All STEM students have experienced contexts that present vulnerabilities and protective factors. However, some contexts are unique to minoritized STEM students, and they comprise minoritized students’ Net Vulnerability. These contexts should not be viewed as deficits or deficiencies, but instead as a part of their everyday environments (Spencer and Swanson, 2016). Students with certain visible characteristics used to determine race, including skin color, facial features, hair texture, and body type (e.g., Stepanova and Strube, 2009), have had a lifetime of socialization experiences from their family, schools, communities, and greater societal norms based on these characteristics (Dupree et al., 2015). In other words, Net Vulnerability represents students’ predisposition to the experience of stress based on their risks and protective factors. These socialization experiences are informed by the greater socio-historical context of minoritized populations, or what Bronfenbrener referred to as the chronosystem and the macrosystem, which have often been exclusionary (McGee, 2016; Riegle-Crumb et al., 2019). Historically people of color, especially African American and Black individuals, have been viewed and treated as secondary citizens and explicitly excluded from educational opportunities (Mutegi, 2013). Even as society now largely disparages overtly racist claims of an inherent deficit of Black and African American individuals in academic performance, these socio-historical beliefs are still commonly seen as implicit biases that play out in students’ contexts day to day (Martin, 2009; Mutegi, 2013). For example, recent studies have shown that the academic struggles of Black or Latinx individuals are still often attributed to assumptions about their race/ethnicity’s lack of intelligence (Gutiérrez, 2013; Spencer et al., 2016). Yet these racist beliefs are often masked by more socially acceptable group attributions/generalizations such as being low-income, urban life, cultural differences, etc. (Martin et al., 2019; Ngo and Velasquez, 2020; Tyson, 2011). Such implicit biases lead to persistent negative stereotypes (Park et al., 2020; Ridgeway and McGee, 2018). Negative racial/ethnic stereotypes do not exist in a vacuum, they are often coupled with a lack of racial/ethnic representation in the classroom and a lifetime of potentially negative academic experiences (Park et al., 2020; Ridgeway and McGee, 2018).

Scholars of color have long been bringing attention to the structures that have neglected to provide equal opportunities for Black children and other minoritized students (Martin et al., 2019; Ridgeway and McGee, 2018). Bannister et al. (2017) point out how recent reforms such as “mathematics for all” fail to acknowledge the roots of disparities in mathematics environments. Berry et al. (2013) outline how Black youth’s math education was neglected in math education reforms taking place from the 1950s to the 2000s. Following legally mandated school desegregation, there were systems put in place that functionally re-established forms of segregation through testing and tracking (Joseph et al., 2017; Larnell, 2016; Martin et al., 2019; Ngo and Velasquez, 2020; Shah, 2017; Tyson, 2011; del Zavala, 2014). Such implicit biases have real impacts on minoritized students’ academic achievement and educational experiences. For instance, Copur-Gencturk et al. (2020) found that high school math teachers hold implicit biases about students’ mathematical abilities based on their race/ethnicity and gender. Teachers rated Black and Hispanic students as lower in mathematical ability than their White counterparts, even when math performance was comparable. These implicit beliefs are concerning since teachers’ expectations and views of their students influence students’ academic achievement (McKown and Weinstein, 2008), and teachers are often the gatekeepers for higher tracks that prepare students for undergraduate STEM education.

Another contextual factor that influences teacher and peer implicit biases and minoritized STEM students’ Net Vulnerability is the lack of representation of minoritized students in STEM majors, also known as low compositional diversity. Minoritized STEM majors, especially at predominantly White institutions, are more likely to find themselves in an environment where their racial/ethnic group is even less represented than during their K-12 experiences (Riegle-Crumb et al., 2019; Weinberg, 2008). Lee et al. (2020) state that low compositional diversity increases the likelihood of microaggressions, “everyday verbal and nonverbal acts of systemic racism that demean and undermine Black Americans,” (Marshall et al., 2021, p. 2), a key component to a negative climate for minoritized students. When institutions have greater compositional diversity, they have higher minoritized student academic success (Dee, 2004; Gershenson et al., 2021; Llamas et al., 2021).

Although the socio-historical context of minoritized STEM students can lead to increased Net Vulnerability, researchers of color have brought attention to the fact that minoritized students also have substantial protective factors they can leverage to successfully navigate academic spaces (McGee and Spencer, 2015). These factors have largely been ignored or assumed to be lacking for these students based on existing stereotypes about minoritized populations. Many assume that minoritized STEM students lack the social support needed for success in STEM education. However, researchers have found that many minoritized students have social supports that assist in the development of positive ethnic-racial identity, positive math self-concept, and academic achievement (Dupree et al., 2015; Hughes et al., 2006). Ethnic-racial socialization is one way in which these social supports provide a protective factor against the vulnerabilities presented by negative stereotypes about minoritized students’ academic aptitude (see Bartell, 2011; Brand et al., 2006; Ellington and Frederick, 2010). When minoritized students have experiences that are positive and/or supportive, they can develop protective factors (e.g., positive attitudes towards their STEM ability), which helps them persist in STEM (Smith et al., 2020).

Central to PVEST is that no one group is predisposed to vulnerability, but rather, the interactions between individuals’ unique socialization based on their socio-historical, more proximal contexts, and stable personal attributes shape their vulnerability. It is the sum of these factors that makes up each minoritized student’s Net Vulnerability in their first-year gateway math course. However, student perceptions of their Net Vulnerability are not uniform, and they are informed by students meaning making of their experiences in various contexts, their Net Stress.

Net Stress consists of the individual’s experience/interpretations of the risks and protective factors in undergraduate math courses (McGee, 2016). Thus, a student’s race or gender may lead them to be predisposed to the experience of an undergraduate math course as stressful. However, not all Black students in undergraduate math courses experience this stress. To use an example from the prior section on Net Vulnerability, Copur-Gencturk et al.’s (2020) findings suggest that Black and Hispanic students are perceived more negatively by their teachers than White students. While being Black makes it more likely that a student will be held to lower academic expectations than being White, Black students’ actual experiences of this are what contribute to their Net Stress.

The cultures of STEM gateway courses have real impacts on minoritized students’ perceived stressors. Many undergraduate STEM programs’ gateway courses are perceived to “weed out” students not considered “strong” enough to persist in scientific endeavors, with calculus courses showing some of the highest D, F, or withdrawal rates (Seymour and Hewitt, 1997; Weston et al., 2019). Such “weed out” courses lead many minoritized students to drop out and thus have a direct impact on diversity in STEM (Mervis, 2011; Seymour and Hewitt, 1997). Many minoritized STEM students state that these gateway courses have a “hostile, competitive classroom culture,” (Weston et al., 2019, p. 201). Such negative student experiences may lead many minoritized students to perceive STEM as stressful (McGee, 2016), especially when paired with social identity threats in the form of racist interactions with their STEM faculty (Park et al., 2020). Seymour and Hewitt (1997) found that the most common reasons students (non-minoritized and minoritized) cited for switching from STEM majors are based on negative experiences from the institution (e.g., “turned off by science,” poor teaching by STEM faculty, and feeling overwhelmed by the pace and load of curriculum demands). Despite this, minoritized students are more likely to “blame themselves rather than departments, faculty, or institutions, for all, or most of their difficulties,” than their non-minoritized peers (Seymour and Hewitt, 1997, p. 324). Such feelings are likely an internalization of our society’s deficit thinking of minoritized students, focusing blame on the individual or their respective racial/ethnic community instead of systemic issues in our society (Jong et al., 2020).

In addition, when minoritized students are underrepresented in their STEM major (i.e., low compositional diversity), many have difficulty seeing themselves succeeding in the majors (Morton and Smith-Mutegi, 2018) and experience a lower sense of belonging (Buck et al., 2020; Rainey et al., 2018), in turn increasing their evaluation of such contexts as stressful. In addition, low compositional diversity increases the chances of stereotype threat, which is a fear of confirming negative stereotypes about one’s racial/ethnic identity (Aronson, 2002; Lewis and Sekaquaptewa, 2016; Spencer et al., 2016; Steele, 1997; Steele and Aronson, 1995; Thoman et al., 2013). We highlight stereotype threat in the current manuscript because of the extensive body of research about its consequences and interventions relative to the literature on other social identity threats. Minoritized students are keenly aware of the stereotypes and implicit biases about their racial or ethnic groups (i.e., social identity threats, which make up part of their Net Vulnerability; McGee, 2016; Mutegi, 2013; Nasir et al., 2017; Rodriguez and Blaney, 2020). Stereotype threat has been considered a significant barrier to minoritized students’ academic achievement (Spencer et al., 2016). Black and African American students in STEM report more concern about stereotyped treatment and less sense of belonging than non-STEM majors (Chavous et al., 2004). Experiencing stereotype threat can negatively influence students’ self-evaluations, their intentions to pursue higher STEM education, and their academic success (McGee, 2016; Muenks et al., 2020).

Both being a member of a stereotyped group and being aware of the stereotype are two factors that lead to students being likely to experience stereotype threat, but stereotype threat is only one way in which students interpret these greater social identity threats (Verkuyten et al., 2019). Just because a student is a member of a group that is stereotyped, aware that there is this stereotype, and in a group context predisposed to experiencing stereotype threat (i.e., a Black student in an undergraduate math course with all other students being white) does not mean the student will automatically undergo stereotype threat and that they will experience their math course as stressful (Steele et al., 2002).

Minoritized STEM students better equipped to navigate hostile environments, are less impacted by low compositional diversity, and likely experience less stereotype threat, when they experience identity-affirming contexts outside of their major, e.g., positive ethnic-racial socialization, supportive family, peers, or organizations (Jong et al., 2020; McGee and Martin, 2011a; McGee and Martin, 2011b). Some people think that awareness of historical oppression may lead to students feeling defeated in STEM contexts; however, having greater ethnic-racial socialization supports minoritized students’ academic success (Dupree et al., 2015; Hughes et al., 2006). In fact, minoritized students’ perceived ethnic-racial socialization is associated with the development of positive ethnic-racial identities and academic achievement (Hughes et al., 2006). Even though minoritized students with positive ethnic-racial identity still face many deficit focused academic stereotypes,

Hence, minoritized STEM students who have learned to navigate such contexts previously might not find these experiences as stressful. Having a faculty member invested in a minoritized student’s success, and who emphasizes collaboration and teamwork, can help mitigate the stress caused by such hostile academic environments (Foltz et al., 2014; Hernandez et al., 2017; Moore et al., 2020). Having access to identity-affirming spaces, either with peers, instructors, or mentors, could help the student shift the blame from themselves, likely reducing their Net Vulnerability and Net Stress (King and Pringle, 2018).

Although Net Vulnerability (the sum of all the supports and vulnerabilities in the context) and Net Stress (the sum of the students’ meaning making/interpretation/perception of those supports and vulnerabilities) play a significant role in their STEM experiences of minoritized students, they do not determine their success in STEM; students’ Reactive Coping Strategies, Emerging Identities, and Stage Specific Coping Strategies also need to be considered. Reactive Coping Strategies are the initial responses the student has to their Net Stress. Stereotype threat, as discussed in the previous section, activates a negative stress response (e.g., worry), leading to anxious thoughts (Johns et al., 2008). A common Reactive Coping Strategy to stereotype threat is attempting to suppress the anxiety and worry (Aronson, 2002; Johns et al., 2008; Schmader and Johns, 2003). However, this imposes a cognitive burden on the individual and limits the cognitive resources available, leading to lower academic performance. This may influence the students’ Emergent Identity formation by making them feel that they are not a math individual and choose not to pursue further STEM education (the Stage Specific Coping Outcome). Research on STEM identity in minoritized populations clearly shows that students’ self-efficacy beliefs are one key component of the development of a STEM identity, which influences their persistence in STEM (Carlone and Johnson, 2007; Dou and Cian, 2022; Godwin et al., 2016; Hazari et al., 2010).

Protective factors not only reduce Net Vulnerability and Stress, but can also promote adaptive Reactive Coping Responses and contribute to positive Emergent Identity formation. Positive emergent identities develop when minoritized students think of their group membership in ways that highlight group strengths, which then leads to persisting in STEM (the Stage Specific Outcome). Spencer and Swanson (2016) suggest that cultural traditions (or religious identity; Brittian and Spencer, 2012) or “referent others” (or culturally affirming mentors or community members; McGee and Spencer, 2013) are influential in how students react to stress. For example, students who have a more salient religious identity may turn towards prayer, as their Reactive Coping, to reduce their autonomic arousal when faced with stress. This then allows for more cognitive resources to be available during academic tasks, increasing achievement, self-efficacy, promoting the development of math/science identities as Emergent Identities, and increasing the likelihood of STEM persistence, the Stage Specific Outcome. Several works specifically demonstrate how supportive experiences lead to the development of math/STEM identities and persistence in STEM for minoritized students (Godwin et al., 2016; Morton and Parsons, 2018; Singer et al., 2020).

No one is solely defined by their race/ethnicity, gender, or any other identity they may subscribe to. This is due to intersectionality (Crenshaw, 1989), that every individual exists within interlocking systems of oppression, and everyone lies at different intersections of these various systems.

According to PVEST, the nature of intersectionality leads to everyone experiencing different supports and vulnerabilities which they then must interpret through the lens of their unique experience (Velez and Spencer, 2018).

Despite it being critical to consider intersectionality to interpret the diverse experiences and outcomes of minoritized STEM students, previous research on minoritized STEM students has not given much consideration to the impact of intersectional identities (Grabe, 2020; Cochran et al., 2020). Currently, there are differing perspectives on how multiple intersectional minoritized identities impact individuals’ experiences of vulnerability (Purdie-Vaughns and Eibach, 2008). Some researchers argue that the more minoritized identities one subscribes to (e.g., being Black and a woman) the more vulnerability and stress one will experience, whereas others argue that when an individual subscribes to multiple minoritized identities they can become invisible due to then being a less prototypical example of their various identities, leading to various advantages and disadvantages.

The intersectionality between race and gender has received the most attention in STEM education. The data clearly shows that women of color have the lowest STEM degree attainment and have the lowest representation in STEM compared to their representation in higher education and the general population (Malcom et al., 1976; Ong et al., 2011). Rainey et al. (2018) found that women of color reported the lowest sense of belonging in STEM fields compared to white men, white women, and men of color, particularly in the physical sciences where they are the least represented. These findings are supported by many rich qualitative studies which suggest that although women of color are just as likely to have intentions/interests in pursuing STEM negative experiences with the competitive culture of STEM that is often at odds with some of their identities (Carlone and Johnson, 2007; Ong et al., 2011; Morton and Parsons, 2018). Ong et al. (2018) show that having access to opportunities for recognition and relationship building in STEM is critical to women of color’s positive experiences in STEM, particularly in counterspaces. Counterspaces are, “academic and social safe spaces that allow underrepresented students to: promote their own learning wherein their experiences are validated and viewed as critical knowledge; vent frustrations by sharing stories of isolation, microaggressions, and/or overt discrimination; and challenge deficit notions of people of color (and other marginalized groups) and establish and maintain a positive collegiate racial climate for themselves,” (Ong et al., 2018, p. 209). This work with a focus on the intersection between race and gender is critical especially since “history has borne out the reality that programs intended to serve women disproportionately benefit White women, and programs intended to serve minorities mainly benefit minority males,” (Ong et al., 2011, p. 176).

According to PVEST, the impact of intersectional identities on STEM success will be unique depending on the different identities and the individual (Velez and Spencer, 2018). Currently, the literature exploring intersectionality with social class, disability, and sexuality is limited (Cochran et al., 2020). This makes it more critical that STEM support programs and interventions be created based on a flexible framework, such as PVEST, to help support the many intersecting identities of STEM students.

According to Liu et al. (2021), most stereotype threat interventions applied to minoritized students can be categorized into two categories: belief-based and resilience-based. Belief-based interventions aim to blur group boundaries, promote sense of belonging, and/or provide successful in-group role models. Resilience-based interventions encourage reappraisal/reattribution, aim to increase confidence in a specific domain, and/or focus on values-affirmation.

Many stereotype threat interventions are based on motivation interventions, such as those that aim to influence student’s attributions of their intelligence (Aronson et al., 2002), increase students’ sense of belonging (Walton and Cohen, 2007), and affirm students’ values (Cohen et al., 2006, discussed in more detail in the motivation section below). Besides motivation-based interventions, other interventions aim to reduce stereotype threat by asking students to reflect on threats to their ethnic-racial identity. Ben-Zeev et al. (2017) evaluated the effects of a stereotype threat reflection intervention on students’ performance in an abstract reasoning task. 40 Black/African American and 210 Latinx STEM students were presented with either a stereotype threat reflection intervention, values affirmation intervention, or no intervention. The stereotype threat reflection consisted of a brief module on stereotype threat followed by reasoning about a hypothetical situation in which they or a friend was experiencing stereotype threat and writing about what they would tell themselves or their friend to help cope. Minoritized students in the stereotype threat reflection intervention reported decreased concerns about stereotype threat and higher abstract reasoning scores compared to the control group.

Most other studies of stereotype threat interventions have focused on age groups and/or content different from undergraduate STEM but may still be relevant. Bikmen (2015) explored the effects of a historical narrative intervention (about the Little Rock Nine, highlighting the resilience of the first 9 Black students to enter Little Rock Central High School during desegregation versus a control narrative about the Berlin Wall) on 51 Black undergraduate students’ performance on a verbal task. Students with high identification with their racial group did worse with the control narrative than the resilience narrative, suggesting that messages of resilience could serve as a protective factor. In another intervention study, Alter et al. (2010) found that framing an activity as an opportunity for learning, instead of as a test of ability, reduced the impact of stereotype threat on Black children’s test performance. Similarly, Johns et al. (2008), found that a reframing intervention improved working memory performance for Latinx undergraduate students.

Despite some stereotype threat specific interventions being conducted on minoritized populations, most have not specifically addressed undergraduate mathematics or STEM. Most stereotype threat specific interventions for mathematics have been applied to women (Liu et al., 2021; Nguyen and Ryan, 2008). For women, effective interventions include teaching them about stereotype threat (Johns et al., 2005; but see Merillat et al., 2018 for a not significant result with high schoolers), completing an interest and personality questionnaire (Ambady et al., 2004), thinking about similarities between males and females (Rosenthal and Crisp, 2006), and replacing stereotype threat related thoughts with thoughts about an important personal identity (Logel et al., 2009). However, recent meta-analyses call into question the effect of stereotype threat on women, with Picho-Kiroga et al. (2021) finding that stereotype threat effects for women have been inflated, while Warne (2022) argues that the stereotype threat effect for women is negligible. However, it is important to note that the vast majority of this work has not considered how stereotype threat in general and stereotype threat interventions more specifically function under the context of intersectional identities, e.g., for women of color.

Using the PVEST framework, stereotype threat interventions can be understood through their effects on Net Stress and their objective to help students have more adaptive Reactive Coping. Stereotype threat interventions are intended to reduce Net Vulnerability and Net Stress by buffering the experience of social identity threats and sometimes explicitly training students in more adaptive Coping Responses. For example, in the Ben-Zeev et al. (2017) intervention, students’ meaning making of stereotype threat is directly addressed by having students explicitly think about how stereotype threat could impact them and to brainstorm ways to reframe the threat(s) to limit its negative effects. Although stereotype threat interventions acknowledge the sociocultural context of the student and can help students focus on the supports and protective factors in their environment, they currently do not account for the individual differences in students’ experiences, particularly those associated with their intersectional identities, which is one of the key contributions of PVEST. Approaching such interventions with a PVEST perspective can help us anticipate which students benefit from stereotype threat interventions and in which contexts, rather than expecting such interventions to benefit all minoritized STEM students across all settings. One of the key conditions for stereotype threat is that an individual must identify with the domain in which they are performing a task (Aronson, 2002; Spencer et al., 2016). In their meta-analysis, Nguyen and Ryan (2008) showed that several moderators (stereotype threat relevance, domain identification, and task difficulty) influence the effects of stereotype threat on minoritized students. For instance, they found that stereotype threat effects were larger in contexts where the threat was explicit. Thus, stereotype threat interventions are only expected to apply to minoritized students who have already developed a STEM identity.

In addition, stereotype threat is not the only source of stress that minoritized STEM students experience. Sackett et al. (2004) state that although stereotype threat might play some role in the difference in achievement between White and minoritized students, it is not necessarily the primary or sole contributor to minoritized student underrepresentation, and that other factors should not be ignored. Factors other than social identity threats, such as math anxiety and low math self-efficacy, can also influence students’ phenomenology with a negative impact on mathematics performance and can interact with processes such as stereotype threat. Utilizing a PVEST perspective helps us consider the role of other factors of Net Stress, how they may interact with stereotype threat, and how interventions can address these different sources of stress.

Mathematics anxiety is “a feeling of tension, apprehension, or fear that interferes with math performance” (Ashcraft, 2002, p. 181). Math anxiety is a significant threat to achievement and persistence in STEM due to the high emphasis in many STEM courses on quantitative skills (Chang and Beilock, 2016; Hembree, 1990; Maloney and Beilock, 2012; OECD, 2013; Ramirez et al., 2018; Stankov and Lee, 2017). Math anxiety reduces math achievement, leads students to opt out of higher mathematics in high school, and makes students less likely to pursue STEM fields in higher education, especially as the material gets more difficult and the stakes get higher (Ahmed, 2018; Hembree, 1990). Some studies find higher rates of math anxiety in minoritized students (Ahmed, 2018; Cheema and Sheridan, 2015; Gabriel et al., 2019; Hembree, 1990; Onwuegbuzie, 1999; Young and Young, 2015), but even moderate amounts of math anxiety could have negative impacts on minoritized students’ STEM success and persistence. Math anxiety is a vicious cycle. Math anxiety leads to math avoidance, math avoidance leads to decreased math performance, and decreased math performance further exacerbates math anxiety. In addition, math anxiety undermines students’ motivation to continue to engage in math (Hembree, 1990; Luttenberger et al., 2018). Thus, minoritized students who want to pursue less computationally heavy STEM fields, such as biology, might move away from their major due to experiences in their math gateway courses.

Historically, the etiology of the relationship between math anxiety and poor math performance has been debated. Some believe that poor math performance and achievement are a product of math anxiety, while others believe that math anxiety is a product of poor math skill (Ramirez et al., 2018). Research supporting the view that math anxiety leads to poor math performance centers on the role of working memory. Working memory is a cognitive workspace in which on-line information is temporarily stored and manipulated (Miyake and Shah, 1999), and it is essential for complex cognitive tasks such as mathematics (Raghubar et al., 2010). Heightened math anxiety is known to increase worry, worry then uses up some of the available working memory resources and limits the amount available for the task at hand (Ashcraft and Kirk, 2001). Ashcraft and Kirk (2001) found that when individuals were required to complete math problems while holding random letter sets in working memory, individuals with high math anxiety made more errors in reciting the letters held in working memory than individuals with low math anxiety. These findings suggest that the math performance impairments associated with math anxiety are an outcome of the additional cognitive burden on working memory.

In contrast, some research supports the idea that math anxiety is a product of poor math skill. Ma and Xu (2004) conducted a longitudinal study of seventh to twelfth grade students, measuring math anxiety and math achievement annually for 5 years. They found that low math achievement at earlier time points predicted higher math anxiety at later time points, and that these effects were significantly larger than those assessing math anxiety at earlier time points predicting math achievement at later time points. Gunderson et al. (2018) also found comparable results, supporting the idea that math anxiety is a product of poor math skill. However, these findings cannot account for how poor math skill leads to math anxiety (Ramirez et al., 2018).

More recently, Ramirez et al. (2018) proposed that “students’ development of math anxiety is largely determined by how they interpret (i.e., appraise) previous math experiences and outcomes (rather than the outcomes themselves),” (p. 151). This view is well aligned with PVEST’s conceptualization of how students’ meaning making of their Net Vulnerabilities shapes their Net Stress. According to PVEST, math anxiety could be more detrimental to minoritized STEM students than it is to their non-minoritized peers. Math anxiety, like stereotype threat, is a factor that is related to the individual’s previous math experiences and identity (Net Vulnerabilities) and their perceptions thereof (Net Stress). A student’s tendency to experience math anxiety in math contexts is part of their Net Vulnerability, however, their experience of math anxiety in real time is part of their Net Stress due to the role of their meaning making of the real-time physiological and psychological experience of math anxiety. The parts of their Net Vulnerability and Net Stress caused by the math anxiety can then interact with other sources of vulnerability, support, or stress to influence their math performance. For example, minoritized STEM students with math anxiety who have had previously supportive math contexts could have lower Net Vulnerability compared to those with math anxiety who have not had supportive math contexts. Having a supportive math context is likely to encourage more positive perceptions of math, thus lowering Net Stress, which could then mitigate the negative effects of math anxiety on math performance. However, many minoritized STEM students have experienced negative math environments due to racialized experiences in the classroom, low compositional diversity, etc. (Park et al., 2020; Ridgeway and McGee, 2018). Such negative contexts make it more likely that students will have negative perceptions of math, which increases their Net Stress and increases the chances of math anxiety having a negative impact on math performance. In each of the scenarios described, stereotype threat could also interact with the individual’s math anxiety, potentially compounding the Net Stress experienced and increasing the likelihood of maladaptive reactive coping responses.

Two categories of interventions show promise for mitigating the negative impacts of math anxiety, and potentially stereotype threat, by targeting reactive coping responses: relaxation training (Brunyé et al., 2013; Sharp et al., 2000) and expressive writing (Park et al., 2014; Ramirez and Beilock, 2011). Relaxation exercises, such as guided breathing and meditation, have positive emotional benefits in a wide variety of groups (Chambers et al., 2009), and there is some evidence to suggest that they reduce the negative experience of math anxiety and improve math performance. Sharp et al. (2000) found that students who were given 5–7 min of relaxation training for 6 class sessions of a mathematics class reported lower math anxiety and had higher scores on math skill measures than students in a “business as usual” class. Similarly, Brunyé et al. (2013) found positive effects of a guided mindfulness exercise (focused breathing) for university students with high math anxiety on math task performance; individuals with low math anxiety were not affected by the breathing condition. Relaxation exercises have also been shown to be effective for stereotype threat (Weger et al., 2012), perhaps because it leads to worry and impaired working memory function (Schmader and Johns, 2003), much in the same way math anxiety does.

Expressive writing has also been shown to benefit students in high-pressure academic settings (Ramirez and Beilock, 2011). Ramirez and Beilock (2011) found that students in a 10-min expressive writing intervention (write about their anxiety) performed better on a modular arithmetic task compared to the control group (write about their day). Park et al. (2014) found that expressive writing improved math performance on a modular arithmetic task for individuals with high math anxiety compared to a control group, but there was no benefit for non-math anxious students.

Both expressive writing and relaxation training provide strategies to manage the negative thoughts associated with math anxiety, theoretically freeing up the cognitive resources for mathematics that may have been consumed by anxious thoughts (Sweller et al., 1998). Reduction of anxiety may also lead to less aversion to mathematics and thus greater engagement with math tasks (Beilock and Maloney, 2015). From the lens of PVEST, interventions such as relaxation training (Brunyé et al., 2013; Sharp et al., 2000) and expressive writing (Park et al., 2014; Ramirez and Beilock, 2011) can be particularly helpful in reducing Net Stress and addressing the maladaptive Reactive Coping responses that are a product of math anxiety, and potentially social identity threats more generally.

Most studies of math anxiety interventions have two methodological strengths: random assignment and utilization of active control groups. Nonetheless, they have several limitations: (1) most notably they do not report racial/ethnic demographics of their sample, making it impossible to conclude how such interventions specifically function across race/ethnicity; (2) they only assess short-term benefits, so it is unclear whether the effects of the interventions are lasting or effective when repeated; and (3) there are very few studies conducted which specifically assess the efficacy of these techniques specifically for individuals struggling with math anxiety. These limitations can be addressed by utilizing a PVEST framework. Considering that minoritized STEM students do not all struggle with the same obstacles, it is important to provide them with interventions that address the different processes that lead to STEM success. Other potential interventions targeting Net Stress are based on the motivation literature.

Like stereotype threat and math anxiety, students entering gateway STEM courses also face threats to their motivation. Motivation is a multi-dimensional construct described by Wentzel et al. (2009, p. 1) as “the energy [students] bring to [academic tasks], the beliefs, values, and goals that determine which tasks they pursue and their persistence in achieving them and the standards they set to determine when a task has been accomplished.” Several frameworks for academic motivation have been used to understand student STEM beliefs and behaviors. For example, prior research has focused on students’ goals in STEM courses (i.e., student’s main objective is to avoid demonstrating failure, demonstrate success, and/or learn the material; Brodish and Devine, 2009; Smith, 2006; Thoman et al., 2013), students’ sense of belonging in STEM courses (Thoman et al., 2013), and students’ decreased domain identification, or how much success in a course is related to their identity (Thoman et al., 2013). Motivation is a crucial factor in minoritized students’ achievement and persistence in STEM fields (Hall and Ponton, 2005; He, 2014; Simon et al., 2015; Stevens et al., 2004; Waller, 2006; Wood et al., 2015). Struggles with motivation in STEM areas are associated with decreased STEM persistence and achievement (Rosenzweig and Wigfield, 2016).

Due to the multidimensional nature of motivation, many different interventions have been developed to address the varied aspects of motivation to increase STEM success. For this review, motivation interventions will be grouped into the following three categories: self-efficacy, attribution, and values interventions.

An individual’s evaluation of his or her abilities (self-efficacy) has important consequences for performance and persistence (Bandura, 1977). A student who has low confidence is likely to get frustrated and give up when faced with challenges during learning. Self-efficacy is positively related to STEM academic outcomes (Parker et al., 2014), and it plays a significant role in minoritized students’ achievement and persistence in STEM (Stewart, 2006).

Luzzo et al. (1999) compared the impact of a direct success experience (completing easy number series tasks that they were told assessed mathematical abilities), to a vicarious success experience (watching a video of a former student share their math and science success experiences), and a control condition. At a four-week follow-up, individuals in the direct success intervention had higher self-efficacy, were more likely to report choosing STEM majors, and enrolled in more math and science courses in the following semesters compared to individuals in the other two groups. Jansen et al. (2013) also found positive effects of direct success experiences on children’s math anxiety, perceived competence, and math performance in elementary-grade students. Vicarious success experiences also have promise, although not in Luzzo et al. (1999). Ashby Plant et al. (2009) randomly assigned students to interact with a male virtual agent, a female virtual agent, or no agent. The virtual models presented information about successful female engineers, the benefits of an engineering career, and presented information to counteract the stereotype that engineering is cold and unwelcoming to women. Both boys and girls assigned to the female agent had greater engineering self-efficacy, improved performance on a math measure, and displayed higher STEM interest than those in the control groups. In related work, presenting African American students with successful models boosted their performance on a GRE-like exam (Shapiro et al., 2013). These findings suggest that seeing diverse models have success in STEM could be important for minoritized students’ STEM self-efficacy.

In the context of PVEST, these interventions may be thought of as reducing Net Stress by making experiences of success more salient. However, there are very few studies in this vein that focus on STEM achievement and even fewer that are specific to minoritized STEM students. The studies that do exist do not address most of the key contributions of PVEST. These types of interventions, although promising, need to be explored with a more holistic approach to assess whether they are key to minoritized students’ STEM success.

Attribution interventions are related to more general self-efficacy interventions but specifically focus on the individual’s interpretation of success and failure experiences, including four main attributions: ability, effort, task difficulty, and luck (Weiner, 1986). There are two types of attribution interventions: those aimed at getting students to attribute success/failure to effort rather than ability, and those aimed at increasing students’ sense of belonging by framing struggle as a normative experience.

In addition to self-efficacy and attributions, another factor that influences students’ motivation is the extent to which a task or goal aligns with one’s values (Eccles, 1983; Eccles and Wigfield, 2002). Current values-based interventions focus on either increasing individuals’ views of task value, specifically utility value (how the task relates to one’s future goals), or reaffirming individuals’ personal values (what they value in their life in general, e.g., family, education, and community). Both types of values have been demonstrated as being important for student persistence (Lazowski and Hulleman, 2015). It is known that experienced and perceived cultural mismatch between minoritized students’ personal values and those of their institution/department is a predictor of leaving STEM fields of study (Beasley and Fischer, 2012; Seymour and Hewitt, 1997).

Acee and Weinstein (2010) evaluated the effect of a comprehensive task values intervention on students enrolled in an undergraduate statistics course. Participants in the intervention group completed a series of activities intended to bring their attention to the possible value of statistics; participants in the control group were given passages on multicultural learning. Acee and Weinstein (2010) found increases in task value and positive effects of the intervention on student exam performance with one instructor. Canning and Harackiewicz (2015) found that undergraduate students’ performance on a mental arithmetic task benefited from a similar intervention targeting students’ task values. Other studies have supported the efficacy of such task-value interventions for minoritized students in biology (Canning et al., 2018; Harackiewicz et al., 2016; Hecht et al., 2019).

In contrast to task value interventions, in which the objective is to get students to think of the specific value of the task in question, values affirmation interventions focus on getting students to affirm their general, core personal values. Although values affirmation exercises are not directly tied to a certain domain, they are thought to benefit the individual by reaffirming one’s identity, making it less vulnerable to outside threats by reminding students of their greater life values (Brady et al., 2016; Harackiewicz et al., 2014). Brady et al. (2016) assessed the long-term effects of a values affirmation exercise (ranking importance of different values such as religion or humor and writing about their most important value) in Latino and White undergraduate students. Latino students positively benefited from the affirmation intervention, receiving higher GPAs and feeling more positive about their academic performance than students who did not receive the affirmation intervention. Similarly, African American middle school students participating in a values affirmation exercise received higher grades than those who completed an exercise based on their least important values; the increased achievement was maintained over a two-year follow-up (Cohen et al., 2006; Cohen et al., 2009). Values affirmation interventions have also shown benefits for academic achievement in other samples, such as Latino middle school students (Sherman et al., 2013), first-generation students in an introductory biology course (Harackiewicz et al., 2014), and African American students on standardized GRE-like tests (Shapiro et al., 2013). Women’s performance in physics (Miyake et al., 2010) and engineering (Walton et al., 2015) courses or math tasks (Martens et al., 2006; Shapiro et al., 2013) have also been found to improve following values affirmation exercises. However, Bancroft et al. (2017) did not find significant effects of their values affirmation intervention on standardized math performance in a sample of ninth-grade African American and Latinx students, making it unclear whether such an intervention is beneficial specifically for minoritized students’ math achievement.

Within a PVEST framework, all the various motivation interventions aim to address students’ Net Stress by intervening on their meaning making in different ways. Self-efficacy interventions address students’ confidence in their abilities, attribution interventions address students’ attributions of their academic achievement or social belonging, and values interventions aim to highlight students’ values. However, when and for whom these motivation interventions successfully reduce Net Stress is currently unclear, as demonstrated by the inconsistent effects on academic achievement (Kost-Smith et al., 2012). Shapiro et al. (2013) argue that not all interventions are likely to be successful under all situations of threat. Shapiro et al. (2013) found that role model interventions are helpful when the threat faced is targeting one’s group, but that affirmation interventions are only helpful when the threat faced targets one’s abilities. The fact that these individual motivation interventions are not consistently effective for minoritized students in general highlights the need for acknowledging the heterogeneity of this population. It is possible that if combined, motivation interventions could have greater efficacy due to the various sources of Net Stress they address. However, like for stereotype threat and math anxiety interventions there is a need for studies assessing the efficacy of these interventions specifically for undergraduate minoritized STEM students specifically with consideration to the key contributions of PVEST.

The interventions reviewed thus far generally do not adequately consider the sociocultural contexts and do not attempt to address the sources of Net Vulnerability in those contexts. One category of interventions has specifically focused on increasing undergraduate minoritized STEM students’ math achievement by specifically intervening on the sources of their Net Vulnerability, collaborative learning interventions.

Over the decades, many institutions have enacted collaborative learning programs to support minoritized students in gateway courses, addressing the importance of social support, specifically peer support, to increase their STEM persistence (Lent et al., 2005). There are many models of near-peer academic support programs currently in use across the country, such as The Emerging Scholars Program (Asera, 2001), Supplemental Instruction (Dawson et al., 2014), Peer Assisted Learning (Arendale, 2014), Peer-Led Team Learning (Wilson and Varma-Nelson, 2016), more general learning communities (Carrino and Gerace, 2016; Johnson et al., 2023; Solanki et al., 2019), and various others. A key feature of such programs is the opportunity to engage with peers in active learning practices, specifically collaborative learning. Collaborative learning, as opposed to lecture-based teaching, has been shown to increase undergraduate student performance in STEM courses (Freeman et al., 2014; Springer et al., 1999) and to be beneficial specifically for minoritized students in STEM (Theobald et al., 2020). Group problem-solving exercises specifically are a promising collaborative learning technique shown to improve undergraduate student achievement in quantitative courses (Asiala et al., 1997; Dees, 1991; Ellington, 2005; Giraud, 1997; Keeler and Steinhorst, 1994). Overall, the benefits of collaborative learning interventions have been demonstrated for a wide range of mathematics courses, including but not limited to statistics (Giraud, 1997; Keeler and Steinhorst, 1994), calculus (Asiala et al., 1997), and university algebra (Ellington, 2005). Collaborative learning promotes achievement, productivity, self-esteem, intergroup attitudes, and positive attitudes toward learning (Springer et al., 1999). Collaborative learning environments likely lead to such positive outcomes for several reasons, including but not limited to having additional support for difficult content from peers, a less competitive environment, and an increasing sense of belonging (Springer et al., 1999; Hausmann et al., 2009).

The following section will focus on the Emerging Scholars Program, a collaborative learning workshop initially created by Uri Treisman at the University of California, Berkeley in the 1970s, since it was developed to specifically support minoritized students in calculus gateway courses (Asera, 2001; Fullilove and Treisman, 1990; Treisman, 1992). The core characteristic of this program is that minoritized students meet outside of lecture every week, working together to solve collaborative calculus problems with the support of a graduate student. The problems are difficult enough to motivate collaboration between students and promote critical thinking about the concepts without being overly challenging.

Several universities have adopted programs like the Emerging Scholars Program for university calculus, for example, the University of Texas at Austin, the University of Wisconsin at Madison, the University of Kentucky (Lexington), and Rutgers University (Asera, 2001; Fullilove and Treisman, 1990). The program was originally designed as a supplementary program (separate from formal courses; Asera, 2001) and had five aims: (1) to increase the time students spent on the subject concepts, (2) to provide students with the opportunity to explore challenging aspects of the subject, (3) to provide students an opportunity to interact more with peers, graduate students, and faculty, (4) to create a supportive student community, and (5) to incorporate academic advising.

The effectiveness of the Emerging Scholars program specifically has been demonstrated for African American and other minoritized students (Alexander et al., 1997; Bonsangue and Drew, 1995; Fullilove and Treisman, 1990; Moreno and Muller, 1999; Moreno et al., 1999; Peterson et al., 2013). Fullilove and Treisman (1990) used data from 646 African American students enrolled at the University of California, Berkeley, between 1973 and 1984, to compare outcomes for demographically similar workshop students to non-workshop students with comparable quantitative SAT scores. Overall, African American students who participated in the workshop were more likely to earn higher grades (B- or greater), less likely to fail the course, and persisted more in university than non-workshop African American students. Although these findings were promising, Fullilove and Treisman noted some limitations, including that workshop students were self-selected, and analyses did not sufficiently control for some demographic factors. However, several follow-up studies with methodological improvements have found similar benefits. Bonsangue and Drew (1995) assessed the efficacy of an Emerging Scholars program for African American and Latinx students enrolled in calculus courses. They found that workshop students received higher grades, had higher retention rates in STEM, and completed the calculus series more quickly than non-participating minoritized students. Furthermore, Moreno et al. (1999) found that when controlling for SAT scores, workshop participants (regardless of race/ethnicity) earned higher grades in the first calculus course than non–participants. Epperson et al. (2015) found that workshop students performed better on more abstract calculus problems than non-workshop students, suggesting that the collaborative workshop fosters a deeper and more flexible understanding of calculus concepts. Importantly, when Moreno and Muller (1999) statistically controlled for self-selection effects, workshop participation positively predicted student achievement and STEM major selection.

Application of collaborative interventions in out of class programs, like Emerging Scholars, is a way immediately to support minoritized STEM students and to surround them with demographically similar peers. Ideally, these collaborative learning techniques need to be imported into curriculum and course design for first-year math/calculus courses (Theobald et al., 2020), but this should not completely replace out of class programs such as Emerging Scholars. Out of class programs specifically for minoritized STEM students, and other informal spaces, offer a unique opportunity for minoritized STEM students to easily access peer support from one another, which is not possible in classes with low compositional diversity (Ong et al., 2018).

In summary, collaborative learning programs are promising for increasing minoritized student achievement in gateway calculus courses (see Theobald et al., 2020 for a large-scale analysis). These programs are also beneficial for other gateway math and science courses (Duncan and Dick, 2000; Peterson et al., 2013; Snyder et al., 2016; Wilson et al., 2012). However, because these programs incorporate multiple components (collaborative learning, advising, graduate student support, etc.), it is currently unclear which component of these programs is leading to these academic gains. But many other studies have demonstrated the specific benefit of collaborative learning activities, suggesting it is a crucial element (Asiala et al., 1997; Dees, 1991; Ellington, 2005; Giraud, 1997; Keeler and Steinhorst, 1994; Theobald et al., 2020).