Examining Organizational Practices That Predict Persistence Among High-Achieving Black Males in High School

by Kenneth Alonzo Anderson - 2016

Background/Context: This article summarizes an increasing trend of antideficit Black male research in mathematics and highlights opportunities to add to the research. A review of the literature shows that antideficit researchers often examine relationships between individual traits and persistence of high-achieving Black males in mathematics. However, opportunities for additional antideficit research include examining relationships between organizational decisions and persistence of high-achieving Black males.

Research Question: Which organizational practices predict persistence among Black males in 11th grade who have demonstrated high mathematics potential in ninth grade?

Population: Data from the High School Longitudinal Study of 2009 (HSLS:09) were used in this study to identify a national sample of high-achieving Black males. Publicly-available data from the base year (2009–2010) and the first follow-up year (2011–2012) were used in this study to examine Black male persistence in high achievement categories from ninth to 11th grades. The sample was limited to public school Black males with mathematics achievement scores in the top two national quintiles. More than 31,000 students (weighted estimates) met the study’s requirements and were included in this study.

Research Design: Using optimal resource theory, logistic and multiple regression was used to examine the relationships between school-based practices in ninth grade and student outcomes in 11th grade.

Findings/Results: Of the Black males who demonstrated high potential in ninth grade and matriculated to pre-calculus in 11th grade, 61% earned mathematics scores in the top 20%, nationally. Contrarily, only 18% of the Black males who demonstrated high potential in ninth grade, but did not matriculate to pre-calculus in 11th grade earned mathematics scores in the top 20%, nationally. Additionally, of the extracurricular activities that were examined, findings show that partnerships with community colleges and universities, science and mathematics guest speakers, and science/math-related field trips were related to increased mathematics efficacy after two years. Teacher sorting practices and professional development activities were not reliably predictive of the student outcomes that were examined in this study.

Conclusions/Recommendations: This study uses national data to demonstrate that some common organizational practices are more beneficial to high-achieving Black males than others. In particular, this study highlights the importance of developing course progress monitoring and support plans to increase the likelihood of persistence—future high achievement and beliefs about ability—for Black males who have demonstrated high potential in ninth grade. Opportunities for future research are also discussed.

Black males are represented in every achievement category, ranging from low to high. Yet, ability is often racialized (Artiles, 2011; Nasir & Shah, 2011) and much of the research about Black males in mathematics has adopted a deficit perspective by focusing on underachievement (Brown, 2011; Stinson, 2006). However, there is a growing body of research that focuses on success patterns of Black males in mathematics. Much of the antideficit research has described the success patterns from the perspective of the Black male. In particular, many of the studies indicate how Black male traits have mitigated societal challenges and facilitated success for Black males in mathematics. Despite the growing body of individual trait research, more organizational research that can inform best practices for promoting Black male success in mathematics is necessary. Thus, this study will add to the literature by examining school-based practices that lead to Black male success in mathematics. To accomplish this aim:

1.

A review of the antideficit literature in mathematics is summarized.

2.

Opportunities for additional research are identified.

3.

Principles of optimal resource theory (Anderson, 2015), the guiding framework for this study, are described.

4.

Findings are summarized in the context of optimal resource theory.

5.

A discussion of how the findings contribute to the literature and best practices for Black male achievement in mathematics is provided.

PERSISTENCE DEFINITIONS

Researchers have indicated a need for consequential interventions and research paradigms that lead to enhanced educational outcomes for Black males (Brown & Donnor, 2011; Howard, 2014). Increased persistence is a commonly-examined factor that has been linked to enhanced educational outcomes for Black males (Graham & Anderson, 2008; Schweinle & Mims, 20082009). Academic persistence among African Americans and other high school students has been conceptualized and operationalized in a number of ways. Some researchers have conceptualized academic persistence through maintenance of conditions or retention (e.g., remaining enrolled in school or programs). In a study of Texas high school students, Domina, Ghosh-Dastidar, and Tienda (2010) measured persistence by examining the number of students who remained enrolled at the same high school two years after the sophomore year. Ellington and Frederick (2010) described persistence as maintenance of grade point averages of 3.0 or higher through junior and senior years of college for Black mathematics majors. Likewise, Caldwell and Siwatu (2003) described persistence of African American and Latino high school students as representation in positive school outcome categories such as remaining enrolled in school or demonstrating high achievement.

Persistence of high school students has also been measured through expectancy. For example, Andersen and Ward (2014) examined survey data of expectancy or plans of high-achieving ninth-grade students to remain engaged in science, technology, engineering, and mathematics. Likewise, academic persistence has been commonly assessed through measurement of latent traits, such as effort, using survey data. When examining persistence among African Americans, Butler-Barnes, Chavous, Hurd, and Varner (2013) measured persistence by adapting items from existing instruments. These adapted items required students to respond to four Likert-type items: (a) If I cant get a problem right the first time, I just keep trying; (b) when I do badly on a test, I work harder next time; (c) if I dont understand something right away, I stop trying; and (d) when I have trouble understanding something, I give up.

Academic self-efficacy and identity are also two popular latent traits that have been examined in relation to persistence. Academic self-efficacy has been defined as ones belief about their ability to produce outcomes (Bandura, 1997). Identity can take many forms, but one popular conceptualization is academic identity. Academic identity is a dimension of self-concept that captures ones commitment to excellence and willingness to persist in the learning process (Bandura, 1997). Academic identity and self-efficacy are important to assess in relation to persistence because latent traits such as beliefs often influence behavior. These latent traits can be especially important for Black males because they can serve as protective factors from deleterious messaging about their ability to succeed in school and life (Graham & Anderson, 2008).

As shown above, persistence definitions can vary and provide unique insight depending on the definitions. Despite the varying definitions, persistence relative to high standardized achievement over time is inadequately addressed in the literature. Assessing persistence relative to standardized test achievement, among other factors, is important because standardized tests often serve as gateways to future opportunities for Black males. Some of these opportunities include access to higher education, financial assistance, acceptance into traditionally underrepresented disciplines, and gainful employment. Thus, high marks on standardized tests over time and latent traitsself-efficacy and identityare used as measures of persistence in this study. A review of the literature is provided next.

REVIEW OF LITERATURE

LATENT TRAITS AND PERSISTENCE

Academic Self-Efficacy

Usher (2009) noted that the literature is replete with studies that affirm the predictive power of academic self-efficacy or students beliefs about their ability to obtain educational outcomes. Bandura (1997) indicated that academic self-efficacy can develop from several sources, including mastery experiences, vicarious experiences, social persuasions, and emotional and physiological states. In more recent years, researchers have found that determinants of academic self-efficacy can differ by race. For example, Usher and Pajares (20062009) found that only two of Banduras (1997) sources of self-efficacy, mastery experience and social persuasion, were evident with a group of Black students in middle school, whereas all four sources predicted self-efficacy among White students. These findings highlight the need for culturally-responsive research designs.

In 2009, Usher also found that the type of research method used, qualitative or quantitative, may also contribute to varying explanations of self-efficacy. Using interview techniques, Usher found that students with high mathematics self-efficacy reported higher mathematics outcomes and students with low mathematics self-efficacy reported having difficulties with mathematics. Additional findings in this study indicated that (a) highly efficacious students tended to use more cognitive and metacognitive strategies in the classroom; and (b) contextual factors, chiefly course placement, had profound and long-lasting effects on students self-efficacy. Students who were placed in higher-level mathematics courses used their placements as sources of mathematics self-efficacy. Yet, students who did not advance to higher mathematics or were moved back to a previous mathematics level after experiencing difficulty generated mixed messages. Specifically, some students felt that moving back to a previous mathematics level provided opportunities for mastery, whereas one student indicated that moving back a level reinforced inadequacy. Lastly, Usher found that one of her Black male participants used the unsuccessful experiences of others as a source of self-efficacy by believing that he could be different from the unsuccessful students. Accordingly, Usher concluded that such nuanced contextual findings about self-efficacy are more likely to emerge using qualitative research.

In another study on self-efficacy and race, Schweinle and Mims (20082009) found that, regardless of the racial breakdown of the class, the self-efficacy of Black/African American students remains stable. Using analysis of variance of survey data of 170 students, Schweinle and Mims found no significant differences for Blacks/African Americans who were placed in predominately White mathematics classes relative to Blacks/African Americans who were placed in predominately Black/African American classes. The authors noted that the findings indicated that Blacks/African Americans possess fortitude or resilience to maintain mathematics self-efficacy that stems from ethnic/racial identity.

Academic Identity and Persistence

Several studies have indicated that academic identity has been associated with high mathematics achievement (Yurt & Sünbül, 2014). Using a phenomenological approach, Berry (2008) found that seven of eight high-achieving Black male participants had high academic identity. The author specifically focused on mathematics and found that academic identity was comprised of four components: (a) motivation to succeed in mathematics, (b) strong beliefs in their abilities, (c) positive self-definition, and (d) identification of a caring and encouraging teacher. Using narrative analysis procedures, McGee (2013) also found that high-achieving Black males relied on internal agency to navigate challenging situations. This form of internal agency is similar to Berrys findings and offer promise for increased mathematics achievement for Black males. McGee and Pearman (2014) reiterated the importance of fostering a positive mathematics identity for high-achieving Black males, noting that Black males are particularly vulnerable due to racialized and gendered schooling experiences. These racialized schooling experiences were also affirmed in Stinsons (2008) participatory inquiry study of four high-achieving Black males. Stinson concluded by noting that the mathematics identity of the participants served as a contributor to the success of the participants.

Despite the abundance of research on latent traits relative to persistence, nationally representative samples of Black males are largely excluded. Although many of the studies included in the review may not have been designed to be generalizable to a national population, many of the implications may be inherently applicable. Thus, findings from the aforementioned studies may be instructive for examining persistence of Black males when using nationally-representative samples.

SCHOOL-BASED DECISIONS, PROGRAMMING, AND PERSISTENCE

In addition to the need to include larger samples, more research that examines the effects of school-based decisions and practices on Black male persistence is necessary. Research has shown that schools can account for substantial variance in tests scores (Carlson & Cowen, 2015). For example, Haertel (2013) found that schools can account for more variation in tests scores than neighborhood conditions. Yet few studies provide clear insight on the effects of school-based decisions and practices, such as access to advanced coursework, teacher sorting practices, professional development opportunities, and school-based programming on Black male persistence. A review of these factors, relative to persistence, is provided next.

 Course Rigor and Persistence

Research has shown that rigorous coursework often leads to positive outcomes for students (Long, Conger, & Iatarola, 2012). In a previous section, it was noted that Usher (2009) found that having or not having access to rigorous mathematics courses can have profound and long-lasting effects on students achievement and beliefs, both positively and negatively. However, research has shown that ethnic minorities do not enroll in advanced coursework at rates similar to their peers (Shifrer, Callahan, & Muller, 2013). Likewise, examination of national data from a recent study revealed that high-achieving Black students are less likely than other racial groups to enroll in higher-level mathematics courses (Anderson, 2014). Despite these findings, implications regarding course enrollment and persistence outcomes for high-achieving Black males are less apparent.

Battey (2013) also reported that mathematics is often presented as a race-neutral discipline, but his findings showed that differential access to advanced curricula (chiefly determined by school-based practices such as tracking, referrals, and advance placement) led to inequity in access to higher education and wealth-building opportunities for students of color. In fact, Battey estimated that the collective wealth accumulation advantage for Whites over Blacks, based on access to advanced mathematics curricula in high school, was approximately $38.4 billion dollars over a 23-year span between 1982 and 2004. These findings corroborated McGee and Pearmans (2014) finding that schooling experiences are highly racialized. Considering the significance or racialized schooling experiences, especially in mathematics, additional research that informs best-practices for increasing Black male persistence in advanced mathematics curricula is necessary. Accordingly, increased persistence can lead to better outcomes for Black males, their respective families, and society.

TEACHER SORTING AND PERSISTENCE

Teacher quality is one of many factors that enhance standardized achievement. Haertel (2013) indicated that teachers account for approximately 10% of the variance on standardized tests in a single year. Anderson (2014) found that teacher self-reports of traditional forms of cognitive engagement were effective for non-Black high achievers, but were not effective for high-achieving Black males, indicating the need for more investigations of access to quality teaching and teachers. One approach to examining access to quality teaching is to examine how teachers are sorted or placed in classrooms.

 

Teacher sorting is especially important because, as mentioned, Berry (2008) indicated that Black males with high academic identity and achievement indicated that supportive and encouraging teachers contribute to the success of Black males. Furthermore, researchers have found that teacher sorting or placement of teachers within classrooms is intentional, not random, and can lead to achievement gaps, turnover, and other negative outcomes (Kalogrides, Loeb, & Beteille, 2013). When analyzing data from a large urban district, the authors found that many underqualified as well as Black and minority teachers were likely to be placed with lower achieving students. Moreover, little is known about the implications of teacher sorting and high-achieving black males. Thus, investigations of teacher sorting practices could clarify the implications for high-achieving Black males.

School-sponsored Extracurricular Activities and Persistence

Participation in extra-curricular activities has generally been associated with positive outcomes (Feldman & Matjasko, 2005). However, studies that examine relationships between Black male participation in school-sponsored extracurricular activities and persistence are negligible. Some studies have found that Black male participation in school-sponsored activities can be lead to increased leadership skills, achievement, and increased parental involvement (see Bailey & Paisley, 2004; Hrabowski, Maton, & Greif, 1998; OBryan, Braddock, & Dawkins, 2006). Despite these findings, relationships between participation in content-based extracurricular activities and Black male persistence are largely unaddressed and will be examined in this study.

 

PROFESSIONAL DEVELOPMENT AND PERSISTENCE

 

For some time, research has shown that quality teaching can enhance Black males and other underrepresented groups (see Hilliard, 2004; Ladson-Billings, 1994). Teacher professional development is one widely-used approach for enhancing mathematics teaching quality. Some researchers advocate for professional development that focuses on specialized forms of mathematics knowledge for teachers that favor strong content knowledge, coupled with pedagogical knowledge (Stylianides & Stylianides, 2010). Others argue for professional development that incorporates social justice perspectives to increase mathematics knowledge (Gutierrez, 2009; Leonard, Brooks, Barnes-Johnson, & Berry III, 2010). Despite the wide-ranging perspectives, the effectiveness of mathematics professional development on Black male mathematics achievement persistence is not apparent. In Jackson and Wilsons (2012) review of the mathematics literature covering a 20-year span, the authors found that the research base does not move beyond broad principles and inadequately informs instructional practice that supports African American students. Likewise, the authors advocate for more empirical studies that link practice with mathematics achievement and identity development. These recommendations will be addressed in this study.

Literature Review Summary

As shown in the review of literature, there is an emerging body of literature that connects latent traits, such as self-efficacy and identity, to Black male achievement in mathematics. However, structural supports matter and the onus of Black male mathematics success is not solely due to individual determination. Schools play a significant role in the development of latent traits, but the extant literature does not directly examine the relationships between school-based practices and latent trait development for Black males. Thus, an empirical investigation of school-based practices that support the development of these latent traits is examined in this study. Considering the scant studies that assess Black male persistence outcomes using standardized tests, this study also addresses this void. In particular, this study investigates school-based practices that support Black male persistencehigh achievement on standardized mathematics tests or enhanced latent trait developmentover time. Thus, this study examines the following overarching research question: Which organizational practices predict persistence among Black males in 11th grade who have demonstrated high mathematics potential in ninth grade?

Based on the overarching research question, two specific research questions are examined.

1.

When controlling for individual characteristics of Black males who have demonstrated high mathematics potential in ninth grade does (a) teacher sorting, (b) course placement, (c) professional development activities, or (d) school-sponsored extra-curricular activities predict which Black males will earn scores that are in the top 20%, nationally, in 11th grade?

2.

When controlling for mathematics course rigor in eighth grade and SES, is there a sustainable relationship between school-sponsored extracurricular activities in ninth grade and mathematics self-efficacy and identity in 11th grade for Black males who have demonstrated high mathematics potential?

THEORETICAL FRAMEWORK

The theoretical framework, optimal resource theory (Anderson, 2015) was selected for this study. Optimal resource theory is defined as an anti-reproduction perspective that assesses the influence of internally-controlled micro-policies and micro-practices on positive student outcomes or personal development (Anderson, 2015, p. 27). Optimal resource theory (ORT) was developed because many theories used in educational research are largely comprehensive and address systemic issues. Yet, systemic theories may unintentionally lead to organizational excuse-making. For example, common narratives such as poverty are often cited as a reason for underachievement (Brown, 2011). However, school leaders make decisions that may support or inhibit learning for students in poverty. Accordingly, ORT provides a framework that allows school leaders to assess outcomes associated with internal decisions, despite systemic circumstances.

Optimal resource theory adopts a pragmatic approach that focuses on incremental, rather than systemic change, by examining micropolicies and micropracticespractices that can be modified at the local education level. Like systemic issues, micropolicies and micropractices warrant theoretical framing because macro or externally-determined factors often lead to excuse-making or limited insight for best practice. ORT requires organizations to assess the effectiveness of unique decisions that are made, despite macrolevel mandates or systemic challenges, such as federal policy, racism, or classism.

Although ORT is not designed for comprehensive reform, it is informed by reproduction theory (Bourdieu & Passeron, 1977), schooling and resource considerations (Bowles & Gintis, 1976), resistance in education (Giroux, 1983), and phenomenological variant of ecological systems theory (Spencer, Dupree, & Hartman, 1997). Specifically, concepts from the noted authors were used to develop ORT principles. The chief ORT principle requires that the outcome of interest must include student achievement or personal development. Additional governing principles denote that (a) youth development is complex, thus multiple variables of interest must be examined, (b) externally controlled variables should only be included as means of accounting for external forces, not alleviating onus of responsibility for youth development, (c) internally-controlled factors should be the primary variables of interest, (d), incremental rather than comprehensive reform should guide studies employing ORT, since externally controlled issues are not primary points of emphasis, and (e) guidance for resource maximization should emanate from the results. Figure 1 provides a graphical representation of ORT.

Figure 1. Optimal Resource Theory (ORT). The center circle represents ORTs chief principle. Outer circles represent governing principles. Reprinted with permission from the Journal of Negro Education.

ORT was selected for use in this study because it provides a framework to address a significant gap in the literature regarding Black males and mathematics achievement. As noted in the literature review, much of the Black male mathematics achievement research documented how internal agency, such as self-efficacy and identity, supports achievement. However, it is unclear how school-based practices support Black male mathematics achievement. ORT aims to inform best practices by providing a framework that examines the influence of school-based practices, while controlling for other factors. This aim is consistent with this study and is therefore selected as the guiding framework.

METHOD

SAMPLE

In order to assess persistence for a national sample of high-achieving Black males, data from the High School Longitudinal Study of 2009 (HSLS:09) (Ingels et al., 2011) were used in this study. HSLS:09 began in 2009 and was primarily designed to examine high school, postsecondary, workforce, and adulthood transitions. Publicly-available data from the base year (20092010) and the first follow-up year (20112012) were used in this study to examine Black male persistence in high achievement categories from ninth to 11th grades. The sample was limited to public school Black males with mathematics achievement scores in the top two national quintiles. Mathematics achievement scores were generated from an algebraic reasoning assessment (M = 50, SD = 10) administered by the HSLS:09 research team. Quintiles were calculated by the HSLS:09 research team, resulting in 20% representation of students in each quintile.

PERSISTENCE

Persistence is operationalized in the study as earning standardized algebra scores in the top national quintile in 11th grade after demonstrating high potential in ninth grade. High potential is defined as having achieved algebra scores in the top 40% in mathematics in ninth grade relative to all other ninth grade students in the United States. Percentiles were determined from quintile rankings provided by the HSLS research team. Quintile rankings were determined by sorting the nationally representative sample of ninth-grade student test scores in order from least to greatest, then splicing them into five equal groups. Thus, the first quintile represents scores in the bottom 20% of test scores; whereas the fifth quintile represents scores in the top 20% of test scores. In other words, scores in the fifth or top quintile represent scores that are higher than 80% of the population of ninth-graders in the United States. Thus, students who persisted earned scores in the top 20% in 11th grade, relative to a national representative sample of students, by remaining in the fifth quintile or moving up to the fifth quintile from the fourth quintile.

MEASURES

Control Variables

ORT principles number one and two indicate that youth development is complex and accordingly externally controlled variables should be included in research designs (Anderson, 2015). Thus, several control variables were included. Eighth-grade course rigor categories were included as a covariate since it may affect high school course enrollment, efficacy, and identity. Four eighth-grade rigor categories were created: (1) math 8, (2) honors math 8 and pre-algebra, (3) algebra I, and (4) algebra II or higher. Another control variable was socioeconomic status (SES). SES was calculated by the HSLS:09 research team using survey items from the parent survey that assessed parents education, occupation, and family income.

Predictors and ORT

ORT principle number three advocated for inclusion of manipulable, internally controlled variables when assessing student achievement or personal development (Anderson, 2015). Consistent with optimal resource principles, variables within the control or sphere of influence of school personnel that predict persistence were primary variables of interest. These variables were advanced course enrollment, teacher sorting, and school-based programming.

Advanced Course Enrollment

The HSLS:09 research team collected data on 17 named mathematics courses and a compilation of courses deemed as other. These courses were grouped into two rigor categories, advanced or not advanced. Accordingly, trigonometry, pre-calculus (or some analysis and functions course), calculus, and advanced placement (AP) calculus were deemed advanced for a junior and pre-algebra, algebra IIII, geometry, and analytic geometry were deemed not advanced for a junior. All remaining courses such as statistics or integrated math had very low frequencies (less than two percent of the population) and were excluded from the analysis. Although matriculation to advanced coursework is not the sole responsibility of school leaders, monitoring course matriculation and associated support for high-ability students is a practice that is within the schools control. Thus, course enrollment is consistent with ORT principle number three.

Teacher Sorting

School administrators consider a host of variables when sorting or assigning teachers to classes. Some considerations include teacher credentials, content knowledge, and experience. Teacher certification was also of interest in this study, but was excluded due to missing data and minimal variation of certification types. Approximately 72% of the students included in the sample, with corresponding teacher certification data, were taught by certified teachers. However, certification data was not available for approximately 27% of the sample. Mathematics content knowledge was assessed using the number of courses taken by the ninth grade mathematics teacher. Thus, the study examines the relationship between teacher assignment to classes based on mathematics content preparation and persistence. Another teacher sorting variable of interest is an item from the HSLS:09 teacher survey. The item asked teachers to respond to the extent to which they agreed or disagreed with the following statement: noncollege prep courses are assigned to teachers who are new to the profession. Teachers response options were: strongly agree (1), agree (2), disagree (3), and strongly disagree (4). Since interpretation of magnitude is challenging, the item was recoded into a dichotomous variable for this study by collapsing the former two categories and the latter two categories into generally agree (0) or generally disagree (1). Inclusion of teacher sorting, or assignment to classrooms, based on content preparation and experience is consistent with ORT principles because teacher sorting is largely determined at the school level.

School-based Practices

Consistent with ORT principle number three (inclusion of internally controlled variables), 10 items from the administrator survey given by the HSLS:09 research team were used to assess the effects of school-based programming and practices. Administrators were required to respond with yes (1) or no (0) regarding whether or not the school offered or required the various activities listed below:

"

holds math or science fairs/workshops/competitions;

"

takes students on math- or science-relevant field trips such as to a city aquarium or planetarium;

"

tells students about regional or state math or science contests, math or science web sites and blogs, or other math or science programs online or in the community;

"

partners with community colleges and universities that offer summer math/science programs;

"

brings in science and math guest speakers;

"

takes students on science/math-related field trips;

"

requires teacher professional development in how students learn math/science;

"

requires teacher professional development in how to increase students interests in math/science;

"

sponsors a math/science after school program; and

"

pairs students with mentors.

Data reduction techniques, specifically, principal components analysis using promax rotation was used to identify underlying factors. Scree plots were examined and components with eigenvalues greater than one were retained. Items with loadings greater than .40 were summed and retained for analysis. This procedure essentially groups the items into larger categories based on the administrators responses, allowing conclusions to be drawn about a set of activities rather than an individual activities.

DEPENDENT VARIABLES

Test Score Categories

Methodological parityrecycling the same types of analysesis common in large-scale, national research. Specifically, continuous outcomes, especially test scores, are often dependent variables of interest. Although test score use is common, increases or decreases in a few points on a standardized test do not often demonstrate the true meaning of test score differences. Thus, categorical outcomes were used in the study. Specifically the outcome of interest, persistence in the top quintile (top 20%), versus not persistent in the top quintile, based on standardized mathematics scores, was chosen. These categories have clear meaning and are more useful for developing policy and practice.

Latent Traits

Mathematics identity and efficacy were used as control variables when assessing standardized achievement, but were also used as outcome variables when assessing the effects of school-based programming. Mathematics identity and mathematics efficacy variables created by the HSLS:09 research team were included. Mathematics identity was captured using principal components analysis of the student survey items: (a) ninth grader sees himself as a math person and (b) others see ninth grader as a math person. Mathematics efficacy was also measured using principal components analysis of the following items: the degree to which the ninth grader (a) is confident that he can do an excellent job on tests in this course, (b) can understand fall 2009 math textbook, (c) can master the skills being taught in this course, and (d) is confident he can do excellent job on fall 2009 math assignments. The HSLS:09 research team reported that the Cronbachs alpha coefficients, indicating reliability, for mathematics identity and efficacy were .88 and .89, respectively.

ANALYSIS

To accommodate the multistage sampling method of HSLS:09, the balanced repeated replication procedure for survey data in Stata 12 was used to correct standard errors and generate population estimates from the sample. Descriptive statistics and pairwise correlations using Bonferroni corrections were examined before conducting analyses. Thereafter, a series of multiple logistic regression models were examined to assess the first research question. Logistic regression allows the researcher to predict group membership. In this case, organizational factors that predict Black males who persist in the top 20% nationally, relative to those who do not persist in the top 20%, after having demonstrated high potential in ninth grade were examined. Lastly, a series of multiple linear regression equations were run to assess the relationship of school-based programming in ninth grade on mathematics efficacy and identity in 11th grade, controlling for rigor of eighth grade mathematics course and SES. Several models were run in this study, but only significant findings are reported.  

RESULTS

 

DESCRIPTIVE STATISTICS

 

Table 1 shows that ninth-grade teachers had taken between five and six mathematics courses before teaching. Mean scores, based on the coding of the courses, show that students who demonstrated high potential in ninth grade had typically taken honors math eight or pre-algebra in eighth grade. Additional means and standard deviations are included in Table 1 as well.

Table 1. Descriptive Statistics for Continuous Variables
Measure	M(SD)	95% CI
Teacher Content Knowledge	5.61 (0.26)	[5.10, 6.11]
Math Identity	0.45 (0.12)	[0.20, 0.69]
Math Efficacy	0.42 (0.15)	[0.13, 0.71]
Mathematics Course Rigor in 8th grade	2.35 (0.14)	[2.07, 2.63]
SES	0.04 (0.10)	[-0.15, 0.22]
Extra-curricular (set one)	1.89 (0.17)	[1.55, 2.22]
Extra-curricular (set two)	1.68 (0.15)	[1.39, 1.97]
Professional Development	1.27 (0.13)	[1.02, 1.52]

Data Reduction

The final solution for the principal components analysis shows that three related factors were retained. The factors were labeled extracurricular set one, professional development, and extracurricular set two. The items and associated loadings are presented in Table 2.

Table 2. Factor Loadings of Principal Components with Promax Rotation of School-Based Practices
Item	Extra-Curricular (Set one)	Professional Development	Extra-Curricular (Set two)
Partners with Community Colleges and Universities that offer Summer Math/Science Programs	0.48	-0.01	0.23
Brings in Science and Math Guest Speakers	0.56	-0.08	0.05
Takes Students on Science/Math-related Field Trips	0.63	0.10	-0.14
Requires Teacher Professional Development in How Students Learn Math/Science	0.17	0.60	-0.11
Requires Teacher Professional Development in How to Increase Students Interests in Math/Science	-0.16	0.71	0.09
Sponsors a Math/Science After School Program	0.02	-0.19	0.53
Pairs Students with Mentors	0.05	0.00	0.62
Note: Factor loadings > .40 are in boldface.

Correlations

Significant correlations (p < .05) show that several relationships between outcome variables are evident. These significant correlations do not imply causality, but offer encouragement for further investigation. In this study, there is a positive relationship between Black males earning scores in the top 20% and several factors. These factors include matriculation to pre-calculus in 11th grade, assigning less experienced teachers to college-prep classes, mathematics course rigor in eighth grade, and SES. In addition, extracurricular activities (set one) were related to mathematics efficacy and professional development was related to mathematics identity after two years (see Table 3).

Table 3. Summary of Pairwise Correlations
Measure	Top 20%	Pre-calculus	Teacher Content Knowledge	New Teacher Placement	Math Identity	Math Efficacy	Mathematics Course Rigor in 8th grade	SES	Extra-curricular (set one)	Extra-curricular (set two)	Professional Development
Top 20%	1.00
Enrolled in Pre-calculus	.42*	1.00
Teacher Content Knowledge	.02	-.06	1.00
New Teacher Placement	.23*	.03	-.23*	1.00
Math Identity	.03	-.02	.04	-.10	1.00
Math Efficacy	.10	-.10	-.03	.02	.45*	1.00
Mathematics Course Rigor in 8th grade	.19*	.24*	-.07	.04	.22*	.02	1.00
SES	.24*	.11	.11	-.01	-.01	-.02	.07	1.00
Extra-curricular (set one)	.15	.24*	-.03	-.13	.13	.27*	-.10	.14	1.00
Extra-curricular (set two)	-.02	-.05	.19*	-.33*	.13	.06	-.17*	.26*	.20*	1.00
Professional Development	-.01	-.09	.05	.11	.25*	.01	.09	-.12	.15	.19*	1.00
Note: Top 20% = Earned Scores on Standardized Mathematics in the Top 20% Nationally *p < .05

Course Enrollment

Enrolling in just any one of the suite of advanced courses (trigonometry, pre-calculus, calculus, and advanced placement calculus) in 11th grade did not predict Black males who scored in the top 20% in 11th grade, so results are not reported. However, Table 4 shows that enrolling specifically in pre-calculus in 11th grade reliably predicts Black males who scored in the top 20% in 11th grade. Specifically, converting the odds ratios (listed in Table 4) to probabilities indicate that Black males who demonstrated high potential in ninth grade were 61% likely to earn scores in the top 20% in 11th grades. Black males who demonstrated high potential in ninth grade, but did not enroll in pre-calculus in 11th grade were about 18% likely to earn scores in the top 20% in 11th grade. Figure 2 shows the breakdown of pre-calculus enrollment in 11th grade for Black males who have demonstrated high potential in ninth grade.

Table 4. Multiple Logistic Regression of Characteristics Predicting Persistence and Growth in Top Quintile in 11th Grade
Variable	Odds Ratio	Standard Error	t	p	95% CI
Pre-Calculus	8.71*	7.72	2.44	0.02*	[1.52, 50.05]
Mathematics Identity	0.86	0.38	-0.34	0.74	[0.37, 2.04]
Mathematics Efficacy	1.62	1.08	0.72	0.47	[0.43, 6.05]
Mathematics Course Rigor in 8th grade	1.52	0.79	0.80	0.42	[0.54, 4.22]
SES	2.43	1.15	1.88	0.06	[0.96, 6.17]
Constant	0.15	0.12	-2.39	0.02	[0.03, 0.72]
F	2.64*			0.02*
Note. Population N = 31,080, Observations n = 162, CI = confidence interval
*p < .05

Figure 2. Breakdown of 11th-grade pre-calculus enrollment for black males who received mathematics scores in the top two national quintiles in ninth grade.

Teacher Sorting

When controlling for mathematics identity, efficacy, eighth-grade course rigor, and SES, models that examined the relationship between teacher sorting (based on teacher content preparation and principal placement of new teachers) were not reliably predictive of Black males who earned top 20% scores in 11th grade. Thus, additional results are not reported.

School-based Programming

Teacher professional development in ninth grade was not predictive of standardized achievement outcomes in 11th grade, so results are not reported. However, Table 5 shows that school-sponsored extracurricular activities (set one) from ninth grade were significantly related to increased mathematics efficacy in 11th grade. Specifically, partnering with community colleges and universities that offer summer mathematics/science programs, bringing in science and mathematics guest speakers, and taking students on science/math-related field trips demonstrated sustainable relationships after two years. For each additional activity offered by the school in ninth grade (partnering with community colleges, guest speakers, and field trips), the model predicted considerable increases in mathematics efficacy (approximately 1.7 standard deviations). Extracurricular activities (set two) and teacher professional development activities were not significantly related to mathematics efficacy and identity after two years.

Table 5. Multiple Regression of Characteristics Predicting Mathematics Efficacy in 11th Grade
Variable	B	Standard Error	t	p	95% CI
Extra-curricular Set 1	0.25*	0.11	2.24	0.03*	[0.03, 0.48]
Mathematics Course Rigor in 8th grade	-0.04	0.15	-0.28	0.78	[-0.34, 0.26]
SES	0.00	0.15	0.01	0.99	[-0.30, 0.31]
Constant	0.45	0.13	3.45	0.00	[0.19, 0.70]
F	2.06			0.11
Note. Population N = 31,850, Observations n = 161, CI = confidence interval
*p < .05

DISCUSSION

Results in this study have a number of implications. A major principle of optimal resource theory is to identify organizational practices that predict positive student outcomes and personal development and can inform best practices. Accordingly, findings are discussed relative to the conceptual framework.

Course Enrollment

Course enrollment findings are consistent with previous findings regarding the need for rigor (see Shifrer, Callahan, & Muller, 2013). However, findings indicate that enrolling in pre-calculus in 11th grade, not just any advanced course, may be conducive to predicting standardized outcomes for Black males. Since pre-calculus enrollment in 11th grade is generally low (24%) for Black males who have demonstrated high potential in ninth grade, these results may be used to set policy and provide guidance for enrollment progressions for Black males who have demonstrated high potential. Although one study should not be used as the sole indicator of future policy and practices, findings suggest that setting goals and establishing progress monitoring plans with Black males (and their caregivers) who have demonstrated high potential in ninth grade to enroll in pre-calculus by 11th grade may be instrumental in improving standardized achievement. Such progress monitoring may provide the additional support advocated by other Black male high-achievement researchers (see Milner, Tenore, & Laughter, 2008). Moreover, these findings provide a research model that can be adapted and tested in local districts and schools. If adapted in local contexts, collective findings may be used to select an appropriate and empirically-supported progression of coursework that promotes high achievement for Black males.
 

Since optimal resource theory emphasizes assessing the effectiveness of micropolicies and micropractices on positive student outcomes, researchers should expect incremental progress, rather than extreme outcomes (Anderson, 2015). As noted in a previous section, the probability of earning top 20% scores based on enrolling in pre-calculus in 11th grade was .62. Thus, the model does not suggest perfect prediction. These findings indicate that there are additional factors that were not addressed in this study that may also be predictive of sustainable standardized achievement outcomes. In particular, examination of teaching quality may provide additional insight for best practices.

School-based Programming

Relative to latent traits, the model predicts that three specific activities may lead to substantial and sustainable effects on mathematics efficacy. These activities were (a) partnering with community colleges and universities that offer summer mathematics/science programs, (b) bringing in science and mathematics guest speakers, and (c) taking students on science/math-related field trips demonstrated sustainable relationships after two years. In concert with optimal resource theory, these findings offer clear guidance to practitioners. Considering that school resources are often limited, school leaders may consider allocating resources and forming partnerships to ensure that the three aforementioned extracurricular activities are included. Furthermore, since (a) school-sponsored mathematics and science after-school activities and (b) pairings with mentors did not enhance mathematics efficacy or identity, the designs and quality of these programs should be examined. For example, mentoring programs often do not generate conclusive results because opportunities for meaningful relationships take time and mentoring benefits are not always quantifiable (Anderson, 2007).

RECOMMENDATIONS FOR FUTURE RESEARCH

One particular nonsignificant finding that is of interest is that mathematics efficacy and mathematics identity did not predict standardized test results for Black males. These findings may suggest that traditional measures of academic efficacy or identity may not appropriately capture McGees (2013) notion of internal agency or Jetts (2010) assertions of spirit. Accordingly, these findings indicate the need for culturally-responsive measures and should be examined in the future. Furthermore, the nonsignificant findings may highlight the need for more academic interventions to complement the development of latent traits. Hence, an appropriate balance between enhancing beliefs and improving actual mathematics knowledge and skills of Black males is warranted.

In this study, teacher sorting or placing teachers based on mathematics content preparation were not predictive of sustainable effects on standardized achievement. These findings should be investigated further because state requirements have evolved over time, with some states relaxing standards while others have tightened standards to obtain teacher certification (Boyd, Goldhaber, Lankford, & Wyckoff, 2007). Moreover, the evolution of standards coupled with the inclusion of new and experienced teachers in this study may confound the meaning of the number of courses taken relative to certification. Interestingly, although not statistically significant in the model, placement of new teachers in ninth grade was significantly correlated with Black male persistence in 11th grade. Specifically, administrators that indicated agreement with the practice of assigning new teachers to college preparation courses were correlated with Black males who persisted in the 20%, nationally. These findings indicate that additional research on teacher placement practices and standardized results for Black males warrant further investigation.

CONCLUSION

 

In this special issue, one chief aim was to identify organizational practices that improve Black male school success. To address this chief aim, this study addressed one overarching question:

Which organizational practices predict persistence among Black males in 11th grade who have demonstrated high mathematics potential in ninth grade?

Findings support the special issues aim to identify structures that improve Black male success by documenting the predictive power of matriculating to pre-calculus, not just any advanced mathematics course in the 11th grade. Despite the promising findings, data in this study show that even when Black males demonstrate high potential on standardized tests, matriculation to pre-calculus in 11th grade is rather limited. In addition, this study identifies specific extra-curricular activities that are predictive of mathematics self-efficacy for Black males who have demonstrated high potential in ninth grade. All findings were sustained over two years and provide explicit guidance for this trend to be examined in local contexts.

This study demonstrates the power of predictive analytics and provides a model that can be adapted to local contexts when attempting to devise strategies to support high-achieving Black males. Overall, findings in this study support the following recommendations for high-achieving Black males.

1.

Schools should establish course progress monitoring procedures during the ninth-grade year to ensure that Black males are receiving appropriate mathematics rigor.

2.

Schools should regularly evaluate the relationship between school-sponsored extra-curricular activities and personal development of Black males.

3.

Schools should use culturally-responsive evaluation and research techniques that inform decisions for investment in promising school-sponsored extra-curricular activities for Black males.

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Cite This Article as: Teachers College Record Volume 118 Number 6, 2016, p. 1-26 https://www.tcrecord.org ID Number: 19965, Date Accessed: 10/20/2021 2:05:40 AM Purchase Reprint Rights for this article or review