Relation of Opportunity to Learn Advanced Math to the Educational Attainment of Rural Youth

Abstract

Our study examined the relation of advanced math course-taking to the educational attainment of rural youth. We used data from the Educational Longitudinal Study of 2002. Regression analyses demonstrated that when previous math achievement was accounted for rural students take advanced math at a significantly lower rate than urban students. Compared to urban students, rural students have less change in their math achievement from 10th to 12th grade, are less likely to be enrolled in a 4-year college two years postsecondary, and these differences are explained by advanced math course-taking. Limitations, implications, and future research directions are discussed.

Opportunity to learn (OTL) is the core of schooling as it refers to the content one has the chance to learn via coursework or instruction (Schmidt and McKnight 2012). Despite the ubiquitous notion of equal educational opportunities for all in the U.S. and considerable efforts by courts and policymakers to improve the OTL (Geiser and Santelices 2004; Santoli 2002; Schmidt and McKnight 2012), substantial inequities in the OTL remain, especially in terms of advanced math course-taking (Lee and Ready 2009; Welner and Carter 2013). Furthermore, inequities in the OTL advanced math are central to differences in the educational attainment (e.g., achievement, college enrollment) of youth from minority, low SES, and English Language Learner backgrounds (Adelman 1999; Flores 2007; Kelly 2009; Lee and Bryk 1988; Riegle-Crumb and Grodsky 2010; Wang and Goldschmidt 1999).

One problem is little research on math education and course-taking has focused on rural youth (Anderson and Chang 2011; Howley et al. 2005; Reeves 2012). This neglect is significant because approximately 10 million public school students (20%) attend rural schools (Provasnik et al. 2007; Strange et al. 2012). In addition, rural youth less often have access to and take advanced math (Anderson and Chang 2011; Haller et al. 1993; Planty et al. 2006). In our view, a more important problem is that previous research has largely not examined whether rural students’ inequity in OTL advanced math actually relates to their educational attainment (for an exception see Reeves, 2012). Moreover, research on advanced math course-taking has rarely examined student diversity in moderating the relation between math course-taking and educational attainment (Gamoran and Hannigan 2000; Rickles 2013; Riegle-Crumb and Grodsky 2010), with only a handful of studies beginning to consider race/ethnicity and SES as moderators (Byun et al. 2015; Long et al. 2012; Roth et al. 2000–2001). Accordingly, our purpose was to examine the relation of the OTL advanced math to the educational attainment (i.e., changes in math achievement across high school, college enrollment) of rural youth. Toward that end, we use data from the Educational Longitudinal Study of 2002 (ELS:2002) that has the most recent, longitudinal, and large-scale nationally representative data available for course-taking research that follows participants across high school and into the postsecondary years.

Concept of and Advanced Math Course-Taking as an OTL

OTL emerged in the 1960’s as concept to clarify the learning process and national differences in achievement (Schmidt and McKnight 2012). OTL has been measured by teacher-reports of whether test content has been covered, the textbooks used, and the content standards that were followed. However, research has demonstrated that course-taking may be the most influential factor in learning and achievement (Lee et al. 1998; Wang and Goldschmidt 2003). Thus, we focus on math course-taking as a key OTL because course-taking captures a vital schooling experience, the curriculum (Schneider et al. 1998; Wang and Goldschmidt 2003), and, as discussed next, course-taking in math may be especially important to educational attainment.

Course-taking represents the level of courses taken over time and provides precise data on students’ OTL. Consequently, course-taking is more predictive of educational attainment than less precise measures such as number of courses completed, credits accrued, and curricular track (e.g., college preparatory, vocational) (Planty et al. 2007; Stevenson et al. 1994). In addition, subjects with more sequentially organized and clearly differentiated courses (e.g., math) are more strongly related to educational attainment than subjects that have less sequentially organized and differentiated courses (e.g., science; Adelman 2006; Schneider et al. 1998). Advanced math course-taking likely relates to math achievement because when students take advanced math they have sufficiently mastered lower level content and then had the OTL additional math concepts and principles (Burkam and Lee 2003; Dalton et al. 2007). Advanced math course-taking may also predict college enrollment because the level of math taken is central to admission decisions and more so than other subjects (Adelman et al. 2003; Riegle-Crumb and Grodsky 2010; Schneider 2003).

Indeed, completing advanced math has a strong link to educational attainment. For example, taking low-level (e.g., basic math or Algebra I) and mid-level (e.g., Algebra II) math relates to significantly smaller gains in math concepts and problem-solving than taking advanced math (e.g., Pre-Calculus, Calculus) (Rock et al. 1995). Advanced math course-taking is more predictive of math achievement than prior achievement and family background (Schneider et al. 1998; Wang and Goldschmidt 1999) and more predictive of college enrollment, selectivity, and adulthood earnings than course-taking in other subjects (Adelman 1999; Adelman et al. 2003; Altonji 1995; Joensen and Nielsen 2009; Levine and Zimmerman 1995; Rose and Betts 2004; Schneider 2003). Furthermore, propensity score matching analyses have indicated that the relation between advanced math course-taking and educational attainment is causal (Byun et al. 2015; Leow et al. 2004; Long et al. 2012).

Advanced Math Course-taking among Rural Youth

Rural high school graduates earn the same number of math credits as urban and suburban graduates, but the level of math they take may differ. For example, data from the ELS:2002 demonstrated rural graduates earn an average of 3.6 math credits whereas urban and suburban graduates earn an average of 3.6 and 3.5 credits, respectively, and these are not significantly different (Planty et al. 2006). Furthermore, findings from the 2005 NAEP High School Transcript Study indicated the proportion of rural high school graduates that earn 3.1 or more math credits is similar to graduates from urban fringe areas/large towns (urban fringe are densely settled places and areas within Metropolitan Statistical Areas or MSAs classified as urban and large towns are places outside MSAs with populations greater than or equal to 25,000) and central cities of MSAs; Anderson and Chang 2011).

However, some findings indicate that rural students are less likely to take and be offered advanced math than urban and/or suburban students. For example, significantly fewer rural high school graduates take Calculus (12%) than urban fringe (17%) and central city (18%) graduates (Anderson and Chang 2011). In addition, significantly fewer rural schools offer AP Calculus AB, AP Calculus BC, and AP Statistics (58%, 17%, and 17%, respectively) than urban fringe (84%, 43%, and 43%, respectively) and central city (84%, 44%, and 44%, respectively) schools (Anderson and Chang 2011). While smaller schools offer fewer advanced courses in all subjects (Iatarola et al. 2011; Monk and Haller 1993), the inequity in advanced course offerings for rural students is larger for math than science or language arts (Barker 1985; Haller et al. 1993).

Though previous research has not directly examined the link between rural students’ OTL advanced math and educational attainment, differences in educational outcomes that may be related to rural students’ inequitable OTL advanced math are apparent. For example, rural youth have lower rates of college enrollment and bachelor’s degree completion than urban and/or suburban youth (Byun et al. 2012a; Kusmin 2007; Provasnik et al. 2007). In addition, rural high school graduates more often attend public and non-selective colleges whereas urban and suburban graduates more often attend private and selective colleges (Byun et al. 2012b). Moreover, advantaged rural students (e.g., have college-educated and professional parents, better paid and educated teachers, school with higher attendance and completion rates, and are in an academic program) complete fewer years of education than advantaged urban students (Blackwell and McLaughlin 1999).

Another potential outcome that may be related to rural students’ inequitable OTL advanced math is math achievement, but findings on this measure of educational attainment have been mixed. Studies that are now dated and/or controlled for SES have found few differences between rural, urban, and/or suburban students. For example, several studies have demonstrated that rural students’ math achievement was comparable to suburban and/or urban students (Coladarci and McIntire 1988; Fan and Chen 1999; Haller et al. 1993; Lee and McIntire 2000). In addition, Howley and Gunn (2003) reviewed NAEP data from 1978 to 1992 and concluded there were little differences in rural students’ math achievement. Williams (2005) used data from the 2000 Programme in International Student Assessment (PISA) and demonstrated that rural youth in the U.S. had significantly lower math achievement than youth from medium-size communities. However, there was no difference after controlling for SES. Most recently, Provasnik et al. (2007) used 2005 NAEP data and found significantly fewer 12^th grade rural students were proficient in math (21%) than suburban students (25%), but these analyses did not account for important confounds such as SES.

Reasons for rural students’ inequitable OTL advanced math have not been clearly identified (Anderson and Chang 2011; Iatarola et al. 2011), but several characteristics unique to rural youth and schools are likely involved. Federal incentives to increase advanced course-taking among minority youth may play a role because this policy leads schools with higher proportions of minority youth to offer advanced courses (Iatarola et al. 2011). These incentives may not affect advanced course offerings in rural schools as much because significantly higher proportions of rural students are White (78%) than urban (35%) and suburban (62%) students (Provasnik et al. 2007). Other reasons for rural students’ inequitable OTL advanced math may be because it is not practical to provide advanced courses for small numbers of students (Anderson and Chang 2011; Hannum et al. 2009; Jimerson 2006) and rural schools have difficulties recruiting and retaining teachers certified to teach advanced courses (Monk 2007; Monk and Haller 1993). Iatarolo et al. (2011) examined these two factors and found that insufficient numbers of students was a determinant of advanced course offerings in small Florida schools, especially for math and science, but teacher shortages was not.

Distinct rural values and perspectives may also be a factor. Specifically, according to the attachment to place perspective rural youth have strong connections to place and people that may shape their educational plans and opportunities to local conditions (Elder and Conger 2000; Howley 2006; Petrin et al. 2014). Consequently, rural youth may not be offered or interested in taking advanced math because many rural jobs (e.g., mining, farming) do not require advanced math (Anderson and Chang 2011). Additionally, according to the cosmopolitan or modern perspective youth should strive for individual success and acquiring wealth, material goods, and status (i.e., more cosmopolitan or modern goals). However, for rural youth pursing these ambitions may require them to leave their community (Howley et al. 1996, 2005; Howley and Gunn 2003; Kannapel and DeYoung 1999). Consequently, rural youth may elect to maintain their connections to place and people over pursuing cosmopolitan goals that require advanced math. Rural district administrators who make decisions regarding curricular offerings (Iatarolo et al. 2011) may believe their students do not want to pursue cosmopolitan goals and so do not offer advanced math courses.

Yet, some findings suggest rural schools want to offer and rural students want to take advanced math. For one, significantly more of the curriculum in smaller schools is dedicated to math than larger schools, but there is no difference for science and English (Haller and Monk 1993). Also, a majority of rural youth want to pursue postsecondary education and their parents want them to as well (Irvin et al. 2016; Meece et al. 2013). Additionally, rural districts use distance education at nearly twice the rate of urban and suburban districts, this is often to provide advanced math, and rural students are, according to rural administrators, adequately prepared for such courses (Hannum et al. 2009; Setzer and Lewis 2005). Lastly, research indicates the math achievement of rural, urban, and/or suburban students is usually similar (Coladarci and McIntire 1988; Fan and Chen 1999; Haller et al. 1993; Howley and Gunn 2003; Lee and McIntire 2000; Williams 2005). Thus, rural students seem prepared and motivated to take advanced math, especially as rural districts are making substantial efforts and using finite resources to do so. Consequently, when rural students have the OTL learn advanced math there may be an interaction such that advanced math course-taking is more strongly related to educational attainment among rural youth.

Research Aims

Our purpose was to examine the relation of the OTL advanced math to the educational attainment of rural high school youth. Toward that end, three specific aims guided analyses. The first aim was to determine if there were differences in advanced math course-taking among rural, urban, and suburban students. The second aim was to investigate the relation of advanced math course-taking to changes in rural students’ math achievement across high school. The third aim was to examine the relation of advanced math course-taking to rural students’ college enrollment.

Method

Participants

Data were from the restricted-use version of ELS:2002 conducted by National Center for Education Statistics (NCES). ELS:2002 first collected data from a nationally representative sample of approximately 16,000 U.S. high school sophomores in spring of 2002. ELS:2002 then collected data two years later (i.e., spring of 2004) when most participants were seniors and again four years later (i.e., spring of 2006) when most participants were two years postsecondary. Though ELS:2002 data were gathered during the last decade, ELS:2002 is, as mentioned, the most recent, longitudinal, and large-scale nationally representative data available for course-taking research that follows participants across high school and into postsecondary years.

Analyses were restricted to students who participated in the base year survey (i.e., 2002), both follow-up surveys (i.e., 2004 and 2006), and had complete high school transcript information. Students were excluded if they changed from rural, urban, or suburban schools between sophomore and senior years (approximately 6% of total sample) or were from Native American background (due to small sample size). Analyses were also restricted to students in public schools as course-taking in private schools is significantly different and largely explains the public-private school achievement gap (Carbonaro and Covay 2010; Lee et al. 1997, 1998; Riegle-Crumb and Grodsky 2010), and there are few private schools in rural areas. The final analytic sample involved 9,700 participants (restricted-use data standards require that unweighted sample sizes are rounded to the nearest 10).

Measures

Rurality

A measure of rurality was available in the ELS:2002 data. Specifically, ELS:2002 used the metro-centric locale categories in NCES Common Core of Data for public schools to describe school location. These locale codes were based on the school address and matched against Census Bureau data to classify schools as rural, suburban, or urban. Rural students attended schools located outside of a Metropolitan Statistical Area (MSA; i.e., one or more contiguous counties that have a core area with large population nucleus and adjacent communities highly integrated economically or socially); suburban students attended schools within an area surrounding a central city and in a county constituting a MSA; and urban students attended schools in a central city of a MSA. For multivariate analyses, we included two dummy variables for suburban and urban students with rural students serving as the reference group (omitted).

Operationalizing rurality is a challenge and many measures have been espoused (e.g., Brown and Schafft 2011; Coladarci 2007; Howley 1997; Theobald 2005; Truscott and Truscott 2005). In addition, there are concerns with formal classification schemes such as the NCES locale codes. For example, several classifications systems exist but their criteria vary and they operationalize rural schools and students as homogenous. Yet, there is substantial variability in occupational structure, median income, culture, ethnic composition, population density, geographic isolation, and school quality across rural communities (Coladarci 2007; Fan and Chen 1999; Howley and Gunn 2003; Provasnik et al. 2007; Strange et al. 2012). Nonetheless, using NCES locale codes provide an initial point to begin to examine overall main effect relations in the OTL advanced math via a broad measure that is similar to the classification schemes previously used in research on rural students’ math course-taking and achievement (Anderson and Chang 2011; Coladarci and McIntire 1988; Fan and Chen 1999; Haller et al. 1993; Howley and Gunn 2003; Monk and Haller 1993; Planty et al. 2006, 2007). Therefore, using a similar classification system may also facilitate interpretation of our results in relation to previous findings.

Advanced Math Course-Taking

Advanced math course-taking was captured using the Burkam and Lee (2003) mathematics pipeline measure. Advanced math course-taking was operationalized by having completed at least one course beyond Algebra II (including Trigonometry, Pre-Calculus, and Calculus) by the end of high school (i.e., 12^th grade). This dichotomous measure (i.e., took at least one course beyond Algebra II vs. did not take a course beyond Algebra II) was consistent with prior studies using the same operational definition and results indicating that taking at least one course beyond Algebra II score has a strong relation to educational attainment (Adelman 1999; Riegle-Crumb and Grodsky 2010; Shettle et al. 2007). For example, Adelman (1999) found that finishing a course beyond Algebra II more than doubled the likelihood of earning a bachelor’s degree. Thus, completing a course beyond Algebra II appears to be a critical threshold (Riegle-Crumb and Grodsky 2010). This threshold may be especially pertinent to our study because, as previously mentioned, rural youth are less often enroll in and complete college than urban and/or suburban youth (Byun et al. 2012a; Kusmin 2007; Provasnik et al. 2007). In addition, using this dichotomous measure provides a concrete and directly applicable target for schools and policies that seek to improve educational attainment.

Math Achievement

Math achievement was measured by a standardized test administered during spring of 10^th and 12^th grades. In the current study, 10^th grade math achievement was a control variable and 12^th grade math achievement was an outcome variable. Test specifications were adapted from National Educational Longitudinal Study of 1988 (NELS:88). The 10^th grade measure had 73 items and 12^th grade measure 59 items. Items were selected from tests previously used in other large-scale studies including NELS:88, NAEP, and PISA. Approximately 90% of 10^th grade items were multiple choice and the other 10% were open-ended. All 12^th grade items were multiple-choice. Content assessed included arithmetic, algebra, geometry/measurement, data analysis/statistics probability, and advanced topics (i.e., pre-calculus and analytic geometry). Cognitive skills and processes measured included skills and knowledge, understanding and comprehension, and problem-solving.

In 10^th grade, students completed a short 15-item multiple-choice routing test that was immediately scored. Based on the number of correct items, students then completed a second-stage form of the 10^th grade test that was low, middle, or high difficulty and ranged from 25 to 27 items. Each student’s score on the 10^th grade routing test was combined with his/her score on the second stage form of the 10^th grade test. Performance on the 10^th grade routing test was later used to assign students to the low, middle, or high difficulty 12^th grade test and all forms had 32 items. Three forms of the math test were used to reduce students’ burden and total number of items. Item Response Theory (IRT) analysis was then used to estimate the correct number of responses had students taken the entire math test in the 10^th and 12^th grades (for more details see Ingels et al. 2007). In short, the IRT analysis used patterns of correct, incorrect, and omitted answers coupled with each test question’s difficulty, discriminating ability, and a guessing factor in mathematical models to estimate the probability each student would correctly answer all items, including those not assigned to the student. Consequently, though there were different forms of the test they actually comprise a single test and IRT estimates are comparable across different test forms.

College Enrollment

College enrollment was participants’ self-reported highest level of education attempted as of 2006 and included non-enrollment, 2-year college enrollment, and 4-year college enrollment.

Control Variables

Measures of several variables that were collected in the 10^th grade and may confound rurality were controlled for in analyses (details in Appendix A1). Statistically controlling for confounds with rurality, especially well known ones such as SES, is imperative otherwise estimated differences between rural and other students may be biased (Coladarci 2007). Research suggests family may be especially important for rural youth because they tend to have close and durable family ties (e.g., Byun et al. 2012c; Elder and Conger 2000; Howley 2006). Consequently, several variables capturing family context were included: SES, family composition, number of siblings, parental educational expectations, parent-child discussion, parent-school contact, and parent-parent interaction. Research has also shown that numerous aspects of the educational context are associated with the educational attainment of rural students (e.g., Irvin et al. 2011; Monk 2007). Thus, several measures of the educational context were controlled for as well: teacher’s educational expectations, importance of getting good grades among student’s friends, percentage of certified full-time teachers, whether the school offered advanced courses via distance learning, academic climate, school poverty, and school size. Finally, the following student characteristics and experiences were also controlled: race/ethnicity, gender, 10^th grade math achievement, cumulative grade point average (GPA), educational expectations, in bilingual/bicultural class or English as a Second Language (ESL) program, in special education, motivation/engagement, and employment. We included both the 10^th grade math achievement measure and cumulative GPA as research consistently demonstrates that prior achievement is one of the most powerful predictors of, and thus potential confounds for, educational attainment.

Analytic Strategies

Preliminary weighted descriptive statistics were first obtained for the overall sample and rural, suburban, and urban students (Table 1). To address the first aim, we used logistic regression to determine whether there were differences in the dichotomous dependent measure of advanced math course-taking for rural students after accounting for control variables. To address the second aim, we conducted ordinary least squares (OLS) multiple regression analysis to examine the relation of advanced math course-taking to changes in rural students’ math achievement across high school. The dependent variable was the continuous measure of math achievement obtained in 12^th grade, but we controlled previous 10^th grade math achievement which made the model an analysis of change in math achievement. Finally, given the categorical measure of college enrollment we used multinomial logistic regression to address the third aim by examining the relation of advanced math course-taking to the college enrollment of rural youth.

TABLE 1.

Weighted Descriptive Statistics of Public School Students by Rurality

	Total			Rural			Suburban			Urban
Variables	M	SE		M	SE		M	SE		M	SE
Outcome Variables
1. Math achievement (12th grade)	49.857	0.122		50.187	0.237		50.695	0.173		48.153	0.227	*
2. Postsecondary educational attainment									*			*
No PSE	0.300	0.005		0.295	0.011		0.280	0.007		0.336	0.011
2-year	0.275	0.005		0.293	0.011		0.281	0.007		0.252	0.010
4-year	0.425	0.006		0.412	0.012		0.438	0.008		0.412	0.011
Independent variable
Advanced math course-taking	0.425	0.006		0.406	0.012		0.445	0.008	*	0.405	0.011
Controls
Previous math achievement (10th grade)	50.205	0.116		51.174	0.231		51.204	0.161		47.760	0.228	*
SES	−0.035	0.008		−0.069	0.016		0.036	0.011	*	−0.135	0.016	*
Family composition												*
Mother and father	0.572	0.006		0.593	0.012		0.605	0.008		0.498	0.011
Mother or father and guardian	0.167	0.004		0.169	0.009		0.166	0.006		0.166	0.008
Single parent	0.222	0.005		0.200	0.010		0.197	0.007		0.283	0.010
Other	0.039	0.002		0.038	0.005		0.033	0.003		0.053	0.005
Number of siblings	2.363	0.020		2.234	0.038		2.265	0.026		2.628	0.043	*
Parental educational expectation	5.313	0.015		5.152	0.031		5.304	0.021	*	5.443	0.028	*
Parent-child discussion	−0.053	0.012		−0.048	0.025		−0.039	0.016		−0.083	0.025
Parent contact school	−0.010	0.015		−0.041	0.024		0.007	0.017		−0.018	0.030
Parent-parent interaction	−0.071	0.012		−0.011	0.023		−0.028	0.018		−0.189	0.027	*
Race/ethnicity									*			*
Asian	0.040	0.001		0.013	0.002		0.039	0.002		0.062	0.003
Black	0.148	0.004		0.072	0.006		0.118	0.005		0.257	0.010
Hispanic	0.159	0.004		0.067	0.006		0.136	0.006		0.266	0.010
White	0.607	0.006		0.808	0.009		0.659	0.008		0.370	0.011
More than one race	0.046	0.002		0.039	0.005		0.049	0.003		0.046	0.005
Female	0.506	0.006		0.499	0.012		0.507	0.008		0.509	0.011
Previous GPA	2.618	0.011		2.728	0.021		2.686	0.014		2.421	0.021	*
Student educational expectations	5.053	0.017		4.949	0.036		5.077	0.024	*	5.086	0.033	*
Bilingual	0.278	0.005		0.300	0.012		0.290	0.008		0.241	0.010	*
ELS	0.083	0.003		0.072	0.006		0.078	0.004		0.101	0.007	*
Special education status	0.085	0.003		0.094	0.007		0.078	0.005	*	0.089	0.007
Motivation/engagement	−0.063	0.014		−0.008	0.026		−0.015	0.019		−0.185	0.027	*
Teacher expectations	4.008	0.021		3.952	0.038		4.089	0.027	*	3.906	0.039
Student employment	0.592	0.006		0.628	0.012		0.602	0.008		0.550	0.012	*
Students’ friends	−0.044	0.013		−0.093	0.027		−0.034	0.017		−0.026	0.027
Time spent on homework	5.565	0.067		5.170	0.137		5.623	0.093	*	5.747	0.137	*
% certified full-time teachers	96.907	0.103		98.342	0.157		97.522	0.125	*	94.799	0.262	*
Offering advanced course via distance learning	0.416	0.006		0.543	0.013		0.402	0.009	*	0.347	0.011	*
School academic climate/press	−0.189	0.011		−0.084	0.020		−0.172	0.016	*	−0.295	0.027	*
School poverty	3.574	0.021		3.156	0.040		3.311	0.029	*	4.336	0.041	*
School size	1508.730	10.134		1019.680	22.984		1492.230	13.415	*	1889.150	16.919	*
Unweighted na	9700			2140			4800			2760

NOTE.—

^aStatistical standards for restricted-use data require that unweighted sample sizes to be rounded to nearest 10. Total analytic sample size is smaller than sum of samples by school location due to rounding.

^*denotes significant differences from rural areas by p < .05

Four models were estimated in the logistic regression analysis addressing the first aim (Table 2). Specifically, Model 1 included rurality (i.e., suburban and urban with rural omitted). This model estimated the bivariate relation of rurality to advanced math course-taking without accounting for control variables. Model 2 introduced previous (10^th grade) math achievement. The control variable that was likely the next most important one, SES, was then added in Model 3. Finally, the remaining controls were added in Model 4. These variables were entered in this order so that we could examine the role the potentially potent control measures of previous math achievement and SES had in explaining the relations between rurality, advanced math course-taking, and educational attainment.

TABLE 2.

Logistic Regression Models Predicting Advanced Math Course-Taking

	1				2				3				4
Variables	B		RSE		B		RSE		B		RSE		B		RSE
Rurality (rural omitted)
Urban	−0.005		0.116		0.487	***	0.132		0.475	***	0.132		0.545	**	0.163
Suburban	0.159		0.097		0.203		0.112		0.149		0.111		0.168		0.131
Controls
Previous math achievement (10th grade)					0.140	***	0.005		0.127	***	0.005		0.075	***	0.006
SES									0.468	***	0.047		0.166	**	0.057
Family composition (two-parent omitted)
Mother or father and guardian													−0.145		0.094
Single parent													−0.108		0.083
Other													−0.270		0.176
Number of siblings													−0.097	**	0.028
Parental educational expectations													0.039		0.033
Parent-child discussion													0.031		0.040
Parent contact school													−0.016		0.043
Parent-parent interaction													0.036		0.036
Race/ethnicity (White omitted)
Asian													0.437	**	0.126
Black													0.754	***	0.142
Hispanic													−0.040		0.133
More than one race													0.055		0.151
Female													−0.097		0.069
Previous GPA													0.911	***	0.079
Student educational expectations													0.145	***	0.033
Bilingual													0.299	***	0.080
ELS													−0.001		0.119
Special education status													−0.183		0.150
Motivation/engagement													0.038		0.058
Teacher expectations													0.248	***	0.037
Student employment													−0.045		0.069
Students’ friends													0.051		0.037
Time spent on homework													0.024	***	0.006
% certified full-time teachers													−0.012	*	0.006
Offering advanced course via distance learning													−0.047		0.114
School academic climate/press													0.018		0.060
School poverty													−0.056		0.037
School size													<0.001		0.000
Constant	−0.381	***	0.079		−7.667	***	0.298		−6.991	***	0.297		−7.315	***	0.732
Log pseudolikelihood	−6610.979				−5168.207				−5089.499				−4305.364
Pseudo R2	0.001				0.219				0.231				0.350
Unweighted N	9700

NOTE.—Data are weighted. B = unstandardized regression coefficient; RSE = robust standard errors; OR = odds ratio. Fit statistics based on one complete and imputed data set. Asterisks indicate regression coefficient significant at level outlined below.

^*p < .05.

^**p < .01.

^***p < .001.

Six models were estimated in analyses addressing the second and third aims. Specifically, Models 1–4 were identical to those just described. Likewise, these models allowed us to examine the role the potentially potent control measures of previous math achievement and SES had in explaining the relation of rurality to changes in math achievement (Table 3) and postsecondary enrollment (Table 4). In Model 5, advanced math course-taking was added. Model 5 determined whether there was a significant relation between advanced math course-taking and educational attainment after accounting for rurality and the control variables. Model 6 introduced the interaction between rurality and advanced math course-taking. Model 6 determined whether the relation between advanced math course-taking and educational attainment was different for rural students in comparison to suburban and urban students.

TABLE 3.

Regression Model Predicting Change in Math Achievement

	1			2			4			5			6
Variables	B		SE	B		SE	B		SE	B		SE	B		SE
Rurality (rural omitted)
Urban	−2.034	***	0.523	0.594	**	0.221	0.661	**	0.247	0.453		0.254	1.099	**	0.369
Suburban	0.507		0.425	0.485	*	0.204	0.386		0.211	0.313		0.211	0.407		0.310
Advanced math course-taking										2.608	***	0.258	3.179	***	0.396
Urban X Advanced math course-taking													−1.554	**	0.524
Suburban X Advanced math course-taking													−0.236		0.431
Controls
Previous math achievement (10th grade)				0.770	***	0.010	0.658	***	0.014	0.628	***	0.014	0.629	***	0.014
SES							0.536	**	0.160	0.458	**	0.155	0.451	**	0.154
Family composition (two-parent omitted)
Mother or father and guardian							−0.106		0.236	−0.030		0.230	−0.021		0.230
Single parent							0.160		0.254	0.208		0.256	0.196		0.257
Other							−0.090		0.619	0.028		0.608	0.013		0.609
Number of siblings							0.033		0.053	0.066		0.053	0.059		0.054
Parental educational expectations							0.066		0.077	0.051		0.076	0.046		0.076
Parent-child discussion							−0.230		0.110	−0.241	*	0.107	−0.244	*	0.107
Parent contact school							−0.029		0.085	−0.024		0.086	−0.022		0.086
Parent-parent interaction							0.093		0.084	0.072		0.085	0.069		0.085
Race/ethnicity (White omitted)
Asian							0.702	*	0.340	0.551		0.332	0.577		0.333
Black							−0.438		0.280	−0.698	*	0.287	−0.725	*	0.285
Hispanic							−0.134		0.314	−0.118		0.317	−0.146		0.315
More than one race							−0.022		0.393	−0.027		0.395	−0.006		0.395
Female							−0.910	***	0.172	−0.878	***	0.172	−0.871	***	0.172
Previous GPA							0.759	***	0.165	0.395	*	0.166	0.398	*	0.166
Student educational expectations							−0.059		0.082	−0.103		0.080	−0.103		0.080
Bilingual							0.421	*	0.182	0.276		0.179	0.255		0.178
ELS							−0.027		0.373	−0.034		0.371	−0.036		0.372
Special education status							−0.793		0.420	−0.773		0.416	−0.759		0.415
Motivation/engagement							−0.373	**	0.121	−0.374	**	0.116	−0.368	**	0.116
Teacher expectations							0.555	**	0.141	0.439	*	0.141	0.431	*	0.140
Student employment							0.198		0.227	0.216		0.230	0.223		0.229
Students’ friends							0.000		0.140	−0.014		0.139	−0.025		0.138
Time spent on homework							0.063	**	0.016	0.052	**	0.016	0.053	**	0.016
% certified full-time teachers							−0.001		0.013	0.003		0.013	0.004		0.013
Offering advanced course via distance learning							0.356		0.178	0.374	*	0.181	0.384	*	0.180
School academic climate/press							−0.104		0.109	−0.109		0.101	−0.097		0.102
School poverty							−0.191	***	0.048	−0.168	**	0.049	−0.153	**	0.049
School size							0.000		0.000	0.000		0.000	0.000		0.000
Constant	50.187	***	0.323	10.791	***	0.544	12.549	***	1.352	14.222	***	1.387	13.826	***	1.399
R2	0.012			0.622			0.642			0.652			0.652

NOTE.—Data are weighted. R² based on one complete and imputed data set. Model 3 is not shown due to space limitations. Asterisks indicate regression coefficient significant at level outlined below.

^*p < .05.

^**p < .01.

^***p < .001.

TABLE 4.

Multinomial Logit Model Predicting Postsecondary Enrollment

	4								5
	No PSE vs. 2-year				No PSE vs. 4-year				No PSE vs. 2-year				No PSE vs. 4-year
Variables	B		SE		B		SE		B		SE		B		SE
Rurality (rural omitted)
Urban	−0.218		0.128		0.390	*	0.155		−0.237		0.128		0.302		0.161
Suburban	−0.065		0.102		0.015		0.127		−0.072		0.101		−0.014		0.131
Advanced math course-taking									0.259	*	0.106		1.027	***	0.112
Urban X Advanced math course-taking
Suburban X Advanced math course-taking
Controls
Previous math achievement (10th grade)	0.006		0.005		0.046	***	0.006		0.004		0.005		0.033	***	0.006
SES	0.380	***	0.061		0.850	***	0.070		0.378	***	0.061		0.842	***	0.071
Family composition (two-parent omitted)
Mother or father and guardian	−0.347	***	0.089		−0.459	***	0.108		−0.347	***	0.089		−0.446	***	0.110
Single parent	−0.131		0.083		−0.065		0.105		−0.126		0.082		−0.046	***	0.107
Other	−0.330	*	0.161		−0.408	*	0.199		−0.324	*	0.161		−0.348		0.201
Number of siblings	−0.090	**	0.026		−0.094	**	0.032		−0.087	**	0.026		−0.077	*	0.032
Parental educational expectations	0.052	*	0.026		0.123	***	0.034		0.053	*	0.026		0.117	**	0.035
Parent-child discussion	0.091	*	0.039		0.184	**	0.052		0.091	*	0.038		0.182	**	0.052
Parent contact school	−0.011		0.039		0.022		0.044		−0.010		0.039		0.025		0.043
Parent-parent interaction	0.084	*	0.040		0.210	***	0.047		0.086	*	0.040		0.209	***	0.049
Race/ethnicity (White omitted)
Asian	0.552	**	0.162		0.702	***	0.174		0.529	**	0.163		0.628	***	0.174
Black	0.259	*	0.120		0.981	***	0.135		0.227		0.119		0.873	***	0.135
Hispanic	0.290	**	0.110		0.298	*	0.135		0.291	**	0.110		0.311	*	0.137
More than one race	−0.591	***	0.165		0.021		0.198		−0.589	***	0.166		0.015		0.202
Female	0.272	***	0.070		0.204	*	0.082		0.273	***	0.069		0.229	**	0.083
Previous GPA	0.464	***	0.061		1.116	***	0.079		0.442	***	0.061		0.968	***	0.080
Student educational expectations	0.178	***	0.025		0.314	***	0.035		0.175	***	0.025		0.291	***	0.035
Bilingual	0.142		0.085		0.261	**	0.097		0.121		0.086		0.202	*	0.100
ELS	0.035		0.112		0.028		0.147		0.036		0.112		0.029		0.148
Special education status	−0.151		0.109		−0.254		0.152		−0.153		0.109		−0.236		0.152
Motivation/engagement	0.036		0.045		0.014		0.060		0.036		0.044		0.007		0.062
Teacher expectations	0.127	**	0.038		0.405	***	0.040		0.119	**	0.039		0.367	***	0.039
Student employment	−0.085		0.076		0.060		0.080		−0.082		0.076		0.071		0.081
Students’ friends	−0.019		0.037		0.043		0.050		−0.017		0.037		0.037		0.051
Time spent on homework	0.006		0.007		0.021	**	0.008		0.005		0.007		0.017	*	0.008
% certified full-time teachers	−0.005		0.003		0.001		0.004		−0.004		0.003		0.003		0.003
Offering advanced course via distance learning	−0.042		0.081		0.083		0.097		−0.041		0.080		0.092		0.094
School academic climate/press	−0.032		0.042		0.019		0.055		−0.034		0.042		0.013		0.054
School poverty	−0.034		0.028		−0.130	***	0.032		−0.035		0.028		−0.124	***	0.032
School size	0.000		0.000		0.000		0.000		0.000		0.000		0.000		0.000
Constant	−1.965	***	0.456		−8.325	***	0.574		−1.869	***	0.466		−7.662	***	0.559
Log pseudolikelihood	−7611.785								−7510.255
Pseudo R2	0.273								0.283

NOTE.—Data are weighted. R² based on one complete and imputed data set. Models 1–3 are not shown due to space limitations. Asterisks indicate regression coefficient significant at level outlined below.

^*p < .05.

^**p < .01.

^***p < .001.

ELS:2002 used a complex two-stage sample selection design (Ingels et al. 2007). Schools were selected first with probability proportional to size. Approximately 26 students per school were then randomly selected from 10^th grade enrollment lists. Thus, ELS:2002 contains clustered data. In addition, students from Hispanic and Asian backgrounds were oversampled. ELS:2002 has weights that compensate for unequal probabilities of selection and adjust for individuals that did not participate. When the appropriate weight is applied, the ELS:2002 sample is nationally representative of 10^th grade students in 2002. The longitudinal base year to second follow-up panel weight (F2BYWT) was applied in descriptive and regression analyses.

While data gathered via multistage sampling is usually not independent and design effects are most affected by clustering, ELS:2002 design effects also partly stem from sample stratification and oversampling (Ingels et al. 2007). Ignoring design effects can underestimate standard errors and increase the likelihood of Type 1 errors (e.g., concluding two groups are different when they are not). Several strategies account for design effects with complex samples (Muthén and Satorra 1995; Stapelton 2008), including design-based aggregated strategies, such as simple to complex adjustments of standard errors, and model-based disaggregated strategies, such as variance component and multilevel models. We used cluster robust standard errors in regression analyses (often called Huber-White corrections; Rogers 1993) which is a design-based strategy commonly employed with large-scale national data that downwardly adjusts standard errors to reduce the chance of Type 1 errors.

We replaced missing data for control measures using multiple imputation (Schafer and Graham 2002). Although the analytic sample was restricted to students with complete high school transcript information in base year (i.e., 2002) and follow-up surveys (i.e., 2004 and 2006), there were students missing data on some control measures (e.g., SES). Following recommendations by von Hippel (2007), we included all dependent and control variables so that missing values for control variables were predicted using existing values from other variables. We generated five imputed datasets as research indicates accurate results can be obtained from two to ten imputations (von Hippel 2005; Rubin 1987). In each imputed dataset, missing values were replaced with a plausible random value drawn on observed values of all variables (von Hippel 2005). We then conducted regression analyses with each of the five imputed datasets. The weight (F2BYWT) was not used when imputing data, but it was applied in descriptive and regression analyses with each imputed data set. Coefficients and standard errors from analyses with the imputed data sets were averaged using Rubin’s (1987) rule.

Results

Preliminary Descriptive Analyses

Table 1 provides the weighted descriptive statistics by rurality. Descriptive analyses indicated that at end of 12^th grade there were differences in advanced math course taking by rurality. Specifically, a significantly smaller proportion of rural students had taken advanced math courses (41%) compared to suburban students (44%). In addition, rural students had higher math achievement than urban students. Two years after most participants were in 12^th grade, the proportion of rural students that were enrolled in a 2-year college was relatively high (29%), compared to urban students (25%). In contrast, the proportion of rural students enrolled in a 4-year college was relatively low (41%), compared to suburban students (44%). There were also significant differences in the control measures that were of particular interest, previous math achievement and SES. Specifically, rural students had significantly higher math achievement in 10^th grade than urban students but there was no significant difference between rural and suburban students. In addition, rural students had significantly higher SES than urban students but significantly lower SES than suburban students.

Differences in Advanced Math Course-Taking

Table 2 summarizes results for the logistic regression model predicting the likelihood of taking advanced math courses during high school. An odds ratio (OR) greater than 1.0 indicates the predictor is associated with an increased likelihood of advanced math course-taking, while a value less than 1.0 indicates a decreased likelihood. In Model 1 there were no initial differences in advanced math course-taking when comparing rural youth to urban and suburban students. However, when previous math achievement was added in Model 2 there was a rural-urban gap in advanced math course-taking (i.e., rural students were less like to have taken advanced math-courses than urban students), but there was no statistically significant difference between rural and suburban students. Moreover, the rural-urban gap in advanced math course-taking was reduced but remained significant after adding SES in Model 3 and the remaining control variables in Model 4 (OR = 1.725, p < .01). In Model 4, urban students were approximately 72.5% (= [1.725 – 1] * 100%) more likely to have taken advanced math than rural students.

Relation of Advanced Math Course-Taking to Changes in Rural Students’ Math Achievement

Table 3 presents results for the multiple regression model predicting math achievement in 12^th grade. In Model 1 urban students had significantly lower math achievement in 12^th grade than rural students (B = −2.034, p < .001) but there was no statistically significant difference between rural and suburban students. However, after adding previous (10^th grade) math achievement in Model 2 both urban students (B = 0.594, p < .01) and suburban students (B = 0.485, p < .05) had significantly more change in math achievement from the 10^th to 12^th grade than rural students. With the addition of SES in Model 3 (model not shown in Table 3) the difference in the change in math achievement between rural and urban students remained significant (B = 0.561, p < .01) but the difference between rural and suburban youth became non-significant (B = 0.387, p > .05). The difference in the change in math achievement between rural and urban students continued to be significant (B = 0.661, p < .01) after entering the remaining control variables in Model 4. However, adding advanced math course-taking in Model 5 significantly predicted change in math achievement (B = 2.608, p < .001) and it also eliminated the significant difference in the change in math achievement between rural and urban students (B = 0.453, p > .05). Finally, Model 6 showed the relation between advanced math course-taking and change in math achievement varied for rural youth. Specifically, a significant interaction between urban students and advanced math course-taking (B = −1.554, p < .01) indicated urban students who took an advanced math course had less change in math achievement than rural students who took an advanced math course. Thus, when rural students take advanced math it has a stronger positive relation to changes in their math achievement across high school than taking advanced math does for urban students.

Relation of Advanced Math Course-Taking to Rural Students’ College Enrollment

Table 4 presents results for the multinomial logit model predicting college enrollment status two years after participants’ senior year. It should be noted that because of space limitations Table 4 only includes the results of Models 4 and 5 and Models 1 through 3 are only reported in the text that follows. Model 1 showed urban students were significantly less likely to be enrolled in a 2-year college (B = −0.281, SE = 0.104, OR = −0.281, p < .01) than rural students. However, when previous math achievement (10^th grade) was entered in Model 2 urban students were significantly more likely to be enrolled in a 4-year college than rural youth (B = 0.109, SE = 3.280, OR = 1.115, p < .05). Again, adding SES in Model 3 and the remaining control measures in Model 4 did not eliminate the significant difference in 4-year college enrollment between rural and urban students. In Model 4, urban students were approximately 47.7% (= [1.477 – 1] * 100%) more likely to have enrolled in a 4-year college than rural students (B = 0.390, OR = 1.477, p < .05). Advanced math course-taking was added in Model 5 and results once again indicated that taking advanced math significantly increased the odds of 4-year college enrollment (B = 1.027, OR = 2.793, p < .001) and adding advanced math course-taking also eliminated the significant difference in 4-year college enrollment between rural and urban students (B = 0.302, OR = 1.353, p > .05). The interaction terms between rurality and advanced math course-taking were entered in Model 6 but these were not statistically significant. It is also important to note that throughout these models there were not any significant differences between rural and suburban students.

Supplementary Analyses

To this point, results indicated that in comparison to urban youth, it does seem that rural students have an inequitable OTL advanced math and that they may be adversely affected by this. Specifically, while descriptive analyses indicate rural students take advanced math at a rate comparable to urban youth (but less often than suburban youth), once the lower previous (10^th grade) math achievement of urban students is accounted for (Table 2) urban students take advanced math courses at a significantly higher rate than rural students. In other words, there is a rural-urban gap in advanced math course taking, especially given the higher level of previous math achievement of rural youth. Similarly, there is a rural-urban gap in changes in math achievement across high school (Table 3) and enrollment in a 4-year college (Table 4) that is explained by advanced math course-taking. However, the question remains as to whether there is a causal relation between advanced math course-taking and the educational attainment of rural youth. Though propensity score matching analyses have indicated that the relation between advanced math course-taking and educational attainment is causal (Byun et al. 2015; Leow et al. 2004; Long et al. 2012), to our knowledge no study has examined whether this holds for rural youth. Therefore, we undertook supplementary analyses that used propensity score matching to estimate the causal effect of advanced math course-taking on the educational attainment of rural youth.

Toward that end, we estimated the effects of advanced math course-taking within rural youth by using a propensity score matching approach as data preprocessing via the following steps. First, we conducted a logistic regression to generate propensity scores from the covariates. This entailed regressing the covariates on the dichotomous measure of advanced math course-taking to obtain the predicted probability (i.e., propensity score) of taking advanced math. Second, we used the propensity scores to match treated (i.e., students who took advanced math courses) and control participants (i.e., students who did not) through the psmatch2 module in Stata. Participants were matched one-to-one (i.e., one control participant for each treated participant) by the nearest neighbor within a caliper matching method and/or kernel matching. Third, we then replicated the previously described regression analyses with the matched samples. In addition, we included all covariates used to generate propensity scores when running these regression models on the matched samples. As is apparent in Tables 5 and 6, results indicated that there was a significant causal relation of advanced math course-taking to the educational attainment of rural youth.

TABLE 5.

Propensity Score Estimates of Effects of Advanced Math Course-Taking on Math Achievement for Rural Students

		Average Treatment Effects for the Treated (ATT)
		Nearest Neighbor Matching			Kernel Matching
		Coef.		SE	Coef.		SE
Advanced math course-taking		1.89	*	0.871	2.37	***	0.69

NOTE.—Estimates are an average of results across five imputed datasets by using Rubin’s (1987) rule. Asterisks indicate regression coefficient significant at level outlined below.

^*p < .05.

^***p < .001.

TABLE 6.

Propensity Score Estimates of Effects of Advanced Math Course-Taking on Postsecondary Enrollment for Rural Students

		Average Treatment Effects (ATE)
		No PSE vs. 2-year			No PSE vs. 4-year
		Coef.		SE	Coef.		SE
Advanced math course-taking		0.16		0.215	0.798	***	0.21

NOTE.—Estimates are an average of results across five imputed datasets by using Rubin’s (1987) rule. Asterisks indicate regression coefficient significant at level outlined below.

^***p < .001.

Discussion

Our results were similar to previous findings indicating that rural students are less likely to take and/or be offered advanced math than urban and/or suburban students (Anderson and Chang 2011; Iatarola et al. 2011; Monk and Haller 1993). However, our results are significant and extend the existing literature because they are, to our knowledge, the first findings to demonstrate the relation of rural students’ OTL advanced math to changes in their math achievement across high school and subsequent college enrollment. In addition, our findings add to the limited research on rural math education and course-taking (Anderson and Chang 2011; Howley et al. 2005), and the few studies that consider student heterogeneity as a possible moderator of the relation between math course-taking and educational attainment (Gamoran and Hannigan 2000; Riegle-Crumb and Grodsky 2010; Rickles 2013).

Our results also reveal that the role of advanced math course-taking for rural students is complex and not straightforward. On the one hand, descriptive analyses indicate that rural youth have significantly less OTL advanced math than suburban youth. Yet, rural students’ 10^th and 12^th grade math achievement, change in math achievement from 10^th to 12^th grade, and postsecondary enrollment were not different from suburban students. Moreover, these did not change when the control measures were added to the statistical models. Thus, it seems that rural students are not adversely affected by the inequitable OTL advanced math compared to suburban students. However, caution is also warranted here as interpreting non-significant differences such as these can be problematic because one cannot be certain whether null differences are due to insufficient power or whether there actually is no difference.

In contrast, when compared to urban youth it does appear that rural students have an inequitable OTL advanced math and they may be adversely affected by this inequity. As mentioned, descriptive analyses indicate rural students take advanced math at a rate comparable to urban youth, but when urban students’ lower previous (10^th grade) math achievement is accounted for urban students take advanced math courses at a significantly higher rate than rural students. In other words, there is a rural-urban gap in advanced math course taking because rural youth are not taking advanced math at a rate that is commensurate with their higher level of previous math achievement. Furthermore, after accounting for differences in previous math achievement there are differences between rural and urban students in relation to changes math achievement across high school and enrollment in a 4-year college.

Unfortunately, little research has been undertaken that could provide more insight as to why rural youth have the inequitable OTL advanced math. To our knowledge, the study by Iatarolo et al. (2011) is the only investigation that specifically sought to determine the underlying source of this inequity. Their results indicated that limited numbers of students available to take advanced math courses was a key determinant of advanced offerings in small Florida schools but difficulties in staffing teachers certified to teach advanced courses was not. In our view, this finding fits with our results indicating that rural students have higher math achievement in 10^th grade than urban students, yet once prior achievement is accounted for, urban students are actually more apt to take advanced math courses. Our findings and those of Iatarolo et al. (2011) also seem to reflect other research demonstrating that rural districts use distance education at nearly twice the rate of urban and suburban districts, this is often to provide advanced math, and rural district administrators report that rural students are adequately prepared for such courses (Hannum et al. 2009; Setzer and Lewis 2005). In sum, these findings collectively suggest that rural youth are prepared to take and would likely benefit from taking advanced math. However, because there are more limited numbers of students to take advanced courses in rural schools then perhaps it is not practical for rural schools to offer such courses and, as such, rural schools turn to distance education to do so.

Strengths

There were several strengths of our study. For one, we accounted for several control variables that may confound rurality. Previous research on rural youth and education has largely been descriptive and not controlled for well-known rural confounds (e.g., SES) that may bias results (Coladarci 2007). Previous findings on rural students’ math course-taking and educational attainment have also typically used a cross-sectional design and data that is now more than 20 years old (for exceptions see Anderson and Chang 2011; Reeves 2012; Williams 2005). Therefore, our use of the most recently available, longitudinal, nationally representative data available that follows youth from the secondary grades into the postsecondary years is a strength. Second, we used propensity score matching to estimate the causal relation of advanced math course-taking to the educational attainment of rural youth. Finally, we also differentiated suburban and urban students whereas previous studies of rural students’ math achievement have usually combined urban and suburban students into a single group labeled non-rural (Haller et al. 1993; Lee and McIntire 2000; Roscigno and Crowley 2001; for exceptions see Coladarci and McIntire 1988; Fan and Chen 1999). Combining urban and suburban students into one group could have obfuscated previous results as our findings and those of others (e.g., Provasnik et al. 2007; Williams 2005) have shown there are differences between urban and suburban students.

Limitations

There were several limitations in our study that also need to be considered. First, ELS:2002 data were collected before the recent Great Recession that may have affected schools’ ability to offer advanced courses. Yet, we believe the economic downturn makes our results even more important. This is because when schools are economically constrained identifying schooling experiences and practices that relate to the educational outcomes rural schools and students want to attain is vital for informing the effective use of finite resources. As discussed earlier, a majority of rural youth aspire to obtain a college education and their parents also want them to (Irvin et al. 2016; Meece et al., 2013), both of which are more likely attainable when rural youth have the OTL advanced math that is commensurate with their level of math achievement. Furthermore, Petrin et al. (2014) found the Great Recession did not alter the long-term plans of rural students and parents. Consequently, it is likely rural students still want to take and rural schools want to offer advanced math.

Second, our study used the NCES locale code trichotomy for classifying schools as rural, urban, and suburban. Though locale codes have, as mentioned, been previously used in research on rural students’ math course-taking and achievement (Anderson and Chang 2011; Coladarci and McIntire 1988; Fan and Chen 1999; Haller et al. 1993; Howley and Gunn 2003; Monk and Haller 1993; Planty et al. 2006, 2007), this classification operationalizes rural students as homogenous. Additionally, while the OTL advanced math is a key aspect of rural students’ school context, there is also substantial variability in several other important factors and contextual features that are not captured by the NCES locale codes. This includes, for example, culture, occupational opportunities, geographic isolation, and population density (Coladarci 2007; Fan and Chen 1999; Howley et al. 2005; Provasnik et al. 2007; Strange et al. 2012). Furthermore, ELS:2002 data do not include alternative measures of location that rural researchers have espoused (e.g., Brown and Schafft 2011; Howley 1997; Theobald 2005; Truscott and Truscott 2005). Nonetheless, the NCES locale code trichotomy provides one broad measure with which to begin to examine overall main effect relations associated with rurality that has been used in previous research and future work can build upon.

Future Research Directions

One key direction for future research is to explore whether our observed relations differ within and across the diversity of rural youth and contexts. For example, future research should investigate whether the inequitable OTL advanced math is similarly evident among and related to educational attainment for rural youth from various racial/ethnic and SES backgrounds. Furthermore, there is evidence the underlying processes involving race/ethnicity and SES may be quite complex, especially within students taking advanced courses. For example, Riegle-Crumb and Grodsky (2010) found more variation in the relation of SES and race/ethnicity to math achievement among students taking advanced math versus those not taking advanced math. Studies should also examine variability across other meaningful units such as states or regions (Howley and Gunn 2003; Lee and McIntire 2000). Lee and McIntire (2000) also demonstrated that there was interstate variability in math achievement between rural and non-rural students. Such research would require data with information on course-taking and educational attainment for rural and other students within numerous states (e.g., NAEP). In addition, investigating the relation of advanced math course-taking to more distal outcomes or across a longer period of time may now be possible with the recently available third follow-up data collection in 2012 as part of ELS:2002.

Future research should also clarify additional determinants of curricular offerings and course-taking for rural students (Anderson and Chang 2011; Iatarola et al. 2011). Toward that end, there is a need to draw on alternatives to the cosmopolitan or modern perspective and related goals of striving for the individual and material success (Howley 2006; Howley et al. 2005). Specifically, factors and processes related to the attachment to place perspective should be considered. As noted earlier, the attachment to place perspective indicates rural youth may give precedence to their connections to place and people rather than material success (Howley, 2006; Howley and Gunn, 2003). Therefore, some rural youth may elect to maintain their connections to place and people over pursuing cosmopolitan ideals that require advanced math. Consequently, future research and policies should be cautious about adopting a myopic deficit-oriented cosmopolitan view of such aspirations. In addition, future research and policies need to consider, and respect, rural students’ connections to family and community, perceptions of local economic and employment opportunities (e.g., farming, mining, recreation tourism), and whether rural students’ educational and occupational aspirations require advanced math (Anderson and Chang 2011; Howley and Gunn 2003; Kannapel and DeYoung 1999; Petrin et al. 2014).

Finally, it is likely several factors related to advanced math course-taking, offerings, and educational attainment simultaneously play a role via complex processes that future research should try to illuminate. For example, Long et al. (2012) demonstrated taking advanced courses in other subjects may interact and have synergistic effects with taking advanced math. Moreover, Petrin et al. (2014) found regional differences within rural females but not males in the relation of school and local economic opportunities to rural adolescents’ residential aspirations. The authors concluded their results suggest interactions “between gender, academic and community integration, and educational aspirations” (Petrin et al. 2014, 314). The findings of Petrin et al. (2014) relate to our research because attaining those educational aspirations and, in particular, pursuing postsecondary education usually requires advanced math (Adelman et al. 2003; Riegle-Crumb and Grodsky 2010; Schneider 2003). In sum, the variability across meaningful units of rurality, involvement of multiple factors, and interactions just discussed support, in our view, recommendations by Coladarci (2007) and Petrin et al. (2014) for research to examine the unique and variable aspects of rural youth and contexts as well as their complex interrelations.

Implications and Conclusion

Our findings have several implications. During the 1990s, federal and state policies increasingly focused on and lawsuits were filed to address inequitable access to advanced courses (Geiser and Santelices 2004; Santoli 2002). Yet, our and others findings (e.g., Anderson and Chang 2011; Iatarola et al. 2011; Provasnik et al. 2007) indicate that rural students have inequities in the OTL advanced math compared to urban students, especially given rural students’ higher level of previous math achievement. Perhaps more importantly, this inequitable OTL advanced math is related to rural students’ educational attainment. Another implication is that accountability policies may need to consider whether youth attend a rural school and, in particular, have an equitable OTL advanced math rather than treating students uniformly because ignoring this inequity, especially in regards to accountability for standard levels of achievement, could be unfair (Hardré 2007; Monk 2007; Wang and Goldschmidt 1999). Likewise, postsecondary institutions may need to consider rural students’ inequitable OTL advanced math in admissions policies because the level of math taken is central to college admissions (Adelman et al. 2003; Riegle-Crumb and Grodsky 2010; Schneider 2003) and a majority of rural youth and their parents want a postsecondary education (Irvin et al. 2016; Meece et al., 2013). To be clear, we are not suggesting postsecondary institutions should completely eliminate advanced math course-taking in admissions policies. Rather, postsecondary institutions may need to consider alternative forms of evidence of academic skills when there is an inequitable OTL advanced math and additional efforts may need to be taken to ensure rural students are successful. Policymakers may also need to direct resources to rural schools in order to improve rural students’ OTL advanced math. Furthermore, clarifying the underlying reasons for the inequity in the OTL advanced math among rural students is needed. Otherwise, policies that are unfair may persist and resources directed towards addressing rural students’ inequity in the OTL advanced math could be ineffective.

Supplementary Material

Appendix A1

APPENDIX A1 Description of Variables