Mindset × Context: Schools, Classrooms, and the Unequal Translation of Expectations into Math Achievement

Introducing the Theoretical Perspective Motivating This Research

This research was organized by a general theoretical perspective that we adapted into a specific operationalization. The general perspective, Mindset × Context Theory (Hecht et al., 2021; Rege et al., 2020; also see Yeager & Dweck, 2020), orients research on educational equity to the reciprocal influences between young people's psychological orientations and their opportunities to enact those orientations, which are organized and controlled by larger social and institutional settings, such as districts, schools, and classrooms. As such, it connects developmental psychology and sociology in the spirit of human ecology (Bronfenbrenner, 1981).

The main principle of Mindset × Context Theory is that educational equity is predicated on planting the seed (i.e., a personal motivation to achieve) and enriching the soil in which the seed grows (i.e., a contextual resource that allows motivation to foster achievement) in a plot of ground that is not already planted (i.e., a context that does not already show near-optimal outcomes) (see Walton & Yeager, 2020). This interplay of seed (mindset) and soil (context) contends that schools and classrooms that have room to grow must create opportunities for young people to achieve, but that those opportunities are effective only if young people are well-positioned to take advantage of them. Otherwise, even young people who want to achieve (and believe they can) may be thwarted when they do not have concrete opportunities to do so. Notably, another principle of the perspective is that the potential benefits of this positive interplay of mindset and context are heightened in the face of societal stratification. Thus, adolescents in vulnerable positions within major stratification systems (e.g., gender, SES, race, and ethnicity) will gain more from this interplay, improving their relative standings with peers in advantaged positions to reduce stratification overall (Dweck & Yeager, 2019; Walton & Yeager, 2020; Yeager & Dweck, 2020). These tenets of the Mindset × Context Theory perspective were borne out by initial results from the National Study of Learning Mindsets (NSLM, see Yeager et al., 2019, 2022). These results showed that a growth mindset promoted key indicators of achievement in schools and classrooms with a growth mindset culture, especially among groups of students who were at risk for low achievement in the first place (also see the College Transition Collaborative; Walton et al., 2023).

Our goal in this monograph was to translate the general Mindset × Context Theory perspective into a more general developmental model that helped us understand the role that expectations for success play in contributing to equity in educational progress within a school system that is highly stratified by family socioeconomic status. To do so, we had to narrow the focus in terms of specific sector of the educational system and in terms of a specific period of the educational career. First, the math curriculum is stratified by gender, SES, and race and ethnicity; it is highly cumulative; and it powerfully predicts educational and occupational attainment in the globalized economy (National Science Foundation, 2020). Second, the first year of high school is a period when young people face new challenges, when they are at risk of getting lost in the shuffle of larger and more impersonal schools, and when their initial experiences have outsized influence on their future trajectories (Benner & Graham, 2009; Crosnoe & Muller, 2014; Domina et al., 2017; Eccles, 2005). Thus, this sector at this point heightens the potential for disparities related to membership in vulnerable groups and the potential for student expectations, contextual resources, and the interplay between them to matter.

To next step was to narrow the consideration of context. Guided by the developmental literature linking students' learning orientations and behaviors to the interpersonal influences of valued others (Eccles, 2009; Wentzel, 1999), we focused on the normative climates of achievement and learning in schools and classrooms. By normative climates, we mean the standards for success and failure that are put forward (or seemingly put forward) by key actors in schools and classrooms: fellow students and teachers (Allen et al., 2013; Crosnoe et al., 2008; Morgan, 2005; Walton & Yeager, 2020). Specifically, we considered the school-level peer norms and the classroom-level perceptions of stereotyping (Crosnoe et al., 2008; Yeager et al., 2019).

Conceptualizing and Operationalizing This Research

Figure 1 presents the conceptual model of this study, in which the mindset (expectations for success in math) is translated into a concrete dimension of progress (10th-grade math course-taking progress) at the start of high school differentially across intersectional identity groups. There are several levels to the model. The first level is shown in the individual-level process box. It shows that mindsets shape motivation, engagement, and challenge seeking, and thereby influence persistence in rigorous math courses. However, intersectional identities can influence this process, such that it is weaker or stronger for different groups. Thus, different groups can experience stronger or weaker translation of expectations for success in math into outcomes (e.g., dashed dreams) depending on their vulnerability within the U.S. educational system (Research Question 1). These individual-level processes play out over developmental time, and can be especially important at critical junctures, or turning points, in the educational system (e.g., progress from 9th to 10th-grade math). Next, the individual life course trajectories are nested within ecological (i.e., contextual) forces. These include schools' peer cultures (e.g., achievement level and academic norms of fellow students at school; Research Question 2) and classroom cultures (e.g., students' perceptions of gendered stereotypes about math; Research Question 3). Although not studied here, we acknowledge that higher-level forces come into play (e.g., the exo-, macro-, and chronosystem). In summary, broader contextual forces moderate the links between students' expectations for success in math and their math progress at the start of high school, particularly among the intersectional identity groups that were most vulnerable to poorer outcomes.

To operationalize this conceptual model, we drew on data from the NSLM, which was ideally suited to this purpose. As the most recent national, longitudinal study of U.S. public high schools, the NSLM's representative sample allowed us to generalize to the public school population and to conduct a systematic investigation of school- and classroom-level moderation with rich measures of peer norms and perceived classroom stereotyping. The NSLM's complete sampling of students within schools allowed comparison of students from different gender or SES groups (as well as racial and ethnic groups) with the same expectations in the same classroom. Its mixture of survey and administrative data enabled the triangulation of the psychological, interpersonal, and institutional processes at the heart of schooling (Yeager et al., 2019). Finally, its large sample size permitted the use of state-of-the-art, Bayesian, machine-learning methods for answering all questions here. This method can result in more robust, replicable, and trustworthy results than would be possible with conventional regression analyses (Dorie et al., 2019; Hill et al., 2020).

In the next section, we elaborate on the motivation for these hypotheses, the distillation of a conceptual model from the Mindset × Context perspective, and its operationalization with the NSLM. Before doing so, our primary focus on the intersectional identity groups defined by gender and SES needs to be addressed. As described below, theoretical and methodological concerns led to this focus on SES and gender, but, mindful of the ways that racial and ethnic identities intersect with other systems of stratification, we conducted extensive analyses of the role of race and ethnicity as well.

A Deeper Dive into the Conceptual Motivation and Methodological Execution of This Study

The broad context of this study is the historical evolution of the U.S. economy in recent decades that raised the value of higher education (especially in STEM) and, in the process, reinforced the significance of societal-level stratification as both an influence on pathways through the educational system and as a consequence of those pathways. Motivated by this complex phenomenon, our team used the Mindset × Context perspective to conceptualize a study focused on student expectations for success in math and innovatively leveraged the NSLM to operationalize it. We detail each point in the development of this monograph below.

The Broader Context of Educational and Labor Market Inequality

Data Showing the Importance of Early Math Progress

To further illustrate why math progress early in high school represents a critical point for long-run adolescent development, Figure 2 previews the complete set of high school math course-taking patterns in the present monograph's dataset (NSLM) among students who attended the same high school from 9th through 12th grades (N = 9,431). Thicker pathways indicate more common math transitions for students. The most common course-taking pattern was for students to start Algebra 1 in 9th grade and advance to Geometry in 10th grade, Algebra 2 in 11th grade, and precalculus or advanced math in 12th grade. Despite starting at a lower level, these students could still complete a rigorous math curriculum by the end of high school. Some of these Algebra 1 students were diverted in 10th grade, as shown by the pathway highlighted in blue. The overwhelming majority of these diverted Algebra 1 students did not reach a math level above Algebra 2 by the end of high school. In fact, many did not continue advancing math levels after completing Geometry in 10th grade.

Figure 2, therefore, illustrates why this ecologically informed study focuses on the transition from 9th- to 10th-grade math. This transition is when students are most likely to repeat a course. Also, unlike later high school transitions, the 9th- to 10th-grade transition is less complicated by student choice. Specifically, once students reach Geometry or Algebra 2, they have more choice about whether they would like to take more advanced math, less advanced math, or stop taking math altogether. Thus, students who do not progress from 9th to 10th grade not only lack the opportunity to reach rigorous math levels in high school, but they also have less choice in their math course-taking than do students who complete Geometry earlier in their high school career.

Another reason to focus on this transition is that it sets the stage for what adolescents can accomplish in high school and beyond. Prior research has shown that completing advanced math in high school is important for college entry, college completion, earnings, and even health later in life (Adelman, 2006; Carroll et al., 2017; Rose & Betts, 2004). A preview of our data (Figure 3) showed that disparities in adolescents' graduation status, rigorous high school course-taking, and postsecondary enrollment vary by whether they progressed in math from 9th to 10th grades. Figure 3 displays the proportion of adolescents who achieved each of these academic milestones among those who advanced in math between 9th and 10th grade (their math progress was “On Track”) and those who did not (their math progress was “Off Track”).

The disparity in long-run outcomes between adolescents who did and did not progress in math between 9th and 10th grades was 27% for high school graduation, 56% for advanced math course-taking, 45% for college-level course-taking, 34% for postsecondary enrollment, and 34% for 4-year college enrollment. Of course, these gaps were partly related to adolescents' prior skills, background, and school context, but they highlight the importance of early high school math progression for success in high school and beyond. Figures 2 and 3, therefore, illustrate why zeroing in on a particular moment in the lifespan—math progress in the transition to high school—can act as a window into the processes that create or sustain inequalities.

The Conceptual Model

As already introduced, the theoretical perspective we draw on here—the Mindset × Context perspective—points us to considering the agency of individual youth from differently vulnerable intersectional identity groups amidst a set of constraints and opportunities created by the settings in which they live. We can break down each part of this perspective and how it sets up a concrete piece of the conceptual model for this study.

The Methodological Plan

Testing the hypotheses derived from the specific conceptual model that we distilled from the general Mindset × Context perspective involves extensive operationalization and analyses of the NSLM. Chapter III describes the NSLM, its measures, and our statistical plan for analyzing this dataset in detail, but we highlight the main points here.

Mindsets

Mindsets are situation-general, socialized belief systems that guide interpretations of the social world to influence self-regulation processes during goal pursuit (see Dweck, 2017; Dweck & Yeager, 2019; Hecht et al., 2021). In this study, the mindset of interest was a person's expectations for success, a concept which has a long history in developmental research (Eccles & Wigfield, 2002, 2020; Muenks et al., 2018).

What do these different components of the definition mean? Situation-general means that mindsets are not beliefs about a particular event—such as one test or one interaction with a peer or teacher. Instead, they are beliefs about categories of attributes or experiences, such as one's potential for future success in math. Socialized means that they are the product of prior experiences with goal pursuit and with socializing environments, such as parents, peers, and teachers (Eccles & Wigfield, 2002; Wentzel & Looney, 2007). They are not solely situationally constructed or ephemeral. We say that mindsets guide interpretations of specific situations in the social world, because they give ambiguous events—such as a moment of frustration or isolation—larger meaning. For example, when people expect to do well, they may appraise an experience of failure as a momentary setback, but, when they expect to do poorly, they may think the failure is a sign that their fears about being incompetent are going to be confirmed. Thus, mindsets offer starting assumptions that are later tested out in daily experiences in pursuing goals (see Walton & Wilson, 2018; Walton & Yeager, 2020). Mindsets affect self-regulation styles through this meaning-making process. For instance, people who expect to do well and then make positive appraisals of frustrations go on to use more resilient self-regulation techniques, such as trying the problem a different way, increasing effort, or asking for help appropriately. When people expect to do poorly, however, they tend to use less resilient self-regulation techniques, such as procrastination, self-handicapping, withdrawing effort, or otherwise hiding their deficiencies to avoid confirming their own or others' low opinions of their abilities.

Research has identified many different mindsets in the literature, and all have some relation to expectations for success in math, the mindset of interest in this study. Examples include growth (versus fixed) mindsets (also called implicit theories; see Dweck, 2006; Dweck & Yeager, 2019; Yeager & Dweck, 2012), belonging mindsets (also called belonging uncertainty; Walton & Cohen, 2007, 2011), relevance mindsets (also called utility value; e.g., Harackiewicz et al., 2016; Hulleman & Harackiewicz, 2009), purpose mindsets (e.g., Reeves et al., 2020; Yeager et al., 2014), stress mindsets (Crum et al., 2020; Yeager et al., 2022), and more. Here we focused on expectations because they are thought to be one central process through which the different mindsets relate to achievement outcomes. This fact will allow us to develop a broader theoretical framework that may well generalize across the different specific mindsets in the literature.

Another key reason to focus on expectations is that they have long been a target of policy action. Dating back to Clark and Clark's (1947) seminal research on self-esteem for Black and White students and the ensuing Brown v. Board of Education decision integrating U.S. public schools (Warren & Supreme Court Of The United States, 1953), enormous effort has been put into raising expectations for success among students from historically segregated and marginalized groups. To this day, investments also have been made in narrowing gender inequalities in expectations for success in math and science (Hulleman & Harackiewicz, 2009; Saujani, 2017). Is it enough, though, for adolescents to have high expectations, or do they need support from their school and classroom learning contexts to realize their high expectations? This question highlights the importance of the context part of the model.

Contexts

As previewed in Chapter I, classic sociological theories of inequality (Coleman & Hoffer, 1987; Domina et al., 2017) define context in terms of the resources it provides for individuals who are striving for social or economic success in a given political system. In the educational system, resources can be formal, which refers to the written policies that provide access to high-quality teachers, curriculum, and schools (Coleman & Hoffer, 1987; Duncan & Murnane, 2011). Resources can also be informal, which refers to emergent factors of the social milieu, such as the peer or classroom culture (Coleman, 1961). In general, both formal and informal resources tend to be less abundant and/or accessible for members of groups that have been historically marginalized in a domain, and more abundant and accessible for members that have been afforded greater power, privilege, and influence in a domain. Thus, resources in the context tend to reproduce inequality. At the same time, the marginal benefit of providing additional resources—either formal or informal—tends to be greater for members of marginalized groups, because any additional resource above the status quo makes a relatively greater difference for those who have less of it. Thus, increasing the availability of a contextual resource that is sorely needed by a given group offers one important way to narrow group disparities.

Mindset × Context Interactions

Although sociological theory speaks to how resources directly affect outcomes across groups, it has not yet systematically explained how resources interact with the psychological orientations—or mindsets—that students bring with them to the school context. Mindset × Context Theory seeks to do just that by combining the psychological perspective on culturally learned mindsets with the sociological perspective on inequality.

According to Mindset × Context Theory, contextual resources could have two kinds of moderating effects (Bailey et al., 2020; Miller et al., 2014). First, the context could have a compensatory effect. Imagine that a student's mindset is a kind of internal psychological resource. An external contextual resource, such as a well-run school with dynamic and motivating teachers, could compensate for a student's lack of that internal resource. Empirically, the compensatory effect would mean that a student who is low on a positive mindset factor would not be any worse off than a student who was high on that factor, provided that they were in a context with abundant resources.

Alternatively, the context's resources could have a complementary effect. This effect would occur if the student's mindset and the context's resources work together to result in progress through the educational system. In a complementary interaction, a mindset is like a “seed” that must be planted in fertile “soil” to have effects (Walton & Yeager, 2020). This pattern has also been called the affordances pattern of results, because the context is affording, or supporting, the student's implementation of their mindsets (Hecht et al., 2021; Walton & Yeager, 2020). This affordances language emphasizes that a mindset is like a starting hypothesis about a context, but students must apply that hypothesis to interpret specific, ambiguous situations. If the context does not afford an opportunity for the student to make the more optimistic appraisal of the situation, then the student may not benefit from the mindset. Likewise, if the context provides resources, but the student is not psychologically prepared to attend to and positively appraise them, then the student may not fully benefit from the context. Empirically, the complementary effect would show up as a positive interaction between a student's positive mindset and the positive contextual supports for that mindset, when predicting academic progress outcomes. This view has also been called an accumulated advantages pattern (see Bailey et al., 2020; Miller et al., 2014), because it is the people who already had more of a beneficial mindset already who then go on to profit more from the resources in the context.

There is one final untested corollary of a complementary effect. Consider negative mindsets and negative contextual factors—factors that do not just fail to provide resources, but that actively undermine a group's pursuit of a given goal. In principle, the complementary effect of a negative mindset and a negative context would give rise to an accumulated disadvantages effect. Those with a negative mindset, in an achievement-suppressing context—for instance, a context with rather severe stereotyping of one's group—would display the poorest outcomes overall. We extend Mindset × Context Theory to examine the accumulated disadvantages hypothesis in Chapter VI.

Evidence From the NSLM

The first two preregistered analyses from the NSLM assessed how the benefits of a short, online, student-directed growth mindset intervention on students' grade point average (GPA) varied across individuals, schools (Yeager et al., 2019), and math teachers (Yeager et al., 2022). These analyses revealed that the growth mindset intervention's effects on student GPA were greater among lower-achieving students (Yeager et al., 2019) and students who previously reported more of a fixed mindset (Yeager et al., 2022). Thus, at the level of individual differences, the intervention changed outcomes the most among students who previously were vulnerable to the processes targeted by the growth mindset (also see Andersen & Nielsen, 2016; Porter et al., 2021).

Further, past NSLM analyses examined the moderating effect of context. At the school level, peer norms were a moderator. Peer norms were measured using a behavioral task (called the “make-a-math-worksheet” task; Rege et al., 2020) that assessed students' desires for academic challenges that could teach them something new, even if they did not get all the answers correct (a “learning” or “mastery” goal) (Elliot & Church, 1997; Elliott & Dweck, 1988). Individual students' choices, from the control group, were averaged at the school level to index peer norms. In contexts with greater challenge-seeking peer norms, the growth mindset intervention had larger and substantively meaningful (in terms of effect size) benefits for GPA. Few effects emerged in contexts with weaker challenge-seeking peer norms. At the classroom level, teachers' mindsets about the malleability of ability were a moderator. In classrooms taught by teachers who reported more of a growth mindset, there were meaningfully large treatment effects on math GPA. There were few effects on math GPA when teachers reported more of a fixed mindset. The overall conclusion from the NSLM, then, was that treatment effects were larger among vulnerable groups who were in school or classroom contexts with more supportive informal resources. This conclusion was bolstered by the NSLM's use of a large, nationally representative sample and conservative, Bayesian machine-learning analysis methods. It was also supported by subsequent randomized experiments that manipulated the classroom culture and directly illustrated their moderating role (Hecht et al., 2023).

Evidence From Experiments to Promote Belonging and Purpose Mindsets

Walton and Yeager (2020) reviewed several other studies showing complementary (affordances) patterns of results, similar to the NSLM. A large multisite experiment (Walton et al., 2023); N = 26,911 students, k = 22 colleges) conducted by the College Transition Collaborative (CTC) evaluated a short online social belonging intervention that had, in previous experiments, improved the college persistence and achievement outcomes for first-generation college students, students of color (Walton & Cohen, 2011; Yeager et al., 2016), and women in male-dominated engineering majors (Walton et al., 2015). The CTC study found that the belonging intervention improved full-time enrollment the year after the study among students whose social class and racial and ethnic identity groups historically showed greater disparities in outcomes and in contexts that afforded more of an opportunity for belonging for members of those groups (Walton et al., 2023).

A field experiment conducted by Reeves and colleagues (2020) manipulated the presence of affordances, or supports, in a classroom culture to test whether they would enhance the academic benefits of a student's mindset. This study focused on the purpose mindset, which is the belief that schooling is an opportunity to acquire skills that help you to make a contribution to something larger than yourself (Damon et al., 2003; Hill et al., 2010; Yeager & Bundick, 2009). In this experiment, 7th and 8th-grade students completed a short, online purpose mindset intervention or a control intervention. A few weeks later, teachers provided students with hand-written notes encouraging them to view a test preparation assignment as an opportunity to take a step toward their self-transcendent purposes, or with control notes. The study showed strong evidence for a complementary Mindset × Context interaction: the student's mindset and the teacher's note each had an effect only when the other was in place. These results were strongest for the group of students who previously had the lowest scores in the English class—nonnative English speakers. Thus, this experiment also provided evidence for the notion that mindsets have larger effects among vulnerable students in supportive contexts.

For Which Gender and Socioeconomic Identity Groups are Mindset Associations Weaker or Stronger?

Mindset × Context Theory is intended to explain a range of group-based inequalities. Research on moderation of psychological intervention effects to date, however, has focused on separate identities, such as gender, SES, race, or ethnicity (e.g., Murphy et al., 2020; Reeves et al., 2020; Stephens et al., 2014; Walton & Cohen, 2007, 2011; Walton et al., 2015; for notable exceptions, see Harackiewicz et al., 2016; Walton et al., 2023). This narrow focus has left many questions about the connections among identities, and their interplay with mindsets, unanswered.

Usually, studying the connections among systems of stratification and identity groups is challenging because of sample size issues that arise from studying rarer subgroups. Consider that studying only two social identities interacting with a single mindset across even just one context factor implies a four-way interaction, which can be difficult to detect reliably in small samples. Studying multiple identities or multiple context factors can make the problem even greater, which is why a large heterogeneous sample is needed to study more complex identities directly. Here we use the large, nationally representative sample from the NSLM to address this gap in the literature. Drawing on the framework of Choo and Ferree (2010), we take a group-focused perspective on the connection among different identities and examine the possibility of “multiple jeopardy” (King, 1988) in the transition to high school. Even with this strength, a limitation of our research was that we did not have statistical power to ask these questions separately for each of the major racial and ethnic groups in the United States.

The two dimensions of inequality we focused on primarily were gender and SES. As explained in Chapter I, these factors stratify access and opportunity to higher-level STEM coursework and workforce opportunities. On average, students from high-SES families are taught in more advantaged contexts that lead to higher academic achievement, challenge-seeking, and progress toward valued credentials. Yet, the story with respect to gender can be more complicated, as noted in Chapter I. Women and girls in the United States and in many other contexts around the world are subjected to negative intellectual stereotypes about their potential in math and science (Spencer et al., 1999; Zhao et al., 2022) and they often face anti-intellectual peer norms that discourage immersion in their studies (Gordon et al., 2013). This bias can keep them out of the upper echelon of STEM performance. Nevertheless, girls are equally represented in advanced math at every grade level in high school and in the first few years of college as compared with boys (Riegle-Crumb & Peng, 2021). Boys—and especially boys from low-SES families—have lower rates of math success and later college matriculation, perhaps in part due to the perceptions that doing well in school and caring about one's education are feminine attributes (e.g., Hartley & Sutton, 2013; Heyder & Kessels, 2013, 2017). In fact, boys' inclusion in higher education has been declining for over 40 years. After the 2020–2021 school year, the year in which the present study's participants should have been in their second year of college, 59.5% of college students were girls, and only 40.5% were boys (Belkin, 2021).

In addition, disparities by race and ethnicity persist in access to educational opportunities in general, and STEM specifically. Students from underrepresented racial and ethnic groups (URGs), including Black, Hispanic/Latinx, and Native American students, on average attend lower-quality schools with fewer resources (Fahle et al., 2020). Even when from high-SES families and when attending higher-quality schools, these students experience inequality in the rigor of their math course offerings (Hanselman & Fiel, 2017; Quillian, 2014). Negative stereotypes about which racial and ethnic groups have innate abilities or can be successful in school and in society are common even among teachers (Chin et al., 2020). This means that groups of Black and Hispanic/Latinx students, on average, do not reach the same level of math achievement as their peers, even when they come from high-SES families or have high achievement levels (Reardon & Robinson, 2008). There is some evidence that these patterns differ by gender; girls from URGs, on average, have higher academic achievement than boys from URG (Riegle-Crumb et al., 2018). While racial and ethnic identities could not be investigated with sufficient power in our contextual moderation analyses, we attended to these disparities in Chapter IV.

Overall, this previous evidence raised intriguing questions about how SES and gender jointly interact with expectations for success in math to create inequitable academic progress in math. Should girls—the traditionally stereotyped group—show the greatest benefit of high expectations for success in math? Or should boys—the group with lower achievement—benefit the most from high expectations? We can also ask how gender differences vary by SES. Should these patterns be greater for youth from high-SES families, perhaps because their families have more resources to support their expectations for success in math? Should they be greater among youth from low-SES families, the group at greater statistical risk for less math progress? Do students from underrepresented racial and ethnic groups and low-SES families face additional risks of not progressing in math? For the first time, using a large, nationally-representative sample, we can answer these questions (see Chapter IV).

How Do School Contexts and Classroom Contexts Weaken or Strengthen Mindset Associations?

Mindset × Context Theory has mostly focused on the complementarity between individuals and their contexts to answer questions of whether supportive contexts make for a stronger association between a mindset and an outcome. This framing comes from the experimental history of Mindset × Context, which focused on understanding where a potentially beneficial intervention had its greatest benefits. As a result, Mindset × Context Theory has not examined the corollary of the complementary discussed above—the possibility that in the least-supportive contexts, the harm caused by a negative mindset would be greatest, which is also called an “accumulated disadvantage” or “double-jeopardy” effect. For example, are the achievement-undermining effects of low expectations most pronounced in high-stereotyping contexts? Indeed, as mentioned in Chapter I, a stereotype about a group can be thought of as a cultural expectation about that group's potential to succeed, which might undermine an adolescent's own internalized expectations for success. In the NSLM we focused on students' perceptions of gendered stereotypes in the classroom. Because stereotypes about ability in math tend to be negative for girls (e.g., Miller et al., 2015; Nosek et al., 2009; Zhao et al., 2022), we expected that girls with low expectations for success in math would be most negatively affected by the negative stereotyping environment. We did not have a priori hypotheses about the role of SES in this interaction, but we explored this possibility in accord with our interest in more complex identities (e.g., gender and SES rather than gender or SES).

In summary, if there is an “accumulated disadvantage” or “double-jeopardy” effect, presented by a negative mindset and a negative context, then the association between the mindset and the outcome would be stronger in the most unsupportive contexts. We examined this possibility in Chapters V and VI. Evidence of an accumulated disadvantage effect would widen the aperture of Mindset × Context Theory's predictions.

Outcome: Math Progress From 9th to 10th Grade

Intersectional SES and Gender Identity Groups

This monograph focuses on understanding whether expectations for success in math are a resource that applies equally to adolescents' math progress across student groups and school and classroom contexts. As discussed in prior chapters, stratification in math progress by gender and SES is particularly apparent. We examined the intersectional interplay of gender and SES by separating adolescents into four categories: boys from high-SES families, girls from high-SES families, boys from low-SES families, and girls from low-SES families.

Intersectionality

Investigating gender by SES intersectional groups helps to shed light on inequality in math progress. Figure 4 presents the proportion of adolescents from each group that did not progress in math from 9th to 10th grades, showing large gaps in math progress. Girls from high-SES families progressed in math between 9th and 10th grades at the highest rates; less than 5% of these adolescents were off track. Boys from high-SES families were about twice as likely to be off track in math as girls from high-SES families; still, fewer than 10% of them failed to progress. Among adolescents from low-SES families, about 20% of boys and 13% of girls were off track. Thus, the off-track rate for boys from low-SES families was 300% greater than it was for girls from high-SES families. Within these SES gaps, there are important gender differences to consider, and vice versa. We examined whether these gaps persisted among adolescents with similar expectations in similar educational contexts.

Expectations for Success in High School Math

The main independent variable, mindset, was operationalized as adolescents' expectations for success in math during high school, which they reported early in their 9th-grade year. Note that this variable is different from the expectations questions that are typically asked in sociological research; those items ask about how far in their educational careers students expect to go (e.g., to college, to a Ph.D.). College-going expectations, however, would not necessarily pinpoint students' expectations in math, because students are not fully aware of the importance of the math curriculum for later postsecondary success. Further, our interest here was in students' mindsets about their abilities, in their contexts, which is more closely aligned with the expectations typically measured in expectancy-value theory (Eccles & Wigfield, 2020).

Expectations Item

The NSLM question was written by a panel of psychological advisors to the NSLM to elicit students' expectations for success in the broader context of their academic self-concept and perceptions of math course difficulty: “Thinking about your skills and the difficulty of your classes, how well do you think you'll do in math in high school?” (1 = extremely poorly, 7 = extremely well, M = 5.25, SD = 1.14). Figure 5 shows the overall distribution of expectations for success in math. The majority of adolescents reported that they expected to do somewhat well or very well; very few respondents expected to do extremely poorly and very poorly.

This measure was designed to capture how expectations for success in math differ across adolescents in different contexts, but with a single, easy-to-interpret item that was inspired by a validated instrument used in previous research (Hulleman & Harackiewicz, 2009; “Considering the difficulty of this course and my skills, I think I will do well in this class”). Hulleman and Harackiewicz's item was revised to fit the focus of the present study (1) on math and (2) on assessing expectations about performance in high school math more generally rather than in a particular course. Similar to other validated items of expectancies or self-efficacy (e.g., “How well do you expect to do in math this year?”; Wigfield & Eccles, 2000), our item assessed students' confidence that they would be able to perform a particular academic task successfully (in this case, high school math). The item also asked students to factor their skills and the difficulty of their courses into their responses; this was done to clarify the point of comparison for their judgment, in an attempt to reduce measurement error. Of note, the expectations item did not ask students to compare themselves to other students in their class, because that relative comparison was not core to our conceptualization of expectations for success in math. In addition, this measure of expectations asked students to focus on their success in high school math in particular, which is more relevant to study inequality in math progress, rather than on their aspirations for educational progress in general (e.g., college-going intentions, which are more commonly studied in sociology, Schneider & Stevenson, 1999).

Ninth-Grade Math Level

A key source of stratification in high school math course-taking was whether students took Algebra 1 in 8th or 9th grade, because it determined whether they started high school in Geometry or not. The majority of 9th-grade students begin high school in Algebra 1 or below, but some, often more advantaged students, begin high school in Geometry or above (74% vs. 26%, respectively). Our primary outcome variable was whether adolescents made progress in math, regardless of where they began, but we also considered math level as a moderator. That is, we assessed whether their likelihood of advancing, as well as the relationship between their expectations and advancement, differed by their math position at the start of high school—in Algebra 1 or below versus in Geometry or above.

Covariates

BCF Modeling

All results presented in Chapters IV and V come from one, multi-level BCF model fit, with students nested within schools. All analyses in Chapter VI come from another multi-level BCF model fit, with students nested within teachers. BCF is an established method for approaching causal inferences from nonrandomized variables while also detecting true sources of effect heterogeneity—that is, differences in the predictive effect of a variable across subgroups or contexts—without lending much credence to noise (Hahn et al., 2020; McConnell & Lindner, 2019; Wendling et al., 2018). Therefore, it is well-suited for the present analyses, or perhaps for any test of ecological models of development.

Intersectional Differences in Expectations for Success in High School Math

As a preliminary matter, we started by examining differences in adolescents' expectations for success in math across gender, SES, and race and ethnicity and what factors related to these expectations. Here we refer to Black, Hispanic/Latinx, or Native American students as students from underrepresented groups (URG) to acknowledge the societal inequalities that have historically led groups with these identities to be less represented in advanced math and science. For reasons explained earlier, we did not have the sample size to generalize to multiple specific underrepresented identity groups. Also recall that due to the small sample size of Asian and Middle Eastern students in this study, and the large amount of diversity within that group, we concluded that results comparing Asian and Middle Eastern students to other groups would not be generalizable. Therefore, although Asian and Middle Eastern students are included when analyses are broken down only by gender and SES, they are not included in comparisons among racial and ethnic groups, which is an important limitation in our findings.

Table 6 shows differences in adolescents' expectations for success in high school math by gender, family SES, and race and ethnicity. On average, adolescents from high-SES families reported higher expectations for success in math than those from low-SES families, boys reported higher expectations than girls, and students categorized as non-Hispanic White reported higher expectations than students categorized as URG. Among adolescents from high-SES families, boys had significantly higher expectations than girls, but the expectations for boys and girls from low-SES families were not significantly different (Tables 6a and 6b).

Diving into the different intersectional groups, boys categorized as non-Hispanic White from high-SES families reported significantly higher expectations for success in math than any other group. Girls categorized as URG from low-SES families reported significantly lower expectations for success in math than any other group. The disparity between these two intersectional groups was substantial: about half a standard deviation.

Differences in expectations for success in math were greater by SES than by gender, although gender differences remained. In fact, although mean levels of expectations differed, the distribution of expectations among boys and girls of the same SES group was very similar, as shown in Figure 6. Across all groups, few adolescents reported very low expectations for success in math, but boys and girls from low-SES families reported neutral or low expectations at almost twice the rate as boys and girls from high-SES families did (Figure 6). Interestingly, a similar percentage of girls from high-SES families and boys from low-SES families reported expecting to do “extremely well” in high school math (about 10%). Thus, although SES gaps in expectations were prominent, there were gender dynamics at play that were also important to consider.

Where Did Expectations for Success in Math Come From?

We also explored other factors that might contribute to how students formed their expectations for success in math and what they mean for development. Table 7 displays zero-order correlations between adolescents’ expectations for success in math during the transition to high school and other measures related to their psychological resources in 9th grade.

On average, adolescents who reported feeling that they did not belong in their school, believed intelligence is fixed rather than malleable, and reported higher levels of academic stress reported lower expectations for success in high school math (Table 7). Adolescents who trusted their math teacher and had more interest in math on average reported higher expectations for success in math.

These correlations in Table 7 speak to how adolescents' backgrounds and learning contexts relate to their expectations. If they do not feel like they fit in their school community, do not feel respected by their math teacher, and are stressed by the amount of schoolwork they have to do, then they may have low expectations for their success in high school math. Their beliefs about the malleability of their intelligence and their level of interest in math may even reflect exposure to societal stereotypes about who can be, is, and should be successful in math.

One potentially confounding factor is adolescents' interest in math. This item, among the factors we examined, had the strongest correlation with expectations for success in math. Expectancy-value theory suggests that adolescents' expectations and interest in math are both strong, proximal determinants of their achievement-related decisions and behaviors (Eccles & Wigfield, 2002, 2020). We examined differences in math interest by adolescent groups (Table 8) to understand the role it may play in gaps in math progress. Boys from high-SES families had the most interest in math, and girls from low-SES families had the lowest, similar to the pattern for expectations. Unlike expectations for success in math, math interest did not differ by family background; girls from high- and low-SES families had similar levels of math interest, as did boys from high- and low-SES families. Among adolescents from high-SES families, boys had greater math interest than girls. We did not find the same difference among adolescent boys and girls from low-SES families. Differences in math interest, therefore, were not sufficient to explain disparities in math progress.

Another important factor to consider was adolescents' math position at the start of high school. (We display the distribution of expectations by gender/SES groups and math level in online Supporting Information: Figures 1 and 2). The expectations question, as stated in Chapter III, asked adolescents to consider the difficulty of their courses when determining their expectations for success in math. This could suggest that adolescents in more challenging math courses would report lower expectations for success in math than those in lower-level courses. In fact, we found the opposite. As Table 9 shows, adolescent boys and girls from both high- and low-SES families reported higher expectations for success in math when they started high school in more advanced math courses. Note that adolescents from low-SES families were overrepresented among the students who began math in Algebra 1 or below in 9th grade. Adolescents in Geometry or above may know they are better positioned to succeed in high school math because they are in a more advanced math course than their peers, which signals higher expectations for success in math from the school community. Yet, within 9th-grade course levels, significant differences in expectations for success in math across SES and gender groups remained. Among students in Algebra 1 or below, adolescents from low-SES families reported lower expectations for success in math than those in high-SES families, and girls from low-SES families reported even lower expectations than boys from low-SES families. We found a similar SES pattern among students in Geometry and above, but girls from high-SES families also reported lower expectations than boys from high-SES families, consistent with past studies of high-achieving girls (Riegle-Crumb & Morton, 2017).

How Did Pathways From 9th to 10th Grade Math Differ among Adolescent Boys and Girls From High- and Low-SES Families?

The average progress in math levels across 9th and 10th grades among intersectional groups appears in Table 10. As noted, progress was calculated as the math level in 10th grade minus the math level in 9th grade for most students. Overall, boys from low-SES families have the lowest math progress and girls from high-SES families have the highest. Unlike expectations for success in math, we mainly find significant differences between students from high- and low-SES families and not differences by gender. Online Supporting Information: Table 4 displays these pathways in more detail.

We also examined math progress among boys and girls, high- and low-SES students, and students from non-Hispanic White and URGs to understand the role of all three facets of inequality in math progress (Table 11). On average, students from URGs and students from low-SES families had the lowest progress in math between 9th and 10th grades. However, girls progressed more than boys overall. Girls categorized as non-Hispanic White from high-SES families progressed the most overall, with an average course level increase over 1, which was higher than every other intersectional group. Boys from URGs and low-SES families progressed the least overall, with an average course level change of 0.79, which was lower than every other intersectional group except girls from URGs and low-SES families. On average, high-SES students progressed at least one-course level in math (math progress is close to 1.00), except for boys from URGs. Students from low-SES families are at risk of not progressing in math (math progress is below 0.90), except for girls the in non-Hispanic White group.

These patterns suggest that inequality in course progress operates on multiple levels. Note that although family SES differences in math progress may reflect the SES differences in students' expectations for success in math, the gender patterns did not. Girls had lower expectations than boys, but they, in fact, progressed further in math than boys. These patterns are evidence of a disconnect between expectations for success in math and math progress by gender and SES. They may reflect overconfidence among boys, and they could reflect differences in how boys and girls are treated in school—a topic we return to in our discussion of gender stereotyping in Chapter VI.

In the present chapter, we next examined how math progress differed by math position in 9th grade. As shown in Table 12, the low rates of progress for boys from low-SES families were pronounced in the on-level, but lower, math course of Algebra 1. Those boys advanced just 0.83 levels, significantly lower than every other intersectional identity group. In the more advanced math course—Geometry—boys from low-SES families still progressed at lower rates compared to boys and girls from high-SES families, but girls from low-SES families were similarly likely to progress to the next level than their male peers. Overall, these results suggest that the groups at greatest risk for being off-track are boys from low-SES families in Algebra 1, the on-level class, and girls from low-SES families in the more advanced, Geometry class.

Did Expectations for Success in Math Predict Math Progress in 10th Grade?

Here and throughout, we present the effect of moving from low expectations for success in math (−1 SD) to high expectations (+1 SD) on the outcome of math progress, to match the conventional way of visualizing results for linear interactions (Aiken, 1991). We call this the “average treatment effect” (or ATE) when referring to the population or the “conditional average treatment effect” (or CATE) when referring to a specific group. Of course, expectations for success in math is a measured variable, not a manipulated variable, and so there is no “treatment” in this case, that is, moving from low to high expectations refers to an increase in level of the measured variable, not to an increase in an individual's expectations. We use the ATE and CATE language to follow convention from econometrics and causal inference, because our results reflect the Bayesian Causal Forest (BCF) model's best estimate for the “effect” of expectations, under the assumption that the propensity score adjustment accounts for all potential confounders. Notably, none of our conclusions depend on this strict assumption.

The BCF algorithm found that adolescents' expectations for success in math at the transition to high school were meaningfully related to their math progress overall, average treatment effect (ATE) = 0.10 [0.09, 0.11], pr(ATE > 0) = 0.99, as expected. This coefficient means that a 2 SD difference (i.e., from 1 SD below the mean to 1 SD above the mean) in expectations for success in math is associated with 0.10 math course levels of progress. To make this concrete, this is equivalent to going from an 84% chance of progressing from Algebra 1 to Geometry at 1 SD below the mean of expectations, to a 94% chance at 1 SD above the mean. Thus, this first model confirmed an assumption of this study, which was that expectations for success in math would predict math progress, when controlling for many potential confounding factors in the conservative model with the propensity score adjustment.

Did Expectations for Success in Math Predict Math Progress Differentially Across Gender and SES Groups?

Results across intersectional identity groups appear in Table 13 and Figure 7. These show that among youth with low expectations for success in math (−1 SD; 4.08 on a 7-point scale, neither well nor poorly), there were striking inequalities in math progress. Girls from high-SES families made the most progress (0.94 math levels in a year) and boys from low-SES families made the least (0.76 math levels in a year) (see Figure 7a). This inequality was much smaller (1.00 vs. 0.90, or 56% of the inequality in math progress among adolescents with low expectations) among youth with high expectations for success in math (+1 SD, 5.21 on a 7-point scale, slightly above “somewhat well”), because expectations for success in math predicted math progress more strongly for boys from low-SES families. The boxplot in Figure 7b shows the posterior distribution of the conditional average treatment effects (CATEs), which, as noted, is another way of portraying the magnitude of a regression coefficient for expectations and the uncertainty around it, separately for the four gender by SES intersectional groups.

Boys from low-SES families had the largest expectations effect, which can be seen by noting that the box does not overlap with the box for any other group (Figure 7b) and when noting that the posterior of the difference in CATEs for all groups (vs. low-SES boys) is lower than zero (Figure 7c). Thus, all groups had meaningfully weaker expectations effects than boys from low-SES families. Overall, the identity group of the adolescents who had the strongest relationship between expectations for success in math and math progress was also the most disadvantaged in math progress from 9th to 10th grade.

Did the Main Patterns Differ by 9th-Grade Math Course Level?

About 74% of the sample started in Algebra 1 or below, but this value was confounded with parental education; on average, only about 20% of adolescents from low-SES families took Geometry in 9th grade compared with about 40% of those from high-SES families.

The findings in the subsample of adolescents who started high school in Algebra 1 or below (n = 7,368) were consistent with the full sample (see Figure 8). We next examined the expectations effects among adolescents in Geometry or above in 9th grade (n = 2,603). In this more advanced course, we saw similar results, which can be seen in the BCF results showing essentially the same CATEs for expectations for success in math among Algebra I students and Geometry students (see Figure 8b,c).

Did the Main Patterns Differ by Race or Ethnicity?

Descriptively, we found that SES-based inequalities in math progress among low-expectations youth were greater for students characterized as URG relative to students characterized as non-Hispanic White (Figure 9a). Boys characterized as URG from low-SES families with low expectations for success in math (−1 SD) were far less likely to make progress in math from 9th to 10th grade relative to girls characterized as non-Hispanic White from high-SES families with high expectations (0.70 vs. 1.02). As a result, by a wide margin, the CATE for expectations for success in math was the largest for boys characterized as URG and low-SES families (CATE = 0.15 [0.13, 0.17], pr(CATE > 0) = 0.99), as shown in Figure 9b,c. The difference in CATEs for expectations for success in math between students characterized as URG and students characterized as non-Hispanic White was meaningful for students from low-SES families (all probabilities of a difference in CATEs > 0.90), and not for students from high-SES families (all probabilities of a difference in CATEs < 0.87; see Figure 9c).

In summary, we found that the overall sample patterns held for students categorized as URG and students categorized as non-Hispanic White, in that boys from low-SES families were the lowest-performing group and showed the largest expectations effect. The magnitudes of these gendered patterns of socioeconomic disparities, however, were greater among students characterized as URG.

Formal Resources: School Achievement Level

The school achievement level variable was developed when constructing the sampling plan for the NSLM to ensure academic diversity among the schools (Tipton et al., 2019). It was estimated as a latent variable indicated by GreatSchools.org ratings and College Board data (including mean PSAT scores, AP Mathematics, and English participation), as well as state 8th-grade proficiency levels from National Assessment of Educational Progress (NAEP). Combining these data sources, the school sampling statisticians used a structural equation model to estimate a latent school achievement variable. Based on this variable and the associated loadings, a school achievement value was estimated for each school and then standardized nationally across the approximately 12,000 regular U.S. public high schools. The resulting nationally z-scored variable was then used in the sampling frame to select schools. School achievement was divided into three strata based on the 25th and 75th percentiles, corresponding to categories of low-, medium-, and high-achieving schools. We fit the BCF model using the full, continuous measure of achievement, which was allowed to have a nonlinear moderating effect. When summarizing the posterior distribution, we followed the preregistration by Yeager and colleagues (2019) in comparing higher-achieving schools (the top 25%) to all other schools (the bottom 75%).

Informal Resources: School Peer Challenge-Seeking Norms

School peer challenge-seeking norms were measured with the “Make a Worksheet” task implemented in the student survey (see Rege et al., 2020 for validation). Students were asked to create a math worksheet they would like to work on based on their current math course. They were given sets of problems from four math chapters and were asked to choose at least two from each chapter. The problems on the worksheet were labeled, “Not very challenging and you probably won't learn a lot;” “Somewhat challenging and you might learn a medium amount;” and “Very challenging but you might learn a lot.” Students were told not to work on the problems when selecting them, but that they would have the opportunity to complete them if there was time. As in the analysis by Yeager and colleagues (2019), we calculated for each school the average number of hard problems the students selected, which corresponded to selecting the “very challenging but you might learn a lot” option on the worksheet. We fit the BCF model using the full, continuous measure of norms, which was allowed to have a nonlinear moderating effect. When summarizing the posterior distribution, we used the cut-point in norms from Yeager and colleagues (2019) to summarize the results (at the median, or 2.95 hard problems out of 8).

Categories of Schools Based on School Formal and Informal Resources

Using these two aspects of peer context, we placed the 56 schools into four categories: low/medium-achieving/low challenge-seeking (27 schools; low formal and informal resources), low/medium-achieving/high challenge-seeking (12 schools; low formal, high informal resources), high-achieving/low challenge-seeking (six schools; high formal, low informal resources), and high-achieving/high challenge-seeking (11 schools; high formal and informal resources).

Table 14 describes the four school contexts and their characteristics related to school quality and challenge-seeking norms. Overall, the patterns of these descriptive statistics matched expectations and pointed to the validity of the categorization scheme. As expected, the four groups of schools differed in terms of characteristics that suggest different levels of formal and informal resources to support students' expectations. Table 14 also shows school characteristics related to SES and the proportion of Black and Hispanic/Latinx students across the four peer contexts. Students in lower-achieving/low challenge-seeking schools had, on average, mothers who had attained an associate degree, while students in lower-achieving/high challenge-seeking schools had, on average, mothers who were slightly more educated but had not received a bachelor's degree. In higher-achieving schools, students' mothers, on average, had completed at least a bachelor's degree. Further, low/medium-achieving/low challenge-seeking schools had the highest rates of students receiving free and reduced-price lunch (43%) and of students from families in poverty (19%). In higher-achieving/high challenging-seeking school, on average, 20% of the students received free or reduced-price lunch and 14% were living below the poverty level. Low/medium-achieving/schools had a similar proportion of students from URG regardless of their peer norms, as did both types of higher-achieving schools.

Overall, schools' achievement levels were related to socioeconomic measures, but challenge-seeking norms did not have a clear relationship to the socioeconomic characteristics we examined. In addition, a school's formal resources (e.g., achievement level) were related to racial/ethnic composition, but the informal resources (e.g., norms) were not. These results suggest structural differences in access to schools with higher-achieving peers, while access to schools with more learning-and-challenge-oriented peers may be more equitable.

Turning our attention to course characteristics, we saw that, on average, students across the four school types were similar in their math course-taking in 9th and 10th grade. Across all peer contexts, on average, students tended to be in a class slightly above Algebra in 9th grade, and they tended to be in Geometry in the 10th grade. Yet when considering the proportion of students in Geometry or higher in 9th grade, we saw that the high challenge-seeking contexts enrolled about 30% of students in Geometry or above compared to the low challenge-seeking contexts, which had about 25% of their students in Geometry or higher. Within each context, the proportion of schools offering an AP course was similar. But all higher-achieving/high challenge-seeking schools offered an AP math course, while only about half the schools in each of the other peer contexts did so. Thus, the four school contexts we examined presented students with different types of peers and opportunities to take math courses. In particular, higher-achieving/high challenge-seeking schools provided many opportunities that might help even low-expectations students to make progress in math (which could attenuate expectations effects).

Table 15 presents descriptive statistics that reveal the characteristics of the students in the four kinds of peer contexts. As expected, high-achieving schools had more students from high-SES families, and low/medium-achieving schools had more students from low-SES families. Still, within each kind of school there was enough variability in student SES to test the present hypotheses.

Did Expectations for Success in Math and Math Progress Differ by School Context?

As a preliminary matter, we asked how students' expectations for success in math and math progress differed by school context. We considered the means and standard deviations of expectations for success in math and 10th-grade math progress by students' gender and SES in each kind of school context. As Table 16 shows, boys and girls from high-SES families and boys from low-SES families were similar in their expectations for success in math across the four different peer contexts. An intersectional difference emerged, however. In low/medium-achieving and low challenging-seeking schools—that is, schools with the poorest outcomes overall—girls from low-SES families had significantly lower expectations for success in math than they did in high-achieving, more supportive contexts.

Turning to the focal math progress variable, adolescents from low/medium-achieving- low challenge-seeking schools generally tended to progress less compared to their peers in other contexts. This finding is not surprising because these schools have the fewest formal and informal resources. Next, math progress differed by gender and SES identity groups across school types, as shown in Table 16. In general, students made the most progress in math, and showed relatively small intersectional disparities, in high-achieving schools.

The group with the lowest rate of math progress in this sample was boys from low-SES families in the least supportive schools, which were schools that were low/medium-achieving (the bottom 75%) with low challenge-seeking norms (see column 5 of Table 16). In those schools, the disparities between boys from low-SES families and students from high-SES families of either gender were strikingly large. Higher challenge-seeking norms, however, were associated with greater math progress overall and also reduced disparities between boys from low-SES families and their higher-SES peers (column 6 of Table 16). Interestingly, math progress for girls from low-SES families was not greater when challenge-seeking peer norms were greater (see Table 16). Overall, boys from low-SES families in low/medium-achieving schools had the greatest risk for inadequate progress in math. Positive peer norms, however, seemed to support that group of boys.

How Does the Association Between Expectations for Success in Math and Math Progress Differ Across Student Intersectional Identity Groups and School Contexts?

The same multilevel BCF model fit that was summarized in Chapter IV also included the context-level moderators described here in Chapter V (also see the 2019 analysis by Yeager and colleagues of school achievement level in this dataset). Expected values of math progress, by expectations level, intersectional identity group, and school type are presented in Table 17.

Considering the gendered pattern of socioeconomic differences in CATEs across schools, we found that the CATE for expectations for success in math was greatest for boys from low-SES families when they were in low/medium-achieving schools (CATE = 0.15 [0.13, 0.16], pr(CATE > 0) = 0.99), and the CATE was weakest for girls from high-SES families in schools with high challenge-seeking norms (CATE = 0.04 [0.02, 0.06], pr(CATE > 0) = 0.99). The posterior probability that the Expectations × School achievement × Challenge-seeking norms interaction was different for boys from low-SES families and girls from high-SES families was 0.98, suggesting strong evidence for an intersectional difference in the moderating effects of school contexts.

Looking closer at the different groups, we found that many of the results were consistent with the compensatory hypothesis. Adolescents from the intersectional identity group with highest average math progress and in schools with the best formal and informal resources showed the weakest effects of expectations for success in math (girls from high-SES families in high achieving, high norms schools); for that group of adolescents, if they had low expectations, they still tended to make progress in math at high rates (see Table 17). Thus, the informal and formal resources in the school context appeared to compensate for low levels of the psychological resource of expectations for success in math. In fact, girls from high-SES families with low expectations in high-achievement, high challenge-seeking schools made more progress in math (0.96) than boys from low-SES families with high expectations in low/medium-achieving, low norms schools (0.87, see Table 17).

The results were also consistent with the accumulated disadvantage (or negative complementarity) hypothesis (see Table 17). This is the hypothesis that the negative effect of low expectations will be the most striking in the most unsupportive contexts. Overall, the math progress rates for students with low expectations for success in math were the weakest in low/medium achieving schools with low peer norms (0.80). As a result, the CATE for expectations was stronger in low/medium achieving schools with low peer norms than it was in high-achieving schools with strong peer norms (posterior probability that overall difference in CATEs > 0 = 0.99). This finding was consistent across intersectional identity groups (see Figure 10c).

We saw a few notable differences in these overall patterns across intersectional gender and SES identity groups. Only girls from high-SES families, and not any other group, showed a compensatory effect for peer norms in low/medium-achieving schools. In low/medium-achieving schools, low-expectations girls from high-SES families profited from a positive peer norm, lifting their outcomes to a level that was comparable to girls from that group in high-achieving schools. For all other intersectional identity groups, norms were compensatory (i.e., reduced the CATE for expectations) only in high-achieving schools (probability of a five-way interaction for differences in CATEs = 0.65).

Another way to describe the findings is that there was moderate evidence for an interactive effect of the school's achievement level and challenge-seeking norms on the compensatory effect for all groups except girls from high-SES families. Looking at Figure 10b, we see that the moderating effect of a school's achievement level on the magnitude of the CATE for expectations was apparent only when it was paired with higher norms (except for girls from high-SES families).

Analytic Subsample

The subsample for these analyses consists of 6,856 adolescents nested within 229 math teachers (see Table 1 in Chapter III for more details). The sample is smaller than the sample used in the previous two chapters because we could only include students who were matched with teachers and for whom there were student ratings of perceived stereotyping. Adolescents with multiple math teachers in this semester were paired with only a single teacher on the basis of which teacher taught the highest-level math class. We assumed that adolescents' experiences in their highest-level math classes would be more relevant to their progress in math the following year than their experiences in lower-level math classes would be. Adolescents were excluded from the sample if they had multiple teachers at the same math level who had completed the survey. (If these adolescents had been included in the sample, we could not have determined in which math classroom they were perceiving gendered stereotyping.) Finally, as with the sample in the previous two chapters, adolescents were excluded from the sample if they were missing an observation for the outcome or if they took a math course higher than Geometry in 9th grade (except in schools where it was normative for students to take Algebra 2 prior to Geometry, in which case students taking Algebra 2 were retained in the sample). Analyses in Chapter III found that the subsample for these analyses did not differ meaningfully along key demographic characteristics relative to the sample included in the previous two analytic chapters.

Measurement

Again, the dependent variable was adolescents' progress in math between 9th and 10th grades. Independent variables included adolescents' expectations for success in math, gender, SES, race and ethnicity, and 8th-grade GPA. For perceived stereotyping in the classroom, adolescents responded to the question, “In math class, how much do you worry that people's judgments of you will be affected by your gender?” on a five-point Likert scale ranging from “not at all” to “an extreme amount.” Unfortunately, the NSLM did not include a similar question about perceived stereotyping by SES.

Descriptive Statistics

Overall, perceptions of classroom stereotyping were low (M = 1.62, SD = 1.00). One-third of adolescents, however, reported a level of perceived stereotyping greater than zero. This is practically significant because any level of perceived stereotyping may impact students as they progress through high school math.

To examine whether perceived gender stereotyping differed by student characteristics, in a preliminary analysis we regressed perceived gender stereotyping on gender and SES in a multilevel model with a random intercept for teacher. Perceived gender stereotyping was somewhat greater among students from low-SES families (M = 1.65, SD = 1.00) than students from high-SES families (M = 1.57, SD = 0.99), although this difference was not very large (b = −0.07, t = −1.77, p = .077). We did not find an interaction between gender and SES on perceived stereotyping, (b = 0.04, t = 0.537, p = .591) and perceived gender stereotyping did not significantly differ by gender (b = −0.02, t = −0.60, p = .547). While this may seem surprising, gendered stereotypes about who is better at math (which preference boys) and who is better in school in general (which preference girls) are potentially both present in math classrooms (Heyder & Kessels, 2017; Riegle-Cumb & Peng, 2021).

Classroom-Level Variation in the Association between Expectations for Success in Math and 10th-Grade Math Progress

For the present chapter, we fit a new BCF model that nested students within teachers. We summarized the posterior distribution of the BCF model fit to examine whether the association between expectations for success in math and 10th-grade math progress varied significantly between classrooms. We tested whether the association between expectations for success in math and 10th-grade math progress varied across local intersectional identity groups (i.e., clusters of demographic groups at the intersection of gender and SES within teachers' course sections (see Walton et al., in press) (N_CLUSTERS = 793; M_{STUDENTS/CLUSTER} = 14.63, Mdn_{STUDENTS/CLUSTER} = 12; Figure 11). We provide more details in the online Supporting Information. For the reasons discussed in Chapter III, we did not test for racial or ethnic variability in the association between expectations for success in math and math progress: There was low racial/ethnic diversity within schools and within SES categories.

We found substantial variability in the association between expectations for success in math and math progress across intersectional identity groups. In a null random intercept model, the standard deviation of the association across intersectional identity groups was 0.03, which was nearly half (49%) of the average association within this analytic sample (0.06). Variability in the association between expectations for success in math and math progress across intersectional identity groups, estimated in BCF, is displayed in Figure 12.

These results indicate that although adolescents' expectations for success in math were an important predictor of their math progress on average, the association between expectations and 10th-grade math progress differed meaningfully across classrooms and intersectional identity groups. From a broad perspective, these findings suggested that to understand the role of adolescents' expectations in their course-taking trajectories in math, we must also assess how these expectations interacted with their classroom contexts. In the following analyses, we examined how one predictor in particular—perceived gender stereotyping in the classroom—moderated the relation between adolescents' expectations for success in math and their subsequent progress in math. We attended to differences by adolescent gender and SES.

The Role of Perceived Gender Stereotyping Within the Math Classroom

The focal context-level moderator in this chapter was perceived classroom gender stereotyping. Because stereotyping could be perceived differently by different groups in the same classroom, we averaged the adolescent-level measure of perceived stereotyping to the intersectional identity group level (i.e., all boys from low-SES families within the same teacher's class contributed to a single mean for that intersectional identity group). Results for this variable therefore represent the role of a particular demographic group's average experience of stereotyping within a given classroom. Predicted values, CATEs for expectations, and differences in CATEs between classes with high versus low perceived stereotyping are presented in Table 18.

First, we found that classroom stereotyping was associated with lower rates of math progress for each subgroup, on average (see Figure 13a). In addition, stereotyping moderated the association between expectations for success in math and math progress. Among boys from low-SES families, girls from low-SES families, and girls from high-SES families, the association between expectations for success in math and math progress was stronger in classrooms with higher perceived gender stereotyping than classrooms with lower perceived gender stereotyping (probability of a difference in CATEs between classes with high vs. low perceived stereotyping >0.94 for each of these three subgroups; see Figure 13b,c). This pattern suggests that high expectations for success in math helped to buffer these groups of students against the negative effects of perceived gender stereotyping (see Figure 13a). Interestingly, this pattern of moderation did not emerge for boys from high-SES families (probability of a difference in CATEs between classes with high vs. low perceived stereotyping = 0.62). That is, perceived stereotyping did not seem to negatively affect math progress more among boys from high-SES families with low expectations than those with high expectations. This finding may reflect that boys from high-SES families are not typically subjected to negative stereotypes about their math ability.

Another way to understand the role of perceived stereotyping is to examine how this classroom factor contributed to math progress as compared to structural markers of disadvantage (e.g., socioeconomic status). For example, when girls from high-SES families (i.e., the group with the highest rates of math progress overall) had low expectations for success in math and experienced classrooms with high levels of perceived gender stereotyping, they showed rates of math progress (0.82 math levels) that were as low as those of boys from low-SES families (i.e., the group with the lowest rates of math progress overall) with low expectations for success in classrooms with low levels of perceived gender stereotyping (0.80 math levels). Thus, girls from high-SES were meaningfully held back by low expectations for success in math if they encountered a classroom in which they perceived a high degree of stereotyping, despite other perceived advantages in school overall (as shown in Chapter IV). That is, even among the demographic group with the highest base rate of math progress, experiencing gender stereotyping while holding low expectations for success substantially reduced the likelihood of making progress in math from 9th to 10th grade.

Three Key Findings

First, we learned that boys from low-SES families were most at risk of not progressing in math early in high school, but that their expectations for success in math were more predictive of math progress than for any other gender-by-SES group. This finding is consistent with the first tenet of Mindset × Context Theory. It also contributes to the literature on gender stereotyping and its effects on students' educational outcomes. Although girls are subject to anti-female stereotypes in math (e.g., Spencer et al., 1999; Zhao et al., 2022), they did not show the lowest progress in this domain. It was boys—and particularly boys from low-SES families—who did, perhaps due to a perceived conflict between school and anti-intellectual masculine norms (e.g., Hartley & Sutton, 2013; Heyder & Kessels, 2017).

What is notable about this finding is that, although antifemale stereotypes in STEM have been the target of sustained research in developmental psychology for decades, there is much less work on the factors holding back boys from achieving their full potential in school. Our evidence suggests that factors limiting boys' progress are potentially powerful, especially when combined with the structural obstacles that students from low-SES families often encounter. With respect to policymaking, this monograph documents an important developmental antecedent to the later, striking absence of boys from low-SES families from higher education: failure to make progress in math from 9th to 10th grade. Therefore, the monograph highlights a key lever for future policies to consider targeting, perhaps through additional programs or curricular reforms that support boys from low-SES families with low expectations for success in math at this critical juncture.

Second, we learned that different school contexts powerfully moderated the link between expectations for success in math and math progress. For all gender and SES intersectional identity groups, the schools with the lowest levels of formal and informal resources (low/medium-achieving schools with unsupportive peer norms) showed a much stronger link between expectations and math progress, relative to schools with the most formal and informal resources (high-achieving schools with supportive peer norms; see Figure 10) As such, the group with the lowest level of math progress was the intersectional identity group at greatest risk (boys from low-SES families with low expectations) in the least-advantaged schools; this group made just 75% of the math progress of students from high-SES families with high-expectations in the most-advantaged schools (Table 17).

One likely reason for this second finding was that low-expectations youth in the most supportive school contexts made progress despite their low expectations. This finding is consistent with a compensatory interaction (Miller et al., 2014), in which the resources in a school context appeared to compensate for reduced levels of individual-level psychological resources (i.e., expectations for success). Overall, this second finding yielded mixed evidence with respect to the Mindset × Context Theory predictions. On the one hand, the mindset of high expectations was less essential for students’ progress in schools that already had abundant resources, formal and informal, to support math progress, which is consistent with the findings in a previous test of Mindset × Context Theory (Yeager et al., 2019). On the other hand, we did not find that the school's informal resource of peer challenge-seeking norms universally led to a stronger link between expectations for success in math and math progress, which is different from a previous test of Mindset × Context Theory (Yeager et al., 2019). Here, the informal resource of positive, challenge-seeking peer norms appeared to have a compensatory effect—aiding low-expectations youth on the path to math progress—although there were some higher-order interactions in this result across intersectional gender and SES identity groups (see Figure 10).

These findings also contribute an important insight to the psychological literature on expectations and their effects on student achievement. Although expectations reside in an individual's mind, like any psychological variable, their effects come about as a function of how the individual interacts with the opportunities available to them in their broader context (or lack thereof). This insight seems basic, but it is not consistently reflected in most research on the role of mindsets in achievement to date, which tends to measure expectations and achievement while paying less attention to the contexts that students find themselves in as a potential moderator of the relation between these variables. The substantial heterogeneity we observed across contexts (e.g., high- vs. low-resourced schools) in the relation between expectations and progress in math suggests that developmental psychologists who study expectations for success as part of students' motivational frameworks could gain new insights by better incorporating contexts into their studies. In addition, these results provide a solid foundation for future psychological theorizing about how contexts shape the relation between expectations and achievement.

Third, we learned that perceived gender stereotyping in the classroom mattered for the strength of the expectations effects on math progress, but not for boys from high-SES families. We analyzed students' perceptions that others held gender-biased judgments about math ability, which potentially include the common stereotype that boys are more “naturally” gifted than girls and that girls can achieve in math only with high levels of effort. We suspect that these perceived gender stereotypes may have contributed to the overall differences in expectations for success in math in the NSLM—namely, that boys expected to do better in math in high school than girls, even though girls, in truth, were making more progress. The results for the moderating role of stereotyping were generally consistent with an accumulated disadvantage pattern of interaction: groups that perceived negative stereotypes about their math abilities (girls and students from low-SES families), and had low expectations for success in math, were the most likely to have their performance suppressed by the gender stereotyping in the classroom (Figure 13). Although we did not explicitly measure stereotypes related to family background, it may be that gender stereotypes differ for students from low- and high-SES families. Interestingly, the “main effect” of stereotyping extended across the intersectional identity groups, even for boys from high-SES families. Thus, although a classroom with high perceived stereotyping did not magnify the expectations effect for boys from high-SES families, it was nevertheless associated with poorer performance. One reason why is that boys may perceive working hard in math as “girly” (Hartley & Sutton, 2013; Heyder & Kessels, 2017), or they may also be hurt by positive gender stereotypes because the stereotypes assume a “natural” ability in math to which boys may struggle to live up.

This third finding broadens the aperture for Mindset × Context Theory. Most importantly, it includes a performance-suppressing contextual factor—perceived stereotyping—which is different from the potentially performance-enhancing contextual factors in previous studies (school formal and informal resources; Yeager et al., 2019). We found that, in the presence of this negative contextual factor of perceived gender stereotyping, the possible harm coming from a lack of expectations was greater, but the potential benefit of high expectations was not necessarily enhanced. Students in every intersectional identity group had the highest math progress when they had high expectations and were in classrooms with low perceived stereotyping (Table 18). This finding advances theory by showing that, although mindsets can be a partial source of resilience against harmful contexts, adolescents do far better when they have both the internal psychological resource of a positive mindset and the contextual resource of a classroom free from gender stereotyping.

For developmental psychologists, these findings also serve as a useful reminder that stereotypes can be harmful even if they are not personally endorsed by the students. The bulk of the developmental literature on gender stereotypes and their relation to student achievement measures students' own endorsement of a particular stereotype (e.g., “math = boys”) (Cvencek et al., 2011) and then looks for relations between students' endorsement of said stereotype and their achievement, aspirations, and so on. Although personal endorsement is undoubtedly one way in which societal stereotypes suppress the educational outcomes of negatively stereotyped groups (Master et al., 2021), stereotypes reified by students' educational contexts (Steele, 1997) are probably at least as powerful, as our monograph makes clear. More research on the relation between gender and racial and ethnic stereotypes and students' achievement in K-12 education should focus on how contextual stereotypes shape educational outcomes.

Implications of These Findings

Study Limitations and Future Directions

Several limitations to this study qualify the strength of the three findings we have highlighted and the take-away messages we have suggested. One key limitation is that our sample was not adequate for understanding racial or ethnic differences in our primary results, which examined cross-school moderation, despite the comparatively large sample size in this research. Therefore, we cannot speak to the complex ways in which racial- and ethnic-based inequality may interact with school informal and formal resources to shape gendered patterns of socioeconomic inequality. Because of the overlap of racial and ethnic and socioeconomic stratification in the United States, young people of color in the United States are more likely to come from socioeconomically disadvantaged circumstances. Yet, because processes of racial and ethnic stratification (e.g., interpersonal discrimination, institutional racism) persist above and beyond socioeconomic stratification, students of color also are less likely to have or be able to capitalize on opportunities for enrollment in advantaged schools and classrooms, even when they are not from socioeconomically disadvantaged circumstances (Kohli et al., 2017; Lewis & Diamond, 2015). Capturing the multiple levels through which structural and interpersonal racism can thwart the expectations of youth from historically underrepresented racial/ethnic groups is critical.

A second limitation is that adolescents' expectations for success in math were measured at high school entry and not before, some adolescents may have already adjusted their expectations during the first few months of high school in relation to their context. If we were to capture expectations before high school entry, we may find even more gaps in adolescents' abilities to translate their expectations for success in math into positive high school math progress. A third limitation is that our measure of expectations was observational, not experimental. Although we included many factors that were related to expectations for success in math (e.g., math interest, math course level in 9th grade, race/ethnicity, and 8th-grade GPA) in the propensity score adjustment that BCF used to address confounding, any causal claim about the link between expectations for success in math and math progress depends on a strict assumption that no additional unmeasured confounders existed, and we cannot confirm this assumption. A fourth limitation is that, although the NSLM measure of peer challenge-seeking norms has been validated by other studies (Rege et al., 2020; Yeager et al., 2019), it is a proxy for peer motivation and engagement in the classroom and school and will have measurement error, like any proxy. For example, students who selected challenging problems for the hypothetical math worksheet task may not have asked for extra work or selected hard problems within their classroom context, and students who regularly challenge themselves in the classroom may not have selected challenging problems for this specific task. A final limitation is that the NSLM measure of perceived classroom gender-based stereotyping did not have a corollary for socioeconomic stereotyping.

These limitations, while not negligible, were also balanced by the many strengths of this study. First, we used the most recent nationally representative sample of 9th graders' mindsets, linked to their administrative outcomes. This allowed us to make generalizable claims about how a psychological variable—expectations for success in math—was related to an outcome of direct policy relevance—math progress. Furthermore, our study was innovative in that it used an interdisciplinary perspective— Mindset × Context Theory—to examine how a mindset variable interacted with multiple moderating factors that have a theoretical basis in the sociological literature—the school's formal resources (achievement level) and informal resources (peer norms, perceived classroom gender stereotyping). We conducted this examination by implementing a state-of-the-art machine-learning algorithm, Bayesian Causal Forest. Using this method, we could interrogate higher-order interactions without raising the possibility of false-positive results that could emerge from fitting dozens of linear models. This method is an advance beyond the common practice in frequentist analysis, and it means that our complex findings are nevertheless trustworthy and serve as a credible basis for building future theory and empirical research.

With both limitations and strengths in mind, this monograph also lays a foundation for future studies. For example, the methods employed here could be used to test whether other mindsets—for instance, about belonging (Walton & Cohen, 2007), relevance (Hulleman & Harackiewicz, 2009), purpose (Yeager et al., 2014), or stress (Crum et al., 2013)—show a similar pattern of results as the present expectations variable. Further, other dimensions of classroom culture—such as a teacher's level of academic press, clarification support, or even relationships of respect (Ferguson & Danielson, 2015)—could be examined in a manner that is similar to the present analysis of perceived stereotyping. The NSLM would be well-suited for all of these analyses, because of its inclusion of rich measures of these student mindsets and classroom context factors and others like them (Yeager et al., 2019).

One particularly exciting extension of the present research will come from the longer-term data from the NSLM that will soon be made publicly available. The schools in the NSLM have been recontacted and re-recruited, and data on high school course-taking and graduation, as well as rich data on college enrollment and voter turnout have been merged. When these data become available to the public, future researchers will be able to examine how different mindsets, at the critical point of the transition to high school, can set young people up for alternate trajectories into adult education and civic participation.

Conclusion

The stakes for building a fair and equitable workforce and society are high, which is why it will be important to build on the foundational research presented here in the coming years. If seemingly small differences in expectations for success in math early in high school—net of actual grades, preparation, and interest in math—can powerfully predict math progress, which is a strong predictor of eventual high school graduation and college matriculation, then developing knowledge of how to either improve expectations or create supportive school structures that help students overcome low expectations could play a meaningful role in making adolescents' transition to adulthood more just and inclusive.