
Exposure to SameRace or SameEthnicity Teachers and Advanced Math CourseTaking in High School: Evidence From a Diverse Urban Districtby Jason A. Grissom, Sarah E. Kabourek & Jenna W. Kramer  2020 Background/Context: Research links advanced mathematics coursetaking to important later outcomes, including college graduation and earnings, yet many students fail to progress into higher math courses as they move through high school. Black and Hispanic high school students are less likely than their white peers to take advanced math courses. A complex set of factors inform decisions about student coursetaking, but teachers play key roles, including providing information about courses, giving students encouragement, helping students form aspirations (e.g., through role modeling), and serving as gatekeepers via grade assignment and formal recommendations. At the same time, growing empirical evidence suggests that students from different racial/ethnic groups benefit from being taught by teachers with similar demographic backgrounds, which motivates an analysis connecting math teacher–student racial or ethnic congruence with progression into higher math courses in high school. Purpose: We investigate the degree to which having a math teacher of the same race or ethnicity predicts subsequent enrollment in more advanced high school math courses, as well as in honors and Advanced Placement (AP) math courses. We also investigate potential mechanisms, including impacts of student–teacher congruence on course grades and standardized test performance, which may in turn predict a higher likelihood of advanced math course enrollment. Setting: We examine studentlevel administrative data from high schools in MiamiDade County Public Schools, the fourth largest school district in the United States. Research Design: We estimate the likelihood that a student will take a higher level math course as a function of student–teacher racial/ethnic congruence, plus student, teacher, and classroom characteristics, and school fixed effects. This research design compares later math coursetaking between students with and without race/ethnicitycongruent teachers within the same school, holding a variety of other factors constant. We estimate similar models for honors and AP coursetaking. We also estimate models for math course grades and endofcourse (EOC) exam scores using schoolbycourse and student fixed effects. Findings/Results: We find that high school students with a samerace or sameethnicity teacher are more likely to take a higher math course in the next year than other students taking the same course in the same school. Associations are largest for Black students, who are 2 percentage points more likely to advance to a higher math course when taught by a Black teacher. Having a demographically similar teacher is also associated with movement into honors and AP courses in the next term, on average, though results vary by student subgroup. Students receive higher EOC scores and higher grades when taught by a demographically similar teacher, with higher grades even than what would be predicted by their EOC score, particularly in algebra.
Conclusions/Recommendations: Our analysis contributes to growing evidence on the importance of teacher diversity for outcomes for students from minoritized groups and is among only a very small set of studies that demonstrate teachers’ impacts on student outcomes not just for one year, but also in subsequent years. Our results underscore the importance of efforts to recruit and retain teachers of color, particularly in high schools. We recommend future research to better understand the mechanisms linking diverse teachers to student coursetaking outcomes.
Black and Hispanic students are underrepresented in upperlevel high school math courses. Black students make up 16% of high school enrollments but only 13% of enrollments in advanced mathematics and 8% in calculus; for Hispanic students, who are 24% of the overall high school population, these numbers are 19% and 16% (U.S. Department of Education Office for Civil Rights, 2018). This underrepresentation constitutes a critical gap in Black and Hispanic students’ opportunities to learn and be challenged, and the consequences can be substantial. For example, students who take more, and more advanced, math courses in high school have a greater likelihood of earning their diploma, entering college, and graduating from college, and also obtain higher future earnings (Adelman, 2006; Gaertner et al., 2014; Long et al., 2009; National Mathematics Advisory Panel, 2008; Rose & Betts, 2001). Moreover, students from historically marginalized groups may benefit even more economically from taking math than other students. Goodman (2017), for example, found that the economic return to an additional high school math course for Black students is 10%, or about half of the total return to an additional year of high school. Indeed, the role of math literacy is not only in giving students access to higher paying employment but also more broadly in facilitating critical thinking, engaging with technology, and participating fully in society has led some scholars to frame opportunities for minoritized students to learn mathematics as a contemporary civil rights issue (Kress, 2005; Moses & Cobb, 2001). Benefits and rightscentered discussions of advanced high school mathematics for students motivate a policy and research interest in the factors that predict secondary coursetaking. Among these factors, studies have highlighted the role of educators in influencing coursetaking patterns. Teacher relationships influence students’ valuing of mathematics (Midgley et al., 1989). Students from different subgroups get different kinds of information about or encouragement for taking more challenging courses (Yonezawa et al., 2002). More generally, student course enrollment decisions are a function of a variety of factors that teachers affect, including prior course grades, achievement test scores, and students’ aspirations (Hoyt & Sorenson, 2001; Oakes & Guiton, 1995). We extend this literature on teacher effects on students’ coursetaking in high school by investigating whether students are more likely to progress in high school mathematics when taught by a teacher of the same race or ethnicity. This investigation is motivated by a growing literature documenting the effects of teacher racial and ethnic diversity on student outcomes, and, in particular, the impacts of racially congruent teachers on outcomes from historically marginalized populations (see Grissom et al., 2015). Black and Hispanic students appear to benefit from being taught by racially and/or ethnically similar teachers with respect to a variety of outcomes, including achievement (Dee, 2004; Egalite et al., 2015), likelihood of being assigned to gifted programs (Grissom & Redding, 2016), and reductions in exclusionary discipline (Lindsay & Hart, 2017). This growing body of research suggests several reasons that teacher racial or ethnic congruence could inform student coursetaking. For example, higher math student achievement associated with such congruence could make students better prepared for subsequent math courses. Also, teachers express higher expectations and aspirations for students of the same racial background (Ehrenberg et al., 1995; Gershenson et al., 2016), which may lead them to give greater encouragement to such students to take higher math courses. Of course, race and ethnicity are not the same concept, and the teacher–student demographic “match” literature has only just begun to examine the extent to which racial congruence and ethnic congruence may behave differently (e.g., Egalite et al., 2015; Grissom et al., 2017). This examination reflects a growing effort to understand the history, and disentangle the conflation, of the labels “race” and “ethnicity” in empirical research (e.g., Laughter, 2018; Li & Koedel, 2018; Prewitt, 2005). Because the specific mechanisms underlying match effects are not yet well understood, it is difficult to make predictions about when such differences may arise. In this study, we take care to use language that differentiates race and ethnicity as demographic categories. However, we are limited in our empirical capacity to disentangle them, given that the administrative data that form the basis of our study followed a coding structure that treated Hispanic ethnicity as a racial category for most years; students identified as Hispanic could not also be identified as Black or White. Thus, while conceptually, we would prefer more nuance in our analysis of race and ethnicity congruence, as a practical matter, we are not able to fully differentiate the two. We examine whether student–teacher race or ethnicity congruence is associated with differential probability of advancement in high school mathtaking using longitudinal data from MiamiDade County Public Schools (MDCPS), the largest school district in Florida and the fourth largest in the United States. The data set includes detailed information on high school students’ course enrollments each year. We ask four questions. First, to what extent does a student’s racial or ethnic congruence with his or her current math teacher predict movement into a higher course in the high school math progression in the next school year? Second, to what extent does this congruence predict movement into an honors or Advanced Placement (AP) math course next year? Third, to what degree do teacher–student congruence effects on coursetaking vary for students of different races and ethnicities? And, finally, to move toward an understanding of potential mechanisms, to what extent are differences in the relationship between racial or ethnic congruence and future math coursetaking explained by differences in math achievement and teacherassigned grade associated with the current math course? We proceed as follows. We begin by synthesizing the literature on teacher–student effects on coursetaking and the growing literature on racial and ethnic “match” effects on student outcomes to describe mechanisms that may link teacher–student racial or ethnic congruence to future math coursetaking. We then describe the data and methods before turning to the results. The concluding section discusses the implications of our results and future directions for research. THE IMPORTANCE OF HIGH SCHOOL MATH COURSETAKING High school coursework aims to improve student skills and knowledge in preparation for postsecondary enrollment or entry to the workforce. Advanced courses—including honors, AP, International Baccalaureate (IB), and upperlevel math, such as calculus—increase academic challenge for students who select into such coursework and open up college coursework opportunities, which many students may not understand (Sells, 1978). Taking advanced coursework has been linked to greater academic performance and better postsecondary education outcomes (Alexander & Cook, 1982; Conger et al., 2009; Gamoran & Mare, 1989; Schneider et al., 1997). A metaphor sometimes adopted to underscore the importance of taking advanced coursework in high school for college success is that of a series of moving walkways (Adelman, 2006; Venezia et al., 2003). Just as one may stumble when stepping from a slower moving walkway to one moving more quickly, taking a less rigorous sequence of high school coursework may lead to less successful academic outcomes as students transition to postsecondary education. Over time, a large body of research has validated this differential coursework hypothesis (Alexander & Pallas, 1984; Pallas & Alexander, 1983). Scholarly discussion of coursework and grades in the 1980s and early 1990s contributed to recommendations and policy changes that resulted in a “new basic” high school curriculum to increase the rigor of students’ academic preparation for college (McCormick, 1999). In spite of differential access to highquality teachers and advanced coursework, new basic requirements have been touted as an important policy change that ensures greater preparation across the entire population of high school graduates, though they may not be rigorous enough given demand for STEMrelated skills (Gamoran & Hannigan, 2000; Long et al., 2009; Teitelbaum, 2003). Empirical examinations of student coursetaking, whether looking at studentdriven differences or the aforementioned curricular policy changes, have revealed that students who take more courses in core academic disciplines perform better in college (Adelman, 1999, 2006; Attewell & Domina, 2008; Rose & Betts, 2001; St. John & Chung, 2006). These results are especially pronounced for mathematics. For example, using the National Education Longitudinal Study (NELS:88), St. John and Chung (2006) found that taking advanced math courses significantly increased high school graduates’ probability of attending fouryear colleges. Rose and Betts (2001) found a significant effect of algebra II on bachelor’s degree attainment; students who completed algebra II were 12% more likely to earn a bachelor’s degree compared with their peers who completed only algebra I and geometry. Adelman (1999, 2006) found additional evidence of a positive association between the level of math courses and degree attainment using NELS and High School and Beyond data. The importance of taking more advanced high school math courses for future outcomes suggests the importance of identifying factors that shape students’ coursetaking trajectories. LINKING STUDENT–TEACHER RACIAL OR ETHNIC CONGRUENCE TO HIGH SCHOOL COURSETAKING Access to schools that offer advanced math courses is the first of such factors. According to 2018 report from the U.S. Department of Education’s Office for Civil Rights, 80% of all high schools offer algebra II, and 65% offer advanced mathematics, but in schools serving large percentages of Black and Hispanic students, those numbers fall to 74% and 55%. Black students are somewhat less likely than other students to attend schools that offer at AP or IB math courses (Ross et al., 2012). Differences in which schools offer more advanced or rigorous courses can reflect a variety of factors, including financial resources, availability of qualified staff to teach such courses, and schools’ prioritization of academic versus “practical” offerings (e.g., Oakes, 1990; Peske & Haycock, 2006). Accounting for structural barriers arising from which schools students from different racial or ethnic groups attend does not close gaps in advanced math coursetaking, however; such gaps are present even within the same school. We focus on this “withinschool” gap in this study, homing in on a set of factors that may affect student coursetaking. We bring together two bodies of research. The first is research documenting the important role that teachers play in decisions about which high school courses students take (e.g., Oakes & Guiton, 1995; Thompson, 2017). The second is a growing body of empirical research that demonstrates that the racial or ethnic match between teachers and students affects numerous important school processes and student outcomes (e.g., Dee, 2004; Egalite et al., 2015; Grissom et al., 2015; Lindsay & Hart, 2017). This research suggests several ways that such congruence may impact student coursetaking patterns. Within high schools, students’ coursetaking is shaped by a number of influences, including information that educators provide to them about courses, their own preferences and interests, level of motivation, how well they performed in prior courses, and encouragement they receive from others to pursue some courses over others (Froiland & Davison, 2016; Sciarra, 2010; Yonezawa et al., 2002). Students, parents, and teachers may also perceive (consciously or not) AP and honors courses as “white spaces,” both in overrepresentation of white students and the emphasis of white social and cultural norms within the classroom (Blaisdell, 2016; Nunn, 2011). This list points to several pathways through which individual teachers may help shape decisions about which future courses a student takes. For instance, a teacher may have a large impact on what a student learns in his or her class, affecting the student’s preparation or motivation to continue in the subject. Alternatively, a teacher may communicate high (or low) expectations to a student about his or her capabilities in the subject, which may affect the student’s desire to progress. To the extent that teacher–student racial or ethnic congruence affects these intermediate outcomes—for example, by impacting student achievement or informing the expectations that a teacher has of a student—there may be impacts on student coursetaking as well. In what follows, we detail several such potential mechanisms. In an attempt to organize these mechanisms, we classify them as “teacherside” or “studentside” according to whether teachers or students are the primary actor—recognizing that such categorization is imperfect, given that each speaks to relationships among teachers and students that are necessarily bidirectional. TEACHERSIDE MECHANISMS A number of teacherside mechanisms may impact the likelihood of subsequent math coursetaking. Research evidence points to differential expectations as a driving force in these mechanisms. For instance, on average, teachers hold more negative perceptions of, and lower expectations of, Black and Hispanic students as compared with their white peers (Dee, 2005; McKown & Weinstein, 2002). These lower expectations link closely to deficit thinking, or the pattern of believing that students from marginalized groups fail to achieve in school because of deficiencies inherent in the students, their families, and their communities. Deficit orientations among teachers can restrict access to meaningful educational opportunities for marginalized students (Ford et al., 2001; Howard, 2013; Liou & RotheramFuller, 2016), because teachers with a deficit mindset may fail to provide them with social capital, academic rigor, caring, and exposure to curricula that reflect high expectations for all students (Liou & Rojas, 2016). Teacher expectations can influence student coursetaking in several ways. Teachers often act as “gatekeepers” to higher courses, both helping to formally decide which future courses a student may take and informally providing students with encouragement regarding coursetaking decisions. Both of these actions are informed by their (potentially biased) perceptions of students’ aptitude or expectations of likely success in subsequent coursework (Blanchard & Muller, 2015; Noguera, 2004). In a study of the intersection of nativity and languageminority status and teachers’ perceptions of student effort, Blanchard and Muller (2015) uncovered suggestive evidence that teachers’ perceptions affect students’ academic progress toward college. Further, researchers found that teachers associated student racial groups with different curricular tracks (even as they denied the link between race and ethnicity and course placement); these associations aligned with their expectations of which racial and ethnic groups tended toward fouryear college attendance and which would enter the workforce immediately after high school (Nunn, 2011; Oakes & Guiton, 1995). These expectations may in turn shape student placement into different academic tracks. At the same time, students of color may perceive advanced courses, such as AP courses, as inhospitable places where they will be uncomfortable—feelings that teachers can help them to overcome if they are aware of and sympathetic to them (Taliaferro & DeCuirGunby, 2008). Given the racialized structures (i.e., historically embedded expectations, pedagogical practices) of American schools, samerace and sameethnicity teachers may be as complicit in constructing oppressive classrooms for students as their white peers. Any teacher, regardless of race or ethnicity, may be unaware of or unable to provide supportive, culturally relevant teaching for their students, instead keeping to established school norms that support teachercentered rather than studentcentered learning (Howard, 2013; LadsonBillings, 1995; Vavrus, 2008). Still, samerace and sameethnicity teachers are more likely to be aware of detrimental deficit and stereotypeoriented practices that often occur in classrooms (Jussim & Harber, 2005). To this point, research has documented the higher expectations that teachers of color hold for students of color. Several studies have found evidence that teachers of color hold more positive perceptions and expectations of students of color than do white teachers (McGrady & Reynolds, 2013; McKown & Weinstein, 2002). For example, Ehrenberg et al. (1995) use NELS 1988 data to examine the relationship between teacher–student race match and student learning, as well as teacher evaluations of students. Although the amount that students learned did not appear to be related to similarity along these dimensions of identity, teachers’ subjective evaluations of students were significantly better when they “matched” along these characteristics. Dee (2005) found that students of color are more likely to be viewed by white teachers as disruptive and inattentive. Conversely, teachers of color may be more empathetic to samerace minority students, or at least less likely to discipline minority students than their white counterparts (Downey & Pribesh, 2004; Lindsay & Hart, 2017; Stewart et al., 1989). Other studies have found that teachers judge the academic and nonacademic skills of ownrace elementaryage students more positively (e.g., Ouazad, 2014), which may in turn affect student outcomes, such as gifted placement (NicholsonCrotty et al., 2016). Gershenson and colleagues (2016) examined two teachers’ educational expectations for students and found that nonBlack teachers of Black students had significantly lower expectations than did Black teachers. The effects were larger for math teachers and Black male students (Gershenson et al., 2016). There is also limited evidence that supports connections among teacher–student race congruence, teacher expectations, and coursetaking. In his analysis of data from the NELS:88, Dee (2005) found some evidence that high school students of whom teachers had a negative view were significantly less likely to take AP classes as upperclassmen and more likely to drop out of high school. STUDENTSIDE MECHANISMS Beyond evidence that teachers can create formal barriers to advanced courses (e.g., refusing to sign off on a student’s course enrollment form) as well as informal ones (e.g., actively discouraging a student from taking a higher course) for students for whom they hold lower expectations (Blanchard & Muller, 2015; Noguera, 2004), students’ behavior may respond to teacher perceptions. Students may perceive and internalize teachers’ expectations of them and change their approach to schooling in response. That is, if students perceive that teachers hold them in high esteem, they may redouble their efforts to learn the material, even carrying this investment forward into subsequent classes. Conversely, students may interpret low teacher expectations as an objective evaluation of their potential, lower their own expectations to meet those of their instructor, and then behave or make choices in ways that are consistent with those expectations. In this way, teachers’ expectations help create a selffulfilling prophecy among students (Ferguson, 2003; Gershenson, 2016; Jussim & Harber, 2005). Students who perceive teachers as having lower expectations for them, relative to their classmates, may experience decreased motivation and achieve at levels lower than their true academic capability, a process that is particularly relevant for historically marginalized groups (Jussim & Harber, 2005). Thus, the link between teacher–student racial/ethnic congruence and teacher expectations remains relevant even if teachers do not act on their expectations specifically with respect to students’ coursetaking decisions. Even in the absence of different teacher expectations, students’ coursetaking decisions may be affected by the presence of a samerace teacher through rolemodeling effects. That is, students of racecongruent teachers may be more drawn toward their teachers as role models and may respond to demographically similar teachers by having greater motivation or expectations for themselves. Working harder in math under a samerace teacher, for example, may make the student better prepared to take the next math course. The rolemodeling hypothesis conjectures that teachers of color provide reinforcement to students of color simply through their presence in the classroom. This mechanism can be a passive one from the point of view of teachers; they need not be active mentors. Students simply may be more motivated by exposure to samerace teachers and their professional success, which students seek to emulate (Adair, 1984; Berry, 2008; Hess & Leal, 1997). In short, numerous mechanisms may link math teacher race or ethnicity congruence with their students’ propensities to take higher math courses. Congruent teachers’ expectations may impact students directly, such as through specific encouragement to move on to more advanced courses, or indirectly, by helping students see their own math potential. Even setting teachers’ expectations aside, the presence of samerace teachers may lead students to work harder and/or perform at a higher level in math, which then prepares the student for higher math and signals to them that they are likely to be successful in a higher math course. In the next section, we turn to testing empirically whether racematching is associated with differences in math coursetaking in high school. DATA, MEASURES, AND METHODS Data for this study come from the MiamiDade County Public Schools, the fourth largest district in student enrollment in the United States. MDCPS educates nearly 350,000 students each year. The district’s population is diverse. As of 2014, 69% of the district’s students are Hispanic, 22% are Black, and 74% are eligible for free or reducedprice lunch. MDCPS is not an outlier in these demographics among its largedistrict peers. In six of the top 10 districts by enrollment across the country, the plurality of students are Hispanic,^{1} including two districts in which the majority of students are Hispanic (Los Angeles Unified School District and MDCPS). This pattern may soon become more the norm than the exception; in 2014, U.S. public school enrollment hit a milestone in which just over 50% of enrolled students identified as nonwhite (Maxwell, 2014). MDCPS provided us with course files listing the courses taken each year by every student between the 2003–04 and 2014–15 school years. A studentlevel identifier permits linking of student course records across years. In this analysis, we focus primarily on mathematics courses taken by high school students (Grades 9–12). For each course record, a course code identifies the specific course taken, and a separate identifier permits identification of the instructor of record. Using an Instructional Course Code Directory obtained from the Florida Department of Education website (Florida Department of Education, n.d.), we grouped course codes into the following categories: algebra I, geometry, algebra II, advanced math (trigonometry, precalculus, and higher), other seniorlevel math courses that are not precalculus or higher, special education math, intensive/remedial/supplemental math, and math courses at a grade level lower than high school. We used the same course codes to identify honorslevel and AP math courses across those topics. In MiamiDade County Public Schools, the secondary math course progression begins with algebra I if the student has not yet taken the course at time of start of ninth grade (G. Feild, personal communication, July 29, 2016). In this case, a student would take algebra I in ninth grade, geometry in 10th grade, and, contingent on passing the endofcourse (EOC) exams for those two courses, algebra II in 11th grade. The student would then take advanced topics (e.g., trigonometry, calculus, statistics) or a math elective in 12th grade. If, however, the student has not passed the EOC exams in ninth and 10th grade, then 11th grade is dedicated to college readiness math, which remediates those skills in preparation for retesting. Students who do not pass the algebra II EOC take liberal arts math the following year in preparation for a retest. Overall, students must take four years of math to graduate from high school, in accordance with Florida state graduation requirements. Across high schools, we observed substantial variation in the proportions of students who take which math courses and in which grade, though all regular high schools offered advanced mathematics courses, honors math courses, and—with the exception of three schools—AP math courses. The course files often show a student taking more than one math course in the same year.^{2} For purposes of identifying transitions in math coursetaking from one year to the next, we focused only on the highest level math course a student took in a given year, with “highest level” defined in the order of the standard Florida math course progression: algebra I, geometry, algebra II, advanced math (FDOE, 2014). Table 1 shows the distribution of the highest math course taken in year t+1 (conditional on taking any classes in MDCPS) for students taking algebra I, geometry, algebra II, and advanced math courses in year t. The table shows that most students during the time of our data followed the typical progression. Eightyfive percent of students taking algebra I took geometry the following year, with 10% appearing in algebra I again. Seventyfour percent of students taking geometry took algebra II the next year, with 11% taking geometry again. Among students taking algebra II, the most common math course the next year was an advanced math course (35%), but the second most common was to take no math at all (30%). Another 18% took a nonadvanced senior math course, which includes options such as advanced algebra with financial applications, business math, or math for college success. Among students taking an advanced math course, 73% of students still enrolled the next year took another advanced math course, while 22% took no math at all, and 3% took a nonadvanced senior math course. Table 1. Highest Course Taken Next Term, by Current Math Course
MDCPS administrative data include other information about students that we use in our analysis, including a binary sex variable (male/female), an indicator for free/reduced lunch eligibility (a proxy for being from a lowincome family), the number of days absent, and the number of days suspended. The data also include a single variable categorizing student race or ethnicity, following U.S. Census practice before 2010. That is, students registered as Hispanic with the school system, regardless of whether they also identified as white, Black, or another racial category, are identified only as Hispanic in the data set, which limits our capacity to disentangle race and ethnicity in the analysis. As Table 2 shows, approximately 61% of high school students in MDCPS are Hispanic, followed by Black students (29%), and white students (9%). We combine all other students—only about 1% of the data set—into a group labeled other race or ethnicity. In addition, we accessed eighthgrade math and reading achievement scores (standardized) on the Florida Comprehensive Achievement Test (FCAT), because eighth grade is the last year in which all students receive common assessments. For a subset of years, we also have access to EOC scores for algebra I (beginning in 2012) and geometry (beginning in 2013). The data also contain grades earned by the student in each course, which we convert to a 5point numerical scale (A = 5, B = 4, C = 3, D = 2, F = 1). Personnel data provided by the district contain information about the teachers of each course, including sex, race or ethnicity (coded in the same manner as for the students), years of experience in the district, and highest degree. As shown in Table 2, 51% of MDCPS high school math students are taught by a female teacher. Fortysix percent are taught math by a Hispanic teacher, 27% by a white teacher, 23% by a Black teacher, and 3% by a teacher from another racial or ethnic group. Table 2. Descriptive Statistics
Given the available race and ethnicity data, we code students as racially or ethnically congruent with their math teacher if the student and teacher are both Hispanic, both Black, both white, or both from another group; results are virtually identical if we drop students from the other race or ethnicity group, given that congruence in this small group is indeterminate. Table 3 breaks down math teacher race or ethnicity congruence by student race or ethnicity and course. Overall, given the large numbers of both Hispanic students and Hispanic math teachers, it is unsurprising that congruence is most common for Hispanic students in MDCPS. Also, just 30% of white students are taught by white teachers in algebra I, but this number climbs to 40% in algebra II and 52% in advanced math, reflecting the relative overrepresentation of white teachers in upperlevel courses. In contrast, the opposite pattern holds for Black students, 51% of whom are taught algebra I by a Black teacher but only 31% of whom are taught an advanced math course by a Black teacher. Table 3. Math Courses Taken by Student Race or Ethnicity and Congruence
METHODS We modeled the probability that a student would progress from the current math course to a “higher” math course in the following year. We coded a student as progressing after year t if the math course taken in year t+1 was a higher level than the one taken in year t. For example, an algebra I student would be coded as progressing if he or she took geometry, algebra II, or a senior or advanced math course the following year as his or her highest math course. He or she would be coded as not progressing if the next year’s (highest) math class was algebra I again, or an intensive/remedial course, or if he or she did not take math at all. We then modeled progression as follows: (1) Equation 1 says that math progression is a function of student characteristics X (sex, race, ethnicity, free/reduced lunch eligibility, eighthgrade math and reading achievement, lagged absences, lagged suspensions), teacher characteristics T (sex, race, ethnicity, years of experience, whether the teacher holds a master’s degree or higher), and classroom characteristics C, which are the classroom aggregates of the variables in X. The model also includes grade (δ), year (π), and school (γ) fixed effects. The inclusion of the school fixed effect estimates these coefficients by comparing observably similar students taking math courses in the same school, implicitly accounting for differences in access to advanced math courses in different kinds of schools. The main coefficient of interest is β_{1}, which is the coefficient on an indicator for whether the student is racially or ethnically congruent with his or her math teacher at time t. To facilitate inclusion of large numbers of fixed effects, Equation 1 was estimated as a linear probability model (i.e., via ordinary least squares).^{3} Coefficients can be interpreted as marginal effects (Angrist & Pischke, 2008). Standard errors were clustered at the classroom level. We ran similar analyses of student movement into honors and AP courses. Here, the dependent variable was set equal to 1 if the student took an honors math course (or, in other models, an AP math course) at time t+1 (and 0 otherwise), which we again modeled as a function of teacher–student race or ethnicity congruence, plus student, teacher, and class characteristics at time t. We show models with and without controls for whether the currentyear math course was an honors course. We again included school, grade, and year fixed effects. In subsequent analysis, we considered the possibility that teacher–student race or ethnicity congruence was associated with higher grades in the current math course, which may be a pathway whereby congruence influences student coursetaking behavior. The dependent variable was the course grade on a 5point scale (A is highest). Independent variables were again race and gender congruence, plus student, teacher, and class covariates. We show models with year, grade, and school fixed effects, but we also show models with schoolbycourse fixed effects and student fixed effects as well. This last approach is feasible because we pooled observations across years and math courses. For algebra and geometry, we were able to model grades in some years as a function of EOC scores as well, which helped us explore whether any observed associations between congruence and grades were driven by differences in student achievement in courses with gender or racecongruent teachers (Egalite et al., 2015) or by, potentially, differences in teacher perceptions that may go beyond student test score performance (Ouazad, 2014). RESULTS This section details the results of our analyses. We begin by estimating models of math progression, testing its association with race or ethnicity congruence among students and teachers, first across all students and then separately for different student race/ethnicity subgroups. Next, we similarly model movement into honors and AP math courses, overall and by subgroup. We conclude with an analysis of whether student grades and scores on EOC exams are associated with student–teacher congruence. MATH COURSE PROGRESSION Table 4 shows the results of models predicting math progression. Column 1 pools across all math courses, while subsequent columns show results for the individual math courses that students took at time t. Before turning to the main results regarding congruence, examination of the covariates in Table 4 is instructive. In general, female students, students with higher eighthgrade standardized scores, and students who were absent or suspended less often were more likely to advance in math. Black students advanced less often than white students, conditional on other factors, except in algebra I, where the two groups were similar. Hispanic students also were less likely than white students to advance, on average, but particularly in earlier math courses (e.g., algebra I and geometry). Among teacher characteristics, female teachers showed the pattern of being associated with lower likelihood of progression in lower math courses but higher likelihood in advanced math. Black teachers saw higher rates of progression on average but particularly in the first two math courses. We also found associations between class composition and probability of taking a higher math course the next year. In particular, taking classes with larger numbers of Black and Hispanic students and students with larger numbers of absences was negatively associated with math progression, whereas being surrounded by students with higher past math achievement was associated with higher likelihood of taking a higher math course the next year. Class composition generally was more associated with progression in more advanced math courses. Table 4. Progression to a Higher Math Course
In most courses, race or ethnicity congruence between teacher and student was positively associated with a move to a higher math course. On average across courses, having a congruent math teacher was associated with an increase of about 0.4 percentage points in the probability of advancing in math. This association was not the same across math courses. It was largest for advanced math courses (1.3 percentage points); in contrast, the point estimate was statistically indistinguishable from zero in others (e.g., algebra I). One concern about the results in Table 4 is that the sample necessarily ignores math coursetaking in middle school. Approximately 28% of students took algebra I in middle school (mostly in eighth grade), which means that the sample in Column 2 is a group of students who were not encouraged or given access to an algebra I course (or chose to wait to take it) until ninth grade. This group is likely to be lower achieving. If teacher–student race or ethnicity congruence effects are concentrated among higher achievers, the algebra I result in Table 4 may be biased. To assess this possibility, we estimated models for middle school math, overall and separately for the standard eighthgrade course (prealgebra), algebra I, and geometry (taken in middle school by only about 5% of students). Results are shown in Appendix. In no cases did we find evidence of teacher–student race or ethnicity congruence effects in middle grades, alleviating concerns about bias in the high school estimates. Returning to the high school sample, we also looked for evidence of differential associations of race congruence with math progression for students of different racial/ethnic backgrounds by reestimating the probability of course progression separately by student race or ethnicity subgroups. The results are summarized in Table 5. Over all courses, the association between course progression and the presence of a samerace or sameethnicity math teacher was largest for Black students (approximately 2 percentage points). We did not find statistically significant associations for other subgroups. Table 5. Progression to a Higher Math Course, by Student Race or Ethnicity
HONORS AND ADVANCED PLACEMENT COURSETAKING Next, we consider students’ movement into honors and AP courses. Table 6 describes honors and AP coursetaking in MDCPS (all AP courses are classified as honors). Panel A shows overall sample enrollment by course, and Panel B shows enrollment by race or ethnicity subgroup. Relatively few students took honors sections of lower math courses (12% in algebra I, 7% in geometry). For advanced math courses, all students were classified as taking honors courses. The table also shows that students in higher math courses were relatively more likely to move into honors courses the following year. About 13% of students in advanced math courses were taking AP courses; 36% of students in advanced math courses moved into an AP course the following year. Table 6. Enrollment in Honors and Advanced Placement Courses
Table 7 shows the results of predicting whether a student would move into an honors or AP course in the next year. The first six columns examine honors. Column 1 pools across math courses. As with progression to future math courses, we see that Black and Hispanic students and lower achieving students (at eighth grade), as well as students who were absent or suspended, more often were less likely to proceed into honors courses. Students were more likely to progress to honors with female, Hispanic, more experienced, and more educated teachers, and less likely in classrooms with higher proportions of boys, Black students, Hispanic students, and lowincome students, and where average achievement was lower. Table 7. Movement Into Honors and Advanced Placement Courses
Column 1 also shows that students were more likely to move into honors the next year if they were racially or ethnically congruent with their current math teacher. Conditional on other factors, this congruence was associated with approximately a 1percentagepoint increase in the probability of moving into an honors course, as compared with other students in the same school. Column 2 adds a control for whether the current math course was designated as honors. The coefficient is essentially unchanged. To provide some context, over all courses, the probability that a student would move into an honors course was 31%, so an increase of 1 percentage point is an increase of about 3% on this baseline probability. Columns 3–6 examine progression to honors separately by current math course. Each model includes the control for whether the current class was designated as honors, except for Column 6, because all advanced math courses have an honors designation in MDCPS. In each case except advanced math, race or ethnicity congruence was associated with higher rates of movement into honors courses, with estimated coefficients ranging from 0.3 (algebra I) to 0.9 (algebra II) percentage points. Columns 7 and 8 show a similar set of patterns for movement into an AP math course.^{4} Compared with other students in the same school, students who shared race or ethnicity with their current math teacher were about 0.5 percentage points more likely to take an AP course in the following year. Overall, the predicted probability of moving into an AP course was only 9.1%, making a 0.5percentagepoint increase practically significant (more than a 5% increase in the baseline probability). We also estimated models of the likelihood of moving into honors and AP courses separately by student race or ethnicity. The results are shown in Table 8. Results were mixed. For honors courses, only Hispanic students showed a statistically significant positive association with teacher congruence. Unexpectedly, Black students in fact had a negative association (p < .01). For AP courses, evidence of benefits from teacher congruence rested primarily with white students. The results suggest that white students taught by white math teachers were 4 percentage points more likely to take an AP course in the next term than other similar white students in the school. Table 8. Movement Into Honors and Advanced Placement Courses, by Student Race or Ethnicity
ANALYZING COURSE GRADES AND ENDOFCOURSE TEST SCORES Teacher–student racial or ethnic congruence may be linked to differences in coursetaking through a variety of mechanisms. One possibility is that, because of impacts on teacher expectations, teachers’ interactions with students, or role modeling effects, for example, students receive higher grades in the current math course when taught by a congruent teacher. Higher grades may reflect either greater student performance in the class (i.e., increased learning) or higher ratings from the teacher that are due to other factors (e.g., bias in grading). Receipt of higher grades may then help explain more advanced coursetaking because they represent greater preparation for future courses or because they signal to the student (or others) that future math course completion is attainable. We partially investigate this chain of logic by estimating models of course grades as a function of teacher–student racial or ethnic congruence. Table 9 shows the results, pooling across math courses. Column 1 displays results from a school fixedeffects model. Here, we found that, conditional on other factors, a student with a congruent math teacher received a grade that was approximately 0.06 points higher, on average, than other students in the same school. For reference, this association was about one fifth the size of the grade advantage that female students had over male students. In Column 2, we added a control for FCAT math score received in that year, which was only available for students in Grades 9 and 10 in 2010–11 and earlier.^{5} This score controls to some degree for math learning during the year, though the endofgrade FCAT tests did not test students on the specific material taught in the course. Results in Column 2 suggest that students received .07 more grade points when they race or ethnicitymatched with their math teacher than would be predicted by measured math achievement and other observable factors. Columns 3–6 repeat the analyses first with schoolbycourse and then with student fixed effects, with and without the FCAT control. Although the coefficient is attenuated, in all cases except in Column 6, we found a statistically significant association between congruence and course grade; the coefficient in Column 6 is virtually identical to the one estimated in Column 5 but less precisely estimated.^{6} In other words, it appears that students received higher math grades in years with congruent teachers relative to other years when those same students had incongruent teachers. Table 9. Math Course Grades
Table 10 looks specifically at algebra I and geometry after 2011, when Florida shifted to EOC testing. Because EOCs test students on course material, we can use EOC scores to investigate more directly whether teacher–student race congruence is associated with higher achievement, then secondarily whether there is a difference in course grade once any such differences in achievement are taken into account. Columns 1 and 2 show that indeed students obtained higher EOC scores with congruent math teachers than did other students in the school. Congruence was associated with about a 0.03 SD gain in both algebra I and geometry. Column 3 instead models the student’s grade in algebra I, conditional on the algebra I EOC score. Unsurprisingly, higher EOC scores were associated with significantly higher course grades. Yet, even taking EOC score into account, students with congruent teachers received course grades that were about 0.08 points higher than other students in the same school. In geometry, after the EOC score was accounted for, racial or ethnic congruence was associated with a grade increase of only about 0.03 points, though this coefficient was not statistically significant at conventional levels (p = 0.12). Table 10. EndofCourse Test Scores and Course Grades in Algebra I and Geometry
Taken together, the results in Tables 9 and 10 suggest that higher course grades associated with teacher–student race or ethnicity congruence were partially attributable to student achievement differences and also reflected, to some degree, a residual grade advantage for students with congruent teachers. Although not a direct test of mediation, these results are consistent with the hypothesis that student grade advantages under samerace or sameethnicity teachers may partially contribute to students’ increased likelihood of progressing to higher math courses when taught by those teachers. DISCUSSION AND CONCLUSIONS In this study, we investigated whether being taught by a math teacher of the same racial or ethnic background predicts greater likelihood that a student will progress in the high school math sequence. Our results are broadly consistent with other recent studies documenting the implications of teacher–student race or ethnicity congruence for student outcomes (e.g., Egalite et al., 2015; Grissom & Redding, 2016), and they contribute to the small set of studies demonstrating impacts of teacher diversity not only on sameyear outcomes but on future student outcomes as well. Using data from a diverse urban school district, we found that students who “matched” with their teachers were more likely, on average, to take higher math courses. In the typical math course, the association between congruence and progression was small for the average student, though in the most advanced courses, racial or ethnic congruence with one’s teacher was associated with a nontrivial increase of about 1 percentage point in taking another advanced course, relative to other students in advanced math courses in the school with incongruent teachers. Moreover, we found that the higher likelihood of moving on to a higher math course was concentrated among Black students. Teacher–student congruence was also associated higher likelihood of the next math course being an honors or AP course. These associations were also approximately 1 percentage point, which for AP courses in particular is relatively large, given the infrequency of AP coursetaking in the sample. The association with honors coursetaking was larger for Hispanic students and for AP courses was larger among white students. Furthermore, Black students’ likelihood of moving into honors courses was in fact negatively associated with race congruence. The mixed subgroup analysis results suggest nuance in understanding the role of samerace or sameethnicity teachers’ impacts on students, particularly in a diverse district in which a traditionally minoritized group is a large majority of the student population, and point out some patterns to be addressed in future research. Additional evidence suggests that students’ math course grades were higher with congruent teachers, and in fact even higher than would be predicted by their endofcourse test results, which were themselves positively associated with racial or ethnic matching. These results are consistent with two hypotheses: that students achieve at higher levels under congruent teachers and that they are evaluated more positively by those teachers, which may reflect positive teacher perceptions or expectations. They are also broadly consistent with the conjecture that more positive achievement outcomes may help explain why students in classrooms with racially or ethnically congruent teachers may be more likely to pursue more advanced or more challenging math course opportunities. Our findings on this point should be taken as suggestive evidence to be explored further in future research. Our findings are consistent with the view that teacher workforce diversity contributes to important educational outcomes. Teachers of color are underrepresented in math courses, and in the profession more generally; this underrepresentation is due to a variety of factors, including underrecruitment and discrimination in hiring processes, and insufficient resources, leadership, and support in their schools when they are hired, which results in higher turnover (e.g., Achinstein et al., 2010; Bianco et al., 2011; D’Amico et al., 2017; Madkins, 2011). Addressing teacher pipeline issues may help address student attainment in math. Further, our estimates highlight the need to think beyond diverse pipelines into schools to consider teacher diversity across course offerings within schools. In MDCPS, for example, we observed that Black teachers are more prevalent in lower level math courses, making it less likely that a Black student will be taught by a Black teacher once she has moved into more advanced math courses. The relative scarcity of Black teachers in upper math courses may be one reason for lower rates of AP coursetaking among Black students. The sample for our study came from MiamiDade County Public Schools, which is an unusual district in size and demographic composition—though perhaps less so on this latter dimension, given that U.S. public schools are rapidly diversifying by race and ethnicity. The setting provides an opportunity to explore teacher–student racial/ethnic congruence in a multiethnic context but also limits generalizability. We did not find much evidence of congruence effects for Hispanic students in MDCPS, which may not be surprising given that Hispanic students make up a majority of the population and that Hispanics in Miami are more socially and economically advantaged than Hispanics in other parts of the United States. Future work may extend this analysis to other urban settings, and certainly to suburban and rural settings, which may produce different results. We were also limited by the nature of the data available for the study. The administrative data coded race and ethnicity coarsely, failing to differentiate, for example, Hispanic students with different racial classifications. Future work with more precise data may be better suited to identify nuance in match effects among students and teachers identifying in multiple categories. Moreover, we lacked student and teacher survey data as well as information on school practices with regard to coursetaking that would have allowed us to delve more deeply into the mechanisms (e.g., teacher expectations, rolemodeling effects) driving the patterns we observed. Accordingly, although we are able to show here that teacher–student racial or ethnic congruence is associated with achievement and coursetaking patterns, we were unable to determine what part of this relationship directly affects student choices. Investigation of mechanisms linking such matching to student outcomes is critical for drawing firm policy recommendations from this body of research. Our findings highlight the importance of future research into the influence of race or ethnicity congruence on student academic outcomes, particularly longer term outcomes such as high school graduation and collegegoing, both of which may be affected by course choices in high school. The current study is one of the first to explore this aspect of teacher–student relationships in high school; other existing studies looked at achievement or behavior rating outcomes of elementary and middle school students. Also, most studies in the proliferating literature on teacher–student racematching concentrated on outcomes in the year that the student was taught by the racecongruent teacher. This study is among the first to consider a longer time horizon, demonstrating connections between current teacher characteristics and outcomes in subsequent years of schooling. Because coursetaking patterns in particular have been linked to outcomes such as high school graduation and collegegoing (Long et al., 2009; Rose & Betts, 2001), the evidence presented here suggests the potential for effects on these longer term outcomes of interest. Notes 1. These districts are The City School District of New York, Los Angeles Unified School District, Chicago Public Schools, MiamiDade County Public Schools, Clark County School District, and Orange County Schools. 2. The most frequent explanation for concurrent enrollment was that the second course was Intensive Math, a course offered by some of the county’s high schools (elective credit, not math credit) to provide additional support for first and second level (i.e., algebra I and geometry) students who did not pass the Florida Comprehensive Assessment Test (FCAT) in the previous year. For instance, if a student took prealgebra in eighth grade and did not pass the FCAT, he would take algebra I and Intensive Math concurrently during 9th grade. 3. Probit models with school indicator variables obtained qualitatively similar results. 4. These models condition on students enrolled in algebra II or above, given the finding in Table 6 that almost no students transition into AP courses from earlier courses. 5. In 2011, the state moved from endofgrade testing to endofcourse testing. 6. In supplementary analysis, we also modeled the probability that a student would receive a failing grade (relative to nonfailing grades) and a grade of A (relative to grades of B or less) to examine whether race congruence was more associated with outcomes at one end of the grade distribution or the other. Race congruence generally was associated with both outcomes, but the coefficients were about twice as large in the failure models than in the “A” models, suggesting that congruence may be more important on the pass/fail margin than elsewhere. References Achinstein, B., Ogawa, R. T., Sexton, D., & Freitas, C. (2010). Retaining teachers of color: A pressing problem and a potential strategy for “hardtostaff” schools. 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