Journal of Youth and Adolescence (2022) 51:984 – 1001 https://doi.org/10.1007/s10964-022-01587-4 E M P I R I C A L R E S E A R C H Racial Stereotype Endorsement, Academic Engagement, Mindset, and Performance among Black and White American Adolescents Ming-Te Wang 1 ● Daphne A. Henry 2 ● Wei Wu 3 ● Juan Del Toro 1 ● James P. Huguley 1 Received: 16 November 2021 / Accepted: 18 February 2022 / Published online: 4 April 2022 © The Author(s), under exclusive licence to Springer Science + Business Media, LLC, part of Springer Nature 2022 Abstract The role of racial stereotypes in youth ’ s academic achievement becomes salient during adolescence. Yet, very few studies have investigated whether associations between Black and White American adolescents ’ stereotype endorsement and their cognitive engagement, mindset beliefs, and performance in math differed by stereotype valence (i.e., positive versus negative) and youth gender. To address these gaps, this 3-year longitudinal study ( n = 2546; age range = 11 – 16; 50% males, 60% White, 40% Black; 57% quali fi ed for free lunch) investigated (a) whether Black and White American adolescents ’ endorsement of positive and negative racial stereotypes differentially related to their cognitive engagement, ability mindset, and math performance and (b) whether gender moderated these relations. The results revealed that endorsing either negative or positive racial stereotypes (as opposed to those with unbiased beliefs) was linked to lower cognitive engagement and stronger fi xed mindsets in math 1 year after, while endorsing negative racial stereotypes was linked to lower math scores. In addition, the intersection of adolescents ’ race and gender moderated some of the observed effects. The inverse link between negative stereotype endorsement and math cognitive engagement was signi fi cant for Black girls but not for Black boys. The positive link between negative stereotype endorsement and fi xed math ability mindset was stronger for Black girls than Black boys, whereas the link was stronger for White boys than White girls. These fi ndings shed light on the direction and strength of the links between racial stereotype valence and math outcomes among Black and White youth. Keywords Racial stereotype ● Student engagement ● Growth mindset ● Math learning ● Academic achievement Introduction Active engagement (i.e., investment and willingness to put forth effort in learning activities) and growth mindsets (i.e., an individual ’ s underlying beliefs about academic ability) are critical socio-cognitive processes that contribute to adolescents ’ math learning (Wang, Zepeda, Qin, Del Toro, & Binning, 2021). Adolescence is also a critical period for the development of values and attitudes toward math achievement, and these beliefs have long-term con- sequences for educational success (Wang, Binning, Del Toro, Qin, & Zepeda, 2020). In particular, adolescents are increasingly aware of racialized expectations regarding who can be successful and competent in math. When these ste- reotypes are ascribed to adolescents, they may internalize and eventually endorse them (Cvencek, Nasir, O ’ Connor, Wischnia, & Meltzoff, 2014). Although researchers have illustrated that domain- speci fi c racial stereotypes uniquely mediate adolescents ’ performance in those domains (Riegle ‐ Crumb, Moore, & Ramos ‐ Wada, 2011), little work has focused on socio- cognitive factors in math learning, such as cognitive engagement and growth mindsets. In addition, Devine (1989) emphasized the importance of differentiating ste- reotype awareness (i.e., automatic and involuntary) from stereotype endorsement (i.e., controlled and mostly volun- tary). Drawing upon this distinction, empirical literature has These authors contributed equally: Daphne A. Henry, Wei Wu, Juan Del Toro These authors jointly supervised this work: Daphne A. Henry, Wei Wu, Juan Del Toro * Ming-Te Wang mtwang@pitt.edu 1 University of Pittsburgh, 230 South Bouquet Street, Pittsburgh, PA 15213, USA 2 Boston College, Chestnut Hill, Boston, MA, USA 3 Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA 1234567890();,: 1234567890();,: focused on implicit stereotype threat or awareness (Nasir, McKinney de Royston, O ’ Connor, & Wischnia, 2016); yet, little attention has been given to the socio-cognitive pro- cesses behind stereotype endorsement. Furthermore, the extant literature examining consequences of stereotype endorsement has been primarily cross-sectional with an emphasis on negative stereotypes about Black adolescents. As such, it is unclear whether Black and White adolescents experience different academic outcomes following their endorsement of stereotypes and whether these outcomes vary by the stereotype ’ s valence. To address these limita- tions, this study investigated whether associations between Black and White American adolescents ’ stereotype endor- sement and their cognitive engagement, mindset beliefs, and performance in math differed by the valence of stereotype (i.e., positive and negative versus unbiased beliefs) and youth gender by using longitudinal data that followed Black and White American adolescents over 3 years during sec- ondary school (i.e., ages 11 – 16). Stereotype Endorsement and Academic Achievement during Adolescence Stereotype endorsement is de fi ned as a conscious belief that an individual ’ s abilities or attributes are based on their social group membership or social identity (Devine, 1989). Ste- reotypes operate along a spectrum, meaning that the content of an individual ’ s stereotype endorsement can range from negative stereotypes (e.g., Black students are more acade- mically incompetent relative to their White peers) to positive stereotypes (e.g., Black students are more academically competent in school relative to their White peers). Individuals may also hold unbiased beliefs about race and academic achievement, in which case they would endorse the idea that both Blacks and Whites perform comparably in school. Wang et al. (2019) integrative development-in- sociocultural-context model offers speci fi c socio-cognitive explanations for how youth ’ s stereotype endorsement can affect their academic performance. According to this model, youth ’ s attributions and responses to stress shape their behaviors and attitudes within and across developmental contexts. For instance, a youth who is frequently exposed to discrimination and prejudice may develop habitual response patterns that become ingrained in their coping responses. Because the nature of academic stereotypes is to erro- neously assume that intelligence is inherent rather than earned through effort, the endorsement of any racial ste- reotype, regardless of content, devalues Black students ’ struggles and successes and contributes to a fi xed math mindset (Wang et al. ’ s (2019)). In situations when adoles- cents seek to either disprove negative stereotypes or prove positive stereotypes, stereotype endorsement can result in self-handicapping while hyper-vigilance may diminish socio-cognitive practices (Schmader, Johns, & Forbes, 2008). As a result, both positive and negative stereotype endorse- ment re fl ect inherent beliefs about ability and the nature of intelligence that can discourage growth mindsets and under- mine cognitive engagement and performance (Pennington, Heim, Levy, & Larkin, 2016; Wang et al., 2019). Identity-based motivation theories further posit that an individual ’ s regard for their own social group in fl uences their self-concept (Oyserman & Destin, 2010). In math classrooms where stereotypes are pervasive, stereotype endorsement may have a substantial impact on adolescents ’ beliefs about their competence and achievement in math (Kurtz ‐ Costes, et al., 2007). Social identities also shape students ’ engagement in a speci fi c academic domain based on their perceptions of whe- ther their social group is accepted and competent in that domain (Eccles, 2009). For example, the presence of a dis- proportionately White, male STEM workforce in America may cue Black and female students to think that their social identity is unvalued and unaccepted in STEM professions (Oyserman & Destin, 2010). In addition, students ’ knowledge and endorsement of math ability stereotypes may become more prominent in adolescence due to an increased differentiation of math performance during secondary school (Copping et al., 2013). For this reason, negative stereotypes about historically stigmatized groups ’ math performance may prime them to perceive greater dif fi culty when engaging in math-related coursework, in fl uence their perception that math is “ not for people like me, ” and ultimately result in disengagement and underperformance in math (Oyserman & Destin, 2010). The integrative development-in-sociocultural-context model posits that the valence of academic stereotypes may be less important than the endorsement or attribution of said stereotypes (Wang et al., 2019). Nevertheless, the stereotype threat literature has suggested that valence may indeed play a role in how stereotypes in fl uence academic performance. For instance, it is a frequently endorsed American stereotype that Black adolescents have lower math abilities than their White counterparts (Burnett et al., 2020; Rowley, Mistry, & Feagins, 2007). This stereotype undermines Black adolescents ’ cognitive fl exibility, atten- tion, and persistence when working on math tasks (Pen- nington et al., 2016). Conversely, the stereotype boost literature has suggested that the endorsement of positive racial stereotypes about academic abilities are bene fi cial for Black American students ’ academic performance (Walton & Cohen, 2003). For instance, positive stereotypes about academic ability may promote racial minority students ’ self- perceptions through self-enhancement processes (Rowley et al., 2013). Studies have also found that individuals from social groups that are negatively stereotyped in a domain show greater cognitive fl exibility and improved academic performance when they think about counter-stereotypes (Goc ł owska et al., 2013). In consideration of these Journal of Youth and Adolescence (2022) 51:984 – 1001 985 con fl icting fi ndings, the question about whether the valence of an endorsed stereotype impacts students ’ math perfor- mance warrants further inquiry. Within the academic domain, Black adolescents are more likely to endorse negative stereotypes about their own group, whereas White adolescents are more likely to endorse posi- tive stereotypes about their own group (Copping, Kurtz ‐ Costes, Rowley, & Wood, 2013). For example, Black and White adolescents both reported academic stereotypes that favored Whites and disparaged Blacks (Copping et al., 2013). Some studies have even suggested that, on average, Black adolescents are more likely to endorse negative aca- demic stereotypes (Nasir et al., 2016; Okeke et al., 2009). Moreover, Rowley and colleagues (2007) found that both Black and White adolescents viewed Whites as “ better ” than Blacks in academic domains. These stereotypes are not void of consequences, as volumes of research have explored the negative effect of implicit stereotypes on school performance (McKown & Strambler, 2009). However, the question of whether the explicit endorsement of race-based stereotypes has similar consequences on adolescents ’ math outcomes remains unclear. In particular, it is unclear whether the endorsement of in-group ability stereotypes yields similar effects for White youth. Although the lynchpin connecting racial stereotypes and psychological and educational out- comes is the presence of widely-held racial stereotypes in the U.S. (Park, Martinez, Cobb, Park, & Wong, 2015; Priest et al., 2014), White youth have not been the focus of ability stereotypes in the arena of academics, neither globally nor in the math domain in particular (Evans et al., 2011; Rowley, Kurtz ‐ Costes, et al., 2007). Hence, the academic con- sequences following the internalization of ability stereotypes among White students in the academic domain is less evident and under-studied. Finally, most studies examining the effect of stereotype endorsement on academic outcomes have focused on gen- der differences relative to racial differences. Indeed, among fi ve studies that examined the topic, four focused on gender stereotypes. In these studies, individuals who endorsed gender-based stereotypes (e.g., “ girls are viewed as less competent in math, but more competent in reading ” ) reported lower competence, less interest, and lower grades in math (Plante, de la Sablonnière, Aronson, & Théorêt, 2013; Schmader, Johns, & Barquissau, 2004). In addition, relations between gender stereotypes and academic out- comes were signi fi cant for girls, but mixed results were observed for boys, as their endorsement of gender stereo- types was positively (Plante et al., 2013; Plante, O ’ Keefe, Aronson, Fréchette-Simard, & Goulet, 2019) or non- signi fi cantly (Bieg, Goetz, Wolter, & Hall, 2015) related to their academic outcomes. In the single study that examined the consequences of race-related stereotypes, Black adoles- cents who endorsed academic stereotypes that White students academically outperform Black students reported lower academic self-concept (Okeke et al., 2009). Subsequently, more research is needed to understand the longitudinal associations between racial stereotype endorsement and academic outcomes for both Black and White adolescents. Math Engagement and Ability Mindset Beliefs in Secondary School Longitudinal studies have shown that as self-concept devel- ops, students in academically stigmatized groups may de- identify with certain educational domains in favor of domains in which public and/or personal regard for their group is higher (Cokley, 2002). For Black students, these threats are particularly salient in math during adolescence (Miller & Wang, 2019; Wang, Guo & Degol, 2019). Active engagement in math learning during secondary school is critical for students ’ educational trajectories (Wang & Eccles, 2013; Wang et al., 2021), and researchers have indicated that students who are more cognitively engaged in math learning also tend to perform better than their less engaged peers (Wang, Ye, & Degol, 2017). Unfortunately, levels of student cognitive engagement in math decline signi fi cantly starting in sixth grade (Wang, Hofkens, & Ye, 2020). Recent studies have also revealed that ability mindset beliefs are important socio-cognitive assets that can support academic learning and achievement, particularly in the face of challenges (Yeager & Dweck, 2012). Mindset beliefs create a motivational context that shapes how students deal with dif fi culties and challenges in academic learning (Wang, Zepeda, Qin, Del Toro, & Binning, 2021). Com- pared to students who believe intelligence is an inherited and unchangeable quality (i.e., a fi xed mindset), students who believe intelligence is malleable (i.e., a growth mind- set) tend to have better academic performance (Paunesku et al., 2015). Students who hold growth mindsets are also more likely to undertake dif fi cult tasks and persist despite setbacks (Dweck, 2006); however, many adolescents view math learning as a dif fi cult process and perceive math ability as fi xed, resulting in the misconception that math is only for those who have a natural predisposition toward it (Boaler, 2016; Leslie et al., 2015). Although socio-cognitive processes have been identi fi ed as signi fi cant antecedents for youth ’ s success in math (Degol, Wang, Zhang, & Allerton, 2018; Wang et al. 2017), most empirical studies examining the consequences of ste- reotypes have focused on academic performance, with very few studies exploring cognitive engagement or ability mindset in math (Fischer, 2010; Lyons, Simms, Begolli, & Richland, 2017; Woodcock, Hernandez, Estrada, & Schultz, 2012). Among these limited studies, one study determined that among Black youth who received a math lesson fol- lowing either a stereotype threat or a neutral condition, 986 Journal of Youth and Adolescence (2022) 51:984 – 1001 those in the threat condition retained less information, found the material less enjoyable, and engaged less in the math lesson than did those in the neutral condition (Lyons et al., 2017). While Lyons and colleagues (2017) provided initial evidence that negative stereotypes affect children ’ s immediate engagement, there is little additional empirical work investigating the differential and persistent effects of negative and positive stereotype endorsement on adoles- cents ’ learning engagement over time. Gender Differences Within Racial Groups The integrative development-in-sociocultural-context model further posits that the social groups to which individuals belong can confer or exacerbate different degrees of advan- tage and disadvantage in academic learning (Wang et al., 2019). As such, the links between adolescents ’ race-based stereotypes and their academic outcomes may vary by gender (Riegle-Crumb et al., 2019). Studies on math achievement suggest that White boys are more visible in the classroom, responded to more positively by teachers and peers, and viewed as more intellectual compared to White girls (Beyer, 1999). Although White boys and White girls have compar- able scores on standardized math tests in high school, the increasing gender gap in math performance and academic attainment among Black students favors girls (Varleas et al., 2012). Black girls also tend to enroll more frequently in advanced math courses and have better standardized test scores than Black boys (National Science Foundation, 2018). Moreover, stereotypes at the intersection of race and gender often place Black boys, relative to other boys and to Black girls, in a negative light academically and behavio- rally (Swanson et al., 2003). For example, in settings that prime negative depictions of Black students, Black boys have reported less positive relationships with teachers (Swanson, Cunningham, & Spencer, 2003) and lower aca- demic expectations from teachers (Cunningham, Swanson, & Hayes, 2013). Although Black boys ’ negative school experiences may undermine their STEM trajectories, scho- lars have suggested that Black women are at risk for dis- crimination in STEM domains due to their “ double jeopardy ” status (King, 1992). In other words, Black women are more likely to experience stigma in math — such as disrespect and underestimation — related to their race, gender, or both (Hanson, 2007; Vining-Brown, 1994). We were only able to locate one empirical study that explicitly examined whether gender moderated links between adolescents ’ race-based stereotypes and academic outcomes. Among a Black cross-sectional sample, Evans, Copping, Rowley, and Kurtz-Costes (2011) found that Black boys ’ ratings of Black individuals as competent in math and science were associated positively with their own academic self-concept, whereas Black girls ’ ratings of Black individuals as competent were unrelated to their own academic self-concept. Given that adolescents may face unique challenges involving both racial and gender stigma in math learning, we examined whether gender moderates the association between racial stereotypes and math out- comes for both Black and White adolescents. The Current Study The role of racial stereotypes in youth ’ s academic achieve- ment increases in salience during adolescence. However, very few empirical studies have investigated whether asso- ciations between Black and White American adolescents ’ stereotype endorsement and their cognitive engagement, mindset beliefs, and performance in math differed by ste- reotype valence and youth gender. To address these gaps, this 3-year longitudinal study aimed to understand whether Black and White adolescents ’ positive and negative racial stereotypes (as opposed to unbiased beliefs) differentially predict their math cognitive engagement, ability mindsets, and test scores over time (Research Question 1) and examine whether relations between racial stereotypes and math out- comes differ by gender (Research Question 2). Because adolescents who endorse negative stereotypes are more likely to attribute math learning outcomes to fi xed abilities as opposed to invested effort, adolescents who endorsed nega- tive in-group stereotypes were expected to have less cogni- tive engagement, lower test scores, and stronger fi xed ability mindsets. While some scholars have identi fi ed academic bene fi ts associated with positive stereotype endorsement, others have indicated that adolescents are more likely to underperform or disengage from learning when they attribute academic performance to the presence of innate ability. Hence, no speci fi c hypothesis was made regarding the impact of positive stereotypes. As Black American girls are more likely to experience double jeopardy from both racial and gender stigma in math, Black American girls were expected to show less favorable outcomes associated with stereotype endorsement relative to Black American boys. Due to the limited racial stereotype research on White American ado- lescents, no speci fi c hypothesis was made about the gender moderation effects among White American adolescents. Methods Participants Participants were part of a large-scale longitudinal study designed to examine the in fl uence of sociocultural contexts on adolescent engagement and achievement in school. The analytic sample of Black and White students ( n = 2546; Journal of Youth and Adolescence (2022) 51:984 – 1001 987 age range = 11 – 16; 50% males, 60% White, 40% Black; 57% quali fi ed for free lunch) was composed of sixth (35%), eighth (36%), and tenth (29%) graders from 17 urban public schools located in the Mid-Atlantic region of the United States. All school populations consisted primarily of White and Black American students; however, schools varied in racial group composition. Two schools had balanced populations of Black and White students, while the other 15 participating schools had student populations where 60 – 70% of students were Black. The teacher population was predominantly White in all schools. Procedure In the fall of the 2016 – 2017 academic year, all sixth-, eighth-, and tenth-grade students in each of the 17 schools were invited to participate in a longitudinal study on school engagement. With assistance from the students ’ teachers, the research team distributed letters with the study description and assent/consent forms for students and their parents. Research staff then administered surveys to eligible students during instructional time. Participating students completed computer-based surveys that took approximately 45 min. To address potential literacy dif fi culties, all survey questions were audio-recorded, and headphones were made available for students to use. Research staff was available during survey administration to answer students ’ questions about the survey ’ s content. Following each survey admin- istration, research staff provided students with a small gift. Measures Racial stereotype endorsement In the fall of years 1, 2, and 3, adolescents ’ stereotype endorsement about racial differences in math competence was measured by adapting the Racial Stereotype Related to Mathematics Scale ( r s = 0.75 – 0.78; Munter & Haines, 2019). This 2-item scale was adapted and validated using a sequential mixed-methods design, and its reliability and validity have been established (Wang et al., 2021). Adoles- cents were asked to disclose their thoughts as to whether certain races are “ typically good at math ” and “ have better performance in math. ” Separate sets of items were presented for Black and White students 1 , such that students rated the ability of each racial group in math with a 5-point response scale (1 = strongly disagree; 5 = strongly agree). The order of racial groups was randomized to control for response bias. Following Wang et al. (2021) approach to assessing stereotype endorsement, a difference score was created to represent students ’ racial stereotypes by subtracting out- group scores from in-group scores (e.g., subtract the item responses about White students from responses about Black students; possible range: − 4.0 to 4.0). Values above zero indicated positive in-group stereotypes (i.e., the belief that Black students are better than White students in math); values below zero represented negative in-group stereotypes (i.e., the belief that Black students are worse than White students in math); and zero values designated unbiased beliefs. Subsequently, we created two categorical variables — one for negative stereotype endorsement and the other for positive stereotype endorsement — and used students with unbiased beliefs as the reference category. Cognitive engagement In the spring of years 1, 2, and 3, the 5-item Math Engagement Scale (Wang, Fredricks, Ye, Hofkens, & Schall, 2016) was used to assess students ’ cognitive engagement in math learning as a latent variable ( α s = 0.74 – 0.76). Students were asked to rate their intellectual investment, use of meta-cognitive strategies, and engage- ment in self-regulated learning in math over the past 6 months (e.g., “ I go through the work that I do for math class and make sure that it ’ s right, ” “ I try to connect what I am learning in math to things I have learned before. ” ). Item responses fell along a 5-point scale ranging from 1 (not at all like me) to 5 (very much like me). The cognitive engagement measure has demonstrated strong reliability, construct validity, and predictive validity (Wang et al., 2016). In addition, a measurement invariance test indicated that the engagement measure met criteria for partial scalar measurement invariance across time, χ 2 (30) = 253.86, p < 0.001, RMSEA = 0.05, 90% CI [0.05, 0.06], CFI = 0.97, TLI = 0.96, SRMR = 0.03. Higher scores re fl ected greater cognitive engagement. Ability mindset beliefs In the spring of years 1, 2, and 3, the well-validated Math Ability Mindset Scale (Blackwell et al., 2007; Dweck, 2006) was utilized to assess students ’ beliefs about the malleability of math ability as a latent variable (four items; α -range = 0.85 – 0.89; e.g., “ You have a certain amount of math ability, and you can ’ t really do much to change it ” ; “ To be honest, you can ’ t really change how smart you are in math ” ). Using a 5-point scale, students indicated the degree to which they endorsed these statements, with responses ranging from 1 (strongly disagree) to 5 (strongly agree). Higher scores re fl ected stronger fi xed math ability mindsets. A measurement invariance test demonstrated the mindset 1 To ensure students had suf fi cient knowledge about other groups to gauge their math abilities relative to their own, we focused on Black and White students, as these two groups best re fl ected the schools ’ racial composition. 988 Journal of Youth and Adolescence (2022) 51:984 – 1001 scale met criteria for partial scalar invariance across time, χ 2 (60) = 233.46, p < 0.001, RMSEA = 0.03, 90% CI [0.03, 0.04], CFI = 0.99 TLI = 0.98, SRMR = 0.03. Math standardized test scores In years 1, 2, and 3, adolescents ’ math test scores from standardized statewide assessments were obtained from schools ’ administrative data at the end of each school year. The test scores were recalibrated to a scale of 0 – 100 points, with a mean of 50 and a standard deviation of 10. Thus, the scores across years are directly comparable. Covariates Four student- and school-level characteristics were included as covariates: students ’ grade level, school racial diversity (0 = less than 50% White students; 1 = more than 50% White students), school membership (i.e., dummy variables for schools), and quali fi cation for free school lunch (a commonly used and valid proxy for economic status in educational research; 0 = free lunch; 1 = paid lunch) col- lected from school administrative data. Federal income eligibility guidelines accounting for household size and income were used by schools to determine students ’ qua- li fi cation for free school meals. Analytic Plan All analyses were conducted in Mplus 8.3. Using an auto- regressive and cross-lagged panel approach (Wu, Selig, & Little, 2012), the longitudinal effects of stereotype endor- sement on math outcomes were examined 1 year later while controlling for baseline outcomes (i.e., cognitive engage- ment, ability mindset, and test scores) and covariates. Within each model, all key constructs were regressed on all covariates each year. In addition, the analyses included random intercepts for the math outcomes to account for trait-like, individual-level variability, thereby permitting the model to estimate more precise cross-lagged parameters (Hamaker, Kuiper, & Grasman, 2015). A chi-square test was fi rst conducted to assess whether the effects of positive stereotype endorsement could be constrained to be equivalent to those of negative stereotype endorsement without resulting in a signi fi cant decrement in model fi t. Next, an additional chi-square test was performed to examine whether the effects of positive and negative stereotype endorsement were equivalent between Black and White adolescents. Then further multi-group analyses were used to test whether the intersection of adolescents ’ race and gender moderated observed pathways among the following four groups: Black boys, Black girls, White boys, and White girls. The multi-group analysis was able to compare the magnitude and standard errors of all coef fi cients across groups using formal statistical procedures. The data structure had three levels: students nested within classrooms (142 classrooms) and schools (17 schools). The intraclass coef fi cients indicated that the majority of the math outcome variance (between 79% and 81%) was at the student level relative to classroom and school levels. Due to the relatively small number of schools, a fi xed-effect approach was used to account for school effects by including dummy variables (i.e., 16 dummy variables) for the schools as cov- ariates in the models (McNeish Stapleton, & Silverman, 2017). Because of the study ’ s focus on student level factors, the “ TYPE = COMPLEX ” command in Mplus and the robust maximum likelihood estimation method (MLR) were used to account for classroom clustering effect and obtain adjusted standard errors. Lastly, effects were constrained to be invariant across time for model parsimony when such constraints did not result in a signi fi cant decrement in model fi t (Wu et al., 2012). Missing Data Within the study ’ s longitudinal design, 2295 adolescents participated at year 1; 2288 participated at year 2; and 1984 participated at year 3. Since fi rst participation, 1752 (68.8%) adolescents had no missing data; 519 (20.4%) had 1 year of data missing; and 275 (10.8%) had 2 years of data missing, which was mainly due to students being absent on the day of survey administration. We then examined whe- ther student characteristics and study variables at baseline were associated with participants ’ missing data patterns. Participants with missing data were more likely to be Black (than White), qualify for free lunch, have lower math test scores, and have lower math cognitive engagement than participants without missing data. After adjusting for cov- ariates, partial correlations indicated that missingness was not related to adolescents ’ racial stereotype endorsement, cognitive engagement, ability mindset beliefs, or test scores each year. To retain sample variability and diversity, a full information maximum likelihood method was used to incorporate missing data patterns in the model estimation process without deleting any incomplete cases. Results Descriptive statistics (e.g., means, standard deviations, cor- relations) for continuous variables and frequency distribu- tions of categorical variables are summarized in Table 1. In the following sections, the authors fi rst describe results regarding the associations between stereotype endorsement and math outcomes and then the intersecting role of race and gender in these associations. Journal of Youth and Adolescence (2022) 51:984 – 1001 989 Table 1 Descriptive Statistics for All Key Constructs ( n = 2546) Predictors 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Mean or % α 1 Math cognitive engagement Y1 1 0.54 0.44 − 0.19 − 0.21 − 0.19 0.27 0.34 0.27 0.01 − 0.02 − 0.02 − 0.06 0.05 − 0.01 3.77 (0.90) 0.87 2 Math cognitive engagement Y2 0.50 1 0.51 − 0.16 − 0.34 − 0.26 0.29 0.34 0.34 − 0.01 − 0.07 − 0.05 − 0.13 − 0.05 0.00 3.77 (0.93) 0.89 3 Math cognitive engagement Y3 0.38 0.48 1 − 0.11 − 0.24 − 0.29 0.19 0.26 0.31 − 0.03 − 0.04 − 0.06 − 0.05 − 0.06 − 0.06 3.73 (0.95) 0.89 4 Math fi xed mindset Y1 − 0.25 − 0.16 − 0.15 1 0.40 0.38 − 0.17 − 0.20 − 0.07 0.11 0.03 0.08 0.01 0.11 0.00 3.76 (0.98) 0.81 5 Math fi xed mindset Y2 − 0.18 − 0.23 − 0.18 0.33 1 0.48 − 0.11 − 0.21 − 0.22 0.10 0.12 0.07 0.02 0.14 0.05 3.81 (0.98) 0.85 6 Math fi xed mindset Y3 − 0.15 − 0.19 − 0.21 0.29 0.45 1 − 0.13 − 0.20 − 0.16 0.14 0.16 0.16 0.04 0.10 0.11 3.74 (0.93) 0.87 7 Math test scores Y1 0.10 0.18 0.16 − 0.12 − 0.12 − 0.08 1 0.60 0.49 0.04 − 0.02 − 0.03 0.00 − 0.06 − 0.02 82.54 (13.21) – 8 Math test scores Y2 0.25 0.24 0.24 − 0.23 − 0.18 − 0.18 0.53 1 0.64 0.04 − 0.05 − 0.02 − 0.08 − 0.03 − 0.06 83.90 (11.84) – 9 Math test scores Y3 0.05 0.20 0.29 − 0.06 − 0.16 − 0.07 0.45 0.53 1 0.02 − 0.03 − 0.04 − 0.07 − 0.03 − 0.05 80.68 (13.22) – 10 Positive racial stereotype Y1 − 0.01 0.06 − 0.05 0.04 0.15 0.08 − 0.01 0.02 0.07 1 0.18 0.12 − 0.11 − 0.01 − 0.12 0.16 – 11 Positive racial stereotype Y2 − 0.01 − 0.01 − 0.06 0.13 0.15 0.11 − 0.04 0.01 0.04 0.23 1 0.29 − 0.01 − 0.05 0.04 0.12 – 12 Positive racial stereotype Y3 − 0.13 − 0.14 − 0.09 0.18 0.21 0.13 − 0.03 − 0.09 − 0.08 0.12 0.25 1 − 0.01 − 0.04 − 0.06 0.08 – 13 Negative racial stereotype (Y1) − 0.15 − 0.08 0.02 0.14 0.06 0.24 − 0.04 − 0.06 − 0.01 − 0.24 0.01 0.07 1 0.04 − 0.04 0.06 – 14 Negative racial stereotype (Y2) − 0.08 − 0.15 − 0.09 0.01 0.09 0.09 − 0.13 − 0.11 − 0.15 − 0.07 − 0.11 0.03 0.15 1 0.09 0.05 – 15 Negative racial stereotype (Y3) − 0.09 − 0.07 − 0.13 0.14 0.15 0.13 − 0.06 − 0.02 − 0.01 0.04 − 0.08 − 0.10 − 0.06 0.17 1 0.05 – Mean or % 3.68 (0.90) 3.61 (0.91) 3.47 (0.92) 3.79 (1.01) 3.75 (0.99) 3.69 (1.00) 73.79 (15.74) 75.06 (14.36) 73.85 (14.09) 0.21 0.10 0.08 0.17 0.09 0.09 α 0.84 0.88 0.89 0.79 0.81 0.82 – – – – – – – – – Bolded coef fi cients indicate signi fi cant p- values < 0.05. Non-bolded coef fi cients indicate p -values ≥ 0.05. Descriptive statistics for Black youth are below the diagonal and White youth are above the diagonal. 990 Journal of Youth and Adolescence (2022) 51:984 – 1001 Endorsement of Positive or Negative Stereotypes Math cognitive engagement Endorsement of either a negative or positive stereotype predicted lower cognitive engagement 1 year later (see upper panel in Table 2). Neither type of endorsement moderated the link between stereotype endorsement and cognitive engagement, Δ χ 2 (1) = 1.42, p = ns . The endor- sement of negative and positive stereotypes operated simi- larly among Black and White adolescents, Δ χ 2 (3) = 3.90, p = ns . In addition, students ’ cognitive engagement did not Table 2 Racial Stereotype Endorsement (Versus Neutral Beliefs) and Mathematics Outcomes by Race ( n = 2546) Black Students White Students Outcome B SE p B SE p Cross-lagged effects on cognitive engagement at Year 2 Boys − 0.07 0.07 ns − 0.16 0.02 <0.001 Grade level − 0.01 0.02 ns − 0.06 0.02 <0.001 School racial diversity − 0.57 0.32 ns − 0.32 0.12 <0.010 Full-priced lunch 0.14 0.14 ns 0.29 0.05 <0.001 Negative stereotype at Year 1 − 0.04 0.01 <0.010 − 0.04 0.01 <0.010 Positive stereotype at Year 1 − 0.04 0.01 <0.010 − 0.04 0.01 <0.010 Cross-lagged effects on cognitive engagement at Year 3 Boys − 0.12 0.09 ns − 0.18 0.03 <0.001 Grade level − 0.01 0.03 ns − 0.05 0.04 ns School racial diversity − 0.09 0.36 ns − 0.47 0.48 ns Full-priced lunch − 0.12 0.11 ns 0.20 0.12 ns Negative stereotype at Year 2 − 0.04 0.01 <0.010 − 0.04 0.01 <0.010 Positive stereotype at Year 2 − 0.04 0.01 <0.010 − 0.04 0.01 <0.010 Cross-lagged effects on fi xed mindset at Year 2 Boys − 0.28 0.05 <0.001 − 0.22 0.04 <0.001 Grade level − 0.09 0.03 <0.010 − 0.11 0.01 <0.001 School racial diversity − 0.43 0.31 ns 0.31 0.19 ns Full-priced lunch 0.01 0.16 ns 0.05 0.05 ns Negative stereotype at Year 1 − 0.14 0.01 <0.001 − 0.14 0.01 <0.001 Positive stereotype at Year 1 − 0.14 0.01 <0.001 − 0.14 0.01 <0.001 Cross-lagged effects on fi xed mindset at Year 3 Boys − 0.10 0.09 ns − 0.26 0.05 <0.001 Grade level − 0.06 0.04 ns − 0.07 0.03 <0.010 School racial diversity − 0.02 0.39 ns 0.03 0.36 ns Full-priced lunch 0.03 0.13 ns − 0.02 0.06 ns Negative stereotype at Year 2 − 0.14 0.01 <0.001 − 0.14 0.01 <0.001 Positive stereotype at Year 2 − 0.14 0.01 <0.001 − 0.14 0.01 <0.001 Cross-lagged effects on math test scores at Year 2 Grade level − 1.56 0.40 <0.001 − 2.85 0.85 <0.010 School racial diversity − 8.49 11.90 ns 13.39 5.28 <0.050 Full-priced lunch 7.62 2.07 <0.001 6.70 1.10 <0.001 Negative stereotype at Year 1 − 1.53 0.49 <0.010 − 1.53 0.49 <0.010 Positive stereotype at Year 1 0.53 0.33 ns 0.28 0.28 ns Cross-lagged effects on math test scores at Year 3 Boys − 4.95 0.94 < 0.001 − 3.23 0.44 <0.001 Grade level − 0.97 0.72 ns − 1.68 0.55 <0.010 School racial diversity − 10.08 11.35 ns 4.28 3.66 ns Full-priced lunch 7.70 2.42 <0.010 5.31 0.72 <0.001 Negative stereotype at Year 2 − 1.53 0.49 <0.010 − 1.53 0.49 <0.010 Positive stereotype at Year 2 0.53 0.33 ns 0.28 0.28 ns Journal of Youth and Adolescence (2022) 51:984 – 1001 991 predict negative or positive stereotype 1 year later. The model fi t the data well, χ 2 (252) = 307.01, p < 0.05, RMSEA = 0.01, 90% CI [0.01, 0.02], CFI = 0.98, TLI = 0.96, SRMR = 0.10. Math ability mindset As shown in the middle panel of Table 2, endorsement of either a negative or positive stereotype was associated with stronger fi xed mindset beliefs 1 year later. Neither type of endorsement moderated the link between stereotype endorsement and mindset beliefs, Δ χ 2 (1) = 1.06, p = ns . In addition, endorsement of both negative and positive ste- reotypes operated similarly among Black and White ado- lescents, Δ χ 2 (3) = 2.50, p = ns . Students ’ mindset beliefs did not predict negative or positive stereotypes 1 year later. The model fi t the data well, χ 2 (473) = 1303.43, p < 0.001, RMSEA = 0.04, 90% CI [0.03, 0.04], CFI = 0.95, TLI = 0.94, SRMR = 0.06. Math test scores As indicated in the lower panel of Table 2, endorsement of a negative stereotype was associated with lower math test scores 1 year later. However, endorsement of a positive stereotype was not associated with test scores, Δ χ 2 (1) = 8.63, p < 0.01. In addition, endorsement of both negative and positive stereotypes operated similarly among Black and White adolescents, Δ χ 2 (2) = 0.96, p = ns . Students ’ test scores did not predict the development of negative or positive stereotypes 1 year later. The model fi t the data well, χ 2 (473) = 64.02, p < 0.001, RMSEA = 0.01, 90% CI [0.00, 0.02], CFI = 0.98, TLI = 0.95, SRMR = 0.16. The Intersecting Effects of Race and Gender Math cognitive engagement When examining the intersectional effects of race and gender, endorsement of negative stereotypes predicted lower cognitive engagement 1 year later for Black girls, White girls, and White boys (but not for Black boys; see Table 3). The effects were negative and equivalent among Black girls, White girls, and White boys [ Δ χ 2 (2) = 1.21, p = ns ]. The effect for Black boys was non-signi fi cant and different from that seen in their female and White coun- terparts [ Δ χ 2 (1) = 8.99, p < 0.01]. In examining the effects of positive stereotypes, adolescents who endorsed more positive stere

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