers. The team has a chance to “play-test” different ideas and assess what was fun and engaging. Mentors can also practice using positive and empowering language while leading a workshop and planning how and what helpful feedback to give. The associated grade for this assignment is based on overall design, interactivity with participants, integration of physical manipulatives, age and learner-appropriate adaptation of material, and provision of helpful/supportive feedback to participants (see Section A.2 for the Mock Workshop Rubric).

3.2. Semester 2: Undergraduate Experiential Learning Course

During the spring semester, IGMI hosts weekend GEM workshops. At these workshops, undergraduate students work in teams of two to mentor groups of 8–15 middle school girls.² Groups are consistent throughout the spring semester. On approximately 10 Saturdays in the spring, middle school girls come to the university campus for these two-hour workshops, which include snacks. Mentors are responsible for setup and cleanup. Faculty members attend the workshops to assist. After each workshop, the team leaders and mentors debrief and reflect on any successes or difficulties.

Prior to the start of the workshops, the IGMI team leaders curate a bank of mathematics puzzles, drawn from the problems discussed with mentors in Semester 1, and create a schedule of gender-and-STEM discussion topics for the workshops. Because the GEM participants and mentors work on the same (or similar) puzzles or problems, the mentors can draw on their own problem-solving experience when assisting GEM participants. Discussion topics may include historic women in STEM (“hidden figures” such as Rosalind Franklin and Katherine Johnson), gender stereotypes, the current landscape of women in mathematics and science fields, busting common myths about the gender gap in STEM, fixed and growth mindset, mathematics self-assessment and self-concept, stereotype threat, and an exploration of STEM jobs (see [41] for example topics).

Undergraduate mentor pairs take turns designing workshop plans. Mentors choose a mathematics puzzle from the curated bank, scaffold it appropriately for middle-grade students, and brainstorm a list of possible manipulatives to use for problem solving. Mentor pairs also plan an interactive discussion activity for the scheduled gender-and-STEM topic. The activity is designed to invite GEM participants to move, think, or play while considering one or more of the factors or skills related to STEM persistence for women. The workshop plans produced by undergraduate pairs include a mentor guide with rough timing, a supply list, extension problems, guidance for encouraging participants, and big takeaways. Faculty members help refine the plans before the lead pair presents to the workshop mentors. This full team (of workshop mentors and faculty) meets a few days before each spring semester GEM workshop for a rough overview of the planned activities. Then, mentor pairs meet separately to think through details for their particular group of GEM girls.

During the spring semester, course meetings are focused around the workshops. Community can be well maintained among the undergraduates during the spring semester through post-workshop debrief sessions and team dinners, as well as awarding “kudos” to mentors for jobs well done at the workshops (each team member receives a specific compliment and small prize). Undergraduate mentor grades for the spring semester course are issued based on workshop attendance. For example, missing more than one workshop means the student cannot receive a grade of A in the course, and students are required to notify team leaders well in advance if they must miss a workshop.

There is an optional summer program component during which ten weekday summer workshops take place. These workshops are extended versions of Spring semester workshops. Undergraduate students who are able can support these workshops for a summer stipend (if funding is available) or for summer semester course credit. Undergraduate students are incentivized to meet expectations during these workshops with pay and/or course grade.

4. EVIDENCE

The IGMI program model is based on three successfully completed cycles led by the authors, an interdisciplinary team composed of a mathematician, an engineer, and a sociologist, in consultation with a developmental psychologist and neuroscientist. The program began in Summer 2018 and has been funded by a university program supporting interdisciplinary projects, the university engineering school and mathematics department, and a MAA Tensor Women and Mathematics grant. During each of the first two cycles, approximately 40 middle school girls participated in the program. Due to the COVID-19 pandemic, the third cycle was disrupted and did not include the in-person GEM workshop component in the spring. However, this provided an opportunity to develop an alternative spring semester module which could serve as a model for virtual engagement with middle school girls in lieu of in-person GEM workshops (see Appendix 2 for details).

The authors are currently collecting quantitative and qualitative data regarding medium- and long-term impacts of the intervention on undergraduate and middle school participants' entry into and persistence in mathematics and other STEM fields. A content analysis of undergraduate student feedback and submitted coursework, along with the authors' own reflections, revealed three emergent short-term potential impacts for these undergraduate women related to their futures in STEM: (1) the development of quantitative reasoning and problem-solving skills, along with related metacognitive practices, which directly translate to improved mathematics and STEM-specific academic and career performance, (2) the acquisition of skills to support resilience, persistence, resourcefulness in pursuing STEM fields, including first-hand experience conducting research about the factors leading to the gender gap in STEM, and (3) increased investment and empowerment to support future cohorts of women and other underrepresented groups in mathematics and STEM. This section explores evidence regarding each of these three impacts in turn.

4.1. Development of STEM-Specific Problem-Solving and Metacognitive Skills

While undergraduates' problem-solving abilities have not yet been formally measured or assessed before or after completing the training course, the authors observed concrete changes in students' approaches to problem-solving throughout the semester. As the training course progressed, students became both more rigorous and more curious in their work on open-ended problems, and their questions indicated an interest well beyond what they would need to know to guide middle school level discussions. Even as mentors were aware that they would likely only lead workshop participants through experimental explorations of problems, they became increasingly motivated to investigate problems using their own current mathematical and STEM skills, including coding to run simulations and writing rigorous proofs.

During the alternative course model (outlined in Appendix 2), students developed additional STEM-specific skills through their smaller group projects. Depending on the project, they gained substantial experience with quantitative data analysis in R (using real data from previous workshop surveys) and research study design (including the development of research questions, hypotheses, and data collection plans). Many students had been introduced to these skills in other courses but were given the opportunity to apply them more realistically here.

Through problem-solving work and related discussions, the undergraduate women engaged in metacognitive practices. They shared and discussed their own strategies and obstacles in written reflections, and during in-class problem-solving activities, they were asked to work together to both solve the problems and consider multiple approaches, including those that would be accessible to middle school students. Similar metacognitive exercises were practiced in student work on spatial reasoning tasks. In written reflections that accompanied problem sets, students reported feeling challenged by the spatial reasoning puzzles. Several students also commented on the importance of the problem-solving exercises and expressed motivation to improve their skills with practice. Through discussions in class about growth mindset, students could consider their own responses to setbacks in their coursework. In an early written reflection, one student described “feeling stupid,” but in a later reflection was able to say that although she did not solve the assigned problem she would try again later. As part of a “gallery walk” exercise at the end of the second semester, students were asked to reflect on several listed topics, including growth mindset, in anonymous written responses. They were prompted to circulate, in silence, around the physical classroom and write observations and goals for themselves in each given topic area (listed at the top of each large paper posted on the wall). One student wrote, about growth mindset, “I can get smarter at things that are hard for me. Therefore, being ‘bad’ at something is just a concept, not a truth. The only truth is that intelligence can be learned.” Another wrote, “Find new ways to learn. Ask lots of questions and be proud of your curiosity, not embarrassed you don't know it yet.” The problem-solving strategies, metacognitive practices, and discussions about the impact of adopting a growth mindset can be applied directly to students' current coursework in their respective STEM fields and can serve to improve their learning self-efficacy.

4.2. Development of Persistence and Resilience, Leadership Skills

Through readings in topics covering current research about the causes of the gender gap in STEM, the undergraduates learned about factors that had directly affected them, and dissuaded them, in their choices to pursue their chosen major, along with the reasons why they may continue to feel hesitant, challenged, or discouraged in their course work and upcoming early career decisions. In written reflections and class discussions, students consistently made connections between these readings, podcasts, and videos with their own stories. In particular, one student, in an online piece, wrote about factors contributing to the gender gap in STEM:

Giving a name to these factors was eye-opening for me. As we talked about the reasons why the gender gap in STEM exists, I noticed myself identifying personal experiences with each of these reasons. Our discussions showed that we had all experienced some level of every one of these factors, and having a space where we could freely discuss this was empowering.'

Many students wrote in their reflections about implementing strategies to combat feelings of anxiety and imposter syndrome, like reframing anxiety as excitement or as a beneficial nervous system response. One class meeting was spent hearing from a panel of women working in STEM careers, about which a student wrote,

This was definitely my favorite class we had all year. Hearing about the stories, paths, and struggles of other women in STEM was extremely motivating and empowering, but also a little saddening that sexism in the workforce is still very real.

Many class discussions began with a conversation about a given cause, but then evolved to a brainstorming session to find responses, reminders, and tactics that individual women could take to effect positive change. During the gallery walk, students generated thoughtful advice about seeking out mentors: “There are other women you can find and talk to that know what you're going through and [are] in your corner (and men too!),” and “Maintain strong relationships with mentors who have your best interests at heart. Let those mentors inspire you to see your full potential.”

Small-group project work in the alternate model semester when the program moved online due to COVID 19, along with assigned readings in the Training Semester, gave students applied experience in research methods. Because these students are primarily majoring in STEM fields, this course gave them new and valuable experience in research methods used more commonly in the social sciences, like conducting a literature review primarily in the areas of sociology, psychology, and education; designing, testing, and gaining human subject research approval of a survey instrument; and analyzing previously collected survey data.

4.3. Increased Investment in Supporting Future STEM Students

The experience of designing and leading GEM workshops gave undergraduate mentors confidence and contributed to the development of their leadership skills. These experiences of guiding the middle school participants, presenting material in an engaging way, and encouraging middle school girls are useful and applicable to the undergraduate mentors regardless of their future career choice. But the experiences also made an impact on the undergraduates by inspiring them to invest in the future of the STEM pipeline. In written reading reflections, students regularly made a connection between the reading material and the GEM participants, including updates to the GEM curriculum in response to the research. Students' sentiments in written reflections included a desire to pave the way for future generations in what are currently male-dominated fields, to make classrooms and workshops more collaborative than competitive, and to help younger girls build their confidence. In her online reflection, one undergraduate mentor wrote,

I loved seeing the girls' faces light up when they understood a solution and their surprise at unexpected answers. Part of our workshops was also devoted to discussing topics related to the gender gap in STEM, and hearing the girls speak about their experiences and sharing mine with them was powerful. Naming the social factors did make a difference and got the girls thinking about the challenges and ways to handle them.

5. RECOMMENDATIONS AND CONCLUSIONS

Through the IGMI program, undergraduate women in STEM serve as mentors for middle-grade girls. The undergraduates complete in-depth training to prepare to lead workshops for younger girls. The training course provides mentors with the tools needed to run mathematics workshops and to have open discussions with adolescent girls about topics related to gender and STEM. In addition, the readings, problem sets, and in-class activities support the undergraduates' own development as women in STEM. The mentors build their mathematical skills, work on developing a growth mindset, identify the experiences in their lives that could contribute to leaks in the STEM pipeline, and think through practical tactics for persistence.

Undergraduates are key to the success of the workshops. Selection of a strong team of mentors is vital, so team leaders recommend describing the program clearly in course recruitment materials prior to Semester 1. In the written application, team leaders recommend asking applicants for details about the experiences, interests, and skills relevant to their potential role in the program. In interviews, team leaders emphasize the time commitment expected of mentors and ask mentors explicitly to commit to workshop attendance if they are selected to participate. Additionally, in-person interviews are critical, as they give team leaders insight about applicants' communication skills that are fundamental to the success of the workshops. Team leaders recommend selecting as diverse a team as possible – in terms of race/ethnicity, year/progress to degree, gender expression, and even major (e.g., non-STEM majors can assist with logistical support and/or collecting and analyzing data for program assessment). Consistent reminders of the responsibility to which undergraduate students have committed, along with the potential they have to positively influence and inspire middle schoolers, is critical for program success.

During the first three cycles of the program, the authors have made adjustments to the syllabus for the undergraduate course based on their experiences. Later cycles included a stronger emphasis on practice workshops with detailed feedback, metacognitive skills-building, more spatial reasoning-focused problems, built-in time to debrief after in-class activities, and additional team building exercises. While this training course is typically offered as an interdisciplinary, for-credit course, it has also been offered in some cases as an independent study in various departments, including psychology and sociology. Practitioners who wish to build a similar model can offer the training course as an independent study, experiential or service-learning course, or internship for undergraduate and graduate students in a wide variety of disciplines including STEM fields and education. The experience would be especially beneficial for STEM graduate students planning to work in the classroom in the future.

The IGMI team has benefited from interdisciplinary collaboration among team leaders and advisors. The authors recommend including mathematicians or other STEM faculty members as well as collaborators with research expertise in disciplines such as sociology, psychology, education, or human development. For practitioners implementing a similar program, the authors recommend spending class time having explicit conversations about experiences as a member of an underrepresented group in mathematics or other STEM fields. While these conversations can sometimes seem intimidating, a major strength of the IGMI model is that it connects emotional experiences to practical actions and existing research. The opportunity to share experiences can help forge relationships among the team members and facilitate students' understandings of their own feelings of belonging in mathematics and related fields.

ACKNOWLEDGMENTS

Authors are listed in alphabetical order. All authors contributed equally.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors wish to acknowledge funding from the Duke University Bass Connections program, the Duke University Department of Mathematics, the Duke University Department of Mechanical Engineering and Materials Science, and the MAA Tensor Women and Mathematics grant.

Notes on contributors

V. Akin

V. Akin earned her doctorate in mathematics from the University of Chicago. Throughout her career, she has enjoyed mathematics outreach, particularly with middle school students.

S. T. Santillan

S. T. Santillan earned degrees in Mathematics and Mechanical Engineering from Duke University. She has worked as an instructor in both fields at the high school and university level.

L. Valentino

L. Valentino earned her doctorate in Sociology from Duke University, where she studied social inequality, including the underrepresentation of women in STEM. She is currently an assistant professor of sociology at The Ohio State University, where she focuses on issues related to race, class, gender, and their intersections.

Notes

1 Recruitment materials make it clear that girls and gender nonconforming or nonbinary middle schoolers are welcome to participate in GEM. Workshop facilitators use age-appropriate techniques for including non-binary middle schoolers by having all participants introduce themselves by name as well as pronouns. Undergraduate students of any gender are encouraged to join the program. Because of the research on the importance of visible same-gender role models, it is recommended to place female undergraduate students in the mentor role. The other key support roles that male undergraduate students can have include workshop planning, administrative support, communication with parents/guardians, and data collection and analysis (see Appendices).

2 Team leaders partner with the local school district to promote GEM workshops. All promotional materials encourage students to attend regardless of their current grade in mathematics and invite students who are uncertain about mathematics, excited by mathematics, or interested in building mathematical confidence to apply. A short application asks students brief questions and invites students to apply even if they are unable to attend all workshops in a given series.

APPENDICES

APPENDIX 1. SEMESTER 1 SYLLABUS

A.1. Schedule: Fall 2019 (Similar to Fall 2018)

As some undergraduates participate in the program for more than one year, some assignments are designated for these students (“Returners”), while others are designated for all students (“Everyone”).

Table

Week	Content	Assignment (due the next week): read/watch/listen and respond
1	Introductions	Everyone: AAUW Chapter 1 “Women and Girls in Science, Technology, and Mathematics” [41].
	Overview of program structure	Returners: “The Secret History of Women in Coding” [71] and “For a Black Mathematician, What It's Like to be the ‘Only One”’ [40]
	Returning mentors share spring/summer experiences Students sign up for discussion leadership day
2	Student-led discussion (#1) on the gender/STEM pipeline	Everyone: Developing Adolescents (pp. 1–47) [2]
		Returners also: “Girls and women in science, technology, engineering and mathematics: STEMing the title and broadening participation in STEM careers” [22]
3	Guest speaker (Psychology) leads discussion about adolescent development	Everyone: Problem set 1
4	Problem set 1 – the problem-based learning approach	Everyone: Problem set 2, and AAUW Chapter 5 “Spatial Skills” [41]
		Returners also: “Eye tracking, strategies, and sex differences in virtual navigation” [4] and “An early sex difference in the relation between mental rotation and object preference” [45]
5	Guest speaker (Neuroscience) leads discussion about spatial reasoning	Everyone: Problem set 3
6	Research presentations from researchers from previous team	Everyone: Problem set 4
7	Problem sets 2–4 – role-playing	Everyone: AAUW Chapter 2 “Belief About Intelligence” [41]
		Returners also: Carol Dweck's TED talk [28] and skim “Effects of Teaching the Concept of Neuroplasticity to Induce a Growth Mindset on Motivation, Achievement, and Brain Activity: A Meta-Analysis.” [59]
8	Student-led discussion (#2) on growth/fixed mindset	Everyone: Problem set 5
9	Problem set 5 – facilitating group work	Everyone: Prep for mock mathematics workshop
10	Mock mathematics workshop teaching (15 mins per pair)	Everyone: AAUW Chapter 3 “Stereotypes” and Chapter 8 “Implicit Bias” [41]
		Take the Gender & Science IAT.
		Returners also: “Girls' Superb Verbal Skills May Contribute to the Gender Gap in Math.” [80] and skim “Girls' Comparative Advantage in Reading Can Largely Explain the Gender Gap in Math-Related Fields” [10]
11	Student-led discussion (#3) on stereotypes and implicit bias	Everyone: Problem set 6
12	Problem set 6 – discovery learning and asking good questions	Everyone: Problem set 7, and AAUW Chapter 4 “Self-Assessment” [41], “No You're Not an Impostor.” [46], and “Impostors Everywhere” [31]
		Returners also: “Why Girls Beat Boys at School and Lose to Them at the Office” [21] and “Women Need More Money. Being More Confident Won't Help Them Get It.” [16]
13	Student-led discussion (#4) on self-assessment, confidence, and impostor syndrome	Everyone: Problem set 8
14	Problem set 7, 8 – trouble-shooting common situations in the classroom	Meet with instructors during Reading Week to review workshop plan
15	Final exam – student pairs give mock workshop

A.2. Rubric for Mock Workshops

During the fall semester of the undergraduate training course, undergraduates design and run mock workshops in lieu of midterm and final exams. The rubric for these mock workshops is included below.

Mock Workshop Rubric

Ice Breaker (10 points)

Table

Category	Description	Points
Preparation	Did you include a fun and age-appropriate ice breaker?	10

Math Activity (45 points)

Table

Category	Description	Points
Preparation	Did you prepare one central problem according to the directions?	5
	Did you plan the logistics/Did the activity run smoothly?	5
	Did you prepare extension activities?	5
Timing	Did you end on time?	5
Appropriate level	Could a middle school girl investigate your problem without having background knowledge of math formulas/advanced math?	5
	Is your problem accessible/fun/engaging?	5
Hands on	Did you incorporate at least one hands-on investigation?	5
	Did the manipulatives that you chose enhance the problem?	5
Facilitation	Did you circulate the room and offer an appropriate amount of help?	5

Gender Activity (45 points)

Table

Category	Description	Points
Preparation	Did you prepare a discussion topic according to the directions?	5
	Did you plan the logistics/Did the activity run smoothly?	5
Timing	Did you end on time and include a wrap up?	5
Appropriate level	Could a middle school girl understand the discussion?	5
	Could a middle school girl connect the topic to her experiences?	5
	Is the content interesting/engaging for a middle school girl?	5
Hands on	Did you incorporate something that involved building/making/doing/moving?	5
	Did the building/making/doing/moving enhance the discussion?	5
Facilitation	Did you create an environment that would encourage a middle school girl to engage with the discussion?	5

APPENDIX 2

OVERVIEW OF CHANGES 2020–2021 ACADEMIC YEAR

During the first two years of the IGMI program, the fall semester of the undergraduate training course focused on preparing undergraduates to work directly with middle school students. However, during the 2020–2021 academic year, the COVID-19 pandemic prevented the IGMI program from running in-person workshops with middle school students. In response, the focus of the project shifted to supporting the undergraduate women in their pursuit of STEM degrees and providing them the opportunity to work on enriching projects related to promoting women in STEM. Team leaders restructured the course curriculum to include readings and speakers geared toward undergraduate persistence in STEM. The team leaders also created structured opportunities for the undergraduates to engage in research and innovative projects related to the gender gap in mathematics and STEM. Twelve undergraduates worked in subgroups on the following subprojects:

1. Analysis of data collected from middle school students in 2019 and 2020

2. Survey instrument design and data collection

3. Literature review and database creation

4. Workshop design for middle school girls

5. Social media and advertising

6. Web applet with spatial reasoning and logic puzzles

Throughout the academic year, team leaders met individually with each subproject team once every one or two weeks. During these meetings, group members and team leaders worked to troubleshoot problems, locate resources, and outline future tasks.

While these subproject groups worked separately, the full team of undergraduates and faculty members met together once each week to discuss a common reading, listen to a guest speaker, or work on a mathematics problem set. As a group, the team worked on understanding potential causes of and solutions for the gender gap in STEM. Team members also reflected on their experiences and considered ways in which they could advocate for themselves and others. During the fall semester, as in previous fall semesters, the primary text for the course was the AAUW report [41]. The Fall 2020 syllabus covered the same main concepts as in previous years to provide a foundation in several potential causes and impacts of the gender gap. The 2020–2021 syllabus focused less time on pedagogy and designing workshops for middle school students but added several new topics tailored toward college students. These new topics included:

• Metacognition – strategies to persevere through difficult work

• Gender equality and representation in STEM

• Group work and collective intelligence

• Confidence in calculus courses

• Social expectations for men and women

• Effective use of social media for promotion

As in previous years, students completed written reflections that related these readings/assignments to their own experiences. During in-class discussions, the undergraduates shared their thoughts with each other. In the spring of 2021, because no GEM workshops took place, the IGMI program had space to focus more on the undergraduates and spend time tackling issues relevant to college-aged students. For Spring 2021, the team leaders created a new curriculum that included:

• Mathematics and anxiety

• A virtual panel of women in STEM jobs

• Quantitative research methods

• Tactics for navigating future workplaces

• Imposter syndrome

• Defining success

• Teaching evaluations and gender bias

In lieu of mock workshops, subgroups presented their project results to the team and program collaborators.

A.3. Detailed Descriptions of Project Teams

A.3.1. Data Analysis

This program collected two years worth of survey data from middle school participants using a pre-test/post-test model. The data analysis subgroup began by cleaning the data and looking for general trends and relationships/correlations (if any) with reported race/ethnicity. The team then looked more carefully at paired data from individuals who took both the pre- and post- tests. The final product from this team was a written report of results with figures and preliminary analysis.

A.3.2. Survey Instrument Design and Data Collection

The survey subgroup designed and implemented a remote research project related to STEM inequality. During the fall semester, this group created a survey for local school district middle school students (of all genders). They next completed pre-testing, updated the survey, and began work with the University Institutional Review Board to gain approval for the research. This team worked together with the social media outreach team to create advertisements for the survey. Finally, the team began collecting responses in Spring 2021.

A.3.3. Literature Review and Database Creation

The literature review team began their work by looking through sources cited in the AAUW report [41]. They created a list of references with brief synopses and key words. The team used Caspio to build a searchable online database of literature, accessible to all team members. They continued to grow the database by including readings from the current and previous course syllabi. This team helped other sub-project teams find relevant sources for their work.

A.3.4. Workshop Design for Middle Schoolers

The workshop design team started by thinking through some of the big concepts from the fall semester (stereotype threat, implicit/explicit bias, growth mindset, confidence, chilly climate, comparative advantage, role models/ mentorship, metacognition, etc.) They then drafted activities that could be used to introduce these ideas to middle school students in a fun and age-appropriate way. The team was charged with keeping topics positive and accessible. They also created facilitation guides for future mentors.

A.3.5. Social Media and Advertising

The advertising team began by thinking creatively about how to reach new participants. They created new pamphlets, fliers, logos, website layouts, mailing lists, and social media content. The team launched an Instagram series highlighting the IGMI undergraduates and faculty leaders. They also worked with the study design team to help advertise to potential survey participants. They finished the year by creating a poster of results describing all of the work the different teams completed over the course of the year.

A.3.6. Web Applet with Spatial Reasoning and Logic Puzzles

The applet team began by brainstorming and investigating a wide variety of potential digital puzzles. They chose to create a digital interface including both a spatial reasoning puzzle and a series of multiple choice logic puzzles. They worked in Python to code an interactive applet. They considered metacognitive strategies and growth mindset while designing the interface.

A.4.

Schedule Fall 2020

Table

Week	Content	Assignment (due the next week): read/watch/listen and respond
1	Introductions	“Developing Adolescents” (pp. 1–47) [2] “Girls and women in science, technology, engineering and mathematics: STEMing the tide and broadening participation in STEM careers” [22]
	Overview of program
	Reading research/journal papers vs mainstream articles
2	Guest speaker (Psychology) leads discussion about adolescent development	AAUW Chapter 1 “Women and Girls in Science, Technology, and Mathematics” [41]
		“Nearly Half of US Female Scientists Leave Full-Time Science After First Child.” [30]
3	Group updates	Problem set 1
	Reading discussion: gender/STEM pipeline	LikeWar (selected chapters) [63]
4	Guest Speaker: engagement and influence on social media	AAUW Chapter 5 “Spatial Skills” [41]
		“Eye tracking, strategies, and sex differences in virtual navigation” [4]
		“An early sex difference in the relation between mental rotation and object preference” [45]
5	Group updates	“The More Gender Equality, the Fewer Women in STEM.” [43]
	Guest speaker (Neuroscience) leads discussion about spatial reasoning
6	Group updates	“Evidence for a Collective Intelligence Factor in the Performance of Human Groups” [79]
	Problems set 1
7	Group updates	AAUW Chapter 2 “Belief About Intelligence” [41]
	Discussion and problem work	Carol Dweck's TED talk [28]
		“Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit” [29]
8	Group updates	“Promoting Student Metacognition” [70]
	Reading discussion: fixed/growth mindset
9	Group updates	AAUW Chapter 3 “Stereotypes” and Chapter 8 “Implicit Bias” [41]
	Guest speaker (university learning consultant) leads discussion about metacognition	“I'm a Black Female Scientist. On My First Day of Work, a Colleague Threatened to Call the Cops on Me.” [6]
		Take the Gender & Science IAT [55]
10	Presentation and feedback: survey instrument	“Enough Leaning In. Let's Tell Men to Lean Out” [78]
		“Separating Implicit Gender Stereotypes regarding Math and Language: Implicit Ability Stereotypes are Self-Serving for Boys and Men, but not for Girls and Women.” [68]
11	Group updates	Problem set 2
	Reading discussion: stereotypes and implicit bias
12	Group updates	AAUW Chapter 4 “Self-Assessment” [41]
	Problem set 2	“How a Dean Got Over Imposter Syndrome – and Thinks You Can, Too” [37]
		“Outperforming yet undervalued: Undergraduate women in STEM” [8]
13	Group updates
	Reading discussion: self-assessment, confidence, and impostor syndrome
14	Final Presentation – project groups present work

A.5. Schedule Spring 2021

Table

Week	Content	Assignment (due the next week): read/watch/listen and respond
1	Math Fun!	“How Harvard's Dark Horse Project is Shattering Old Beliefs about Success” [7]
		“Redefining Success so it Doesn't Crush Your Soul” [69]
2	Math Fun!	Battle Tactics for Your Sexist Workplace (BTSW) podcast, “The danger of bringing cupcakes to work” [14]
	Feedback/reporting from survey instrument testing	“Everyone gets mad at work. Guess who gets penalized for it” [15]
3	STEM women panel	“Spotlight on Math Anxiety” [48]
4	Guest speaker (university learning consultant) leads discussion on math anxiety/imposter syndrome	How to Analyze Survey Data, Chapter 3 [32]
5	Guest speaker (qualitative research) leads discussion about social science research and data analysis	BTSW podcast “How the patriarchy makes you feel like an imposter” [13]
6	Guest speaker (university dean) leads discussion on imposter syndrome	Preface and Introduction from Invisible Women: Exposing Data Bias in a World Designed for Men [20]
7	Guest speaker (Sociology) leads discussion about the gender gap in STEM
8	Guest speaker (Sociology) leads discussion on sociology research	Picture a Scientist [62]
9	Discussion of previous readings	“The Fatal Flaw of the Queen's Gambit” [51]
		“How to Undo Gender Stereotypes in Math – with Math!” [18]
10	Math Fun!	Problem set 1
		“Effects of Everyday Romantic Goal Pursuit on Women's Attitudes Toward Math and Science” [54]
11	Math Fun!	“Self-discipline gives girls the edge: gender in self-discipline, grades, and achievement test scores” [25]
		TED talk by Angela Duckworth [24]
12	Discussion of previous readings	“What's in a Name: Exposing Gender Bias in Student Ratings of Teaching” [49]
		Play with this interactive site: https://benschmidt.org/profGender [60]
13	Discussion of readings
14	Gallery walk – how can we apply the lessons learned from the past two semesters?
15	Final presentations – project groups present work