Ability Grouping in the Early Grades: Long-Term Consequences for Educational Equity in the United States

by Anthony Buttaro, Jr. & Sophia Catsambis - 2019

Background: Ability grouping has resurged in U.S. schools despite long-standing debates over its consequences for educational equity. Proponents argue that it is the best response to variation in academic skills because it allows teachers to customize the content and pace of instruction to students’ diverse needs. Critics answer that this practice places students in divergent educational paths that reproduce educational and social inequalities. Despite the contested nature of ability grouping, research has yet to produce reliable longitudinal evidence to evaluate critics’ claims.

Objective: We examine the degree to which exposure to within-class grouping for reading instruction from kindergarten to third grade is predictive of students’ reading test scores and English coursework in the middle grades.

Research Design: We use multilevel achievement growth models predicting average reading achievement from kindergarten to eighth grade as a function of years of exposure in low, average, or high ability groups in kindergarten through third grade and control variables relevant to each grade. We evaluate the achievement differences between students who are grouped in these ability groups for one or more years and those who were never ability grouped. We use multinomial logistic regression models to estimate the degree to which number of years in each ability group in K–3 grades predicts placements in eighth-grade English classes (below grade or honors, as opposed to regular English classes).

Data: We use data from the Early Childhood Longitudinal Study–Kindergarten Cohort (ECLS–K), a national panel study of the 1998 U.S. kindergarten cohort sponsored by National Center for Education Statistics, U.S. Department of Education. Our sample consists of 7,800 students with data for fall of kindergarten, and spring of kindergarten and first, third, fifth, and eighth grades.

Findings: Compared with similar students who were ungrouped in the early grades, those in high-ability reading groups have higher test scores, whereas those in low-ability groups have lower test scores in every grade from kindergarten to the eighth grade. In addition, compared with their ungrouped counterparts, students in low-ability groups in the early grades are more likely to enroll in eighth grade English classes that are below grade level, whereas those in high-ability groups in these grades are more likely to enroll in honors eighth-grade English classes. Achievement gaps between previously grouped and ungrouped students increase with every additional year of exposure to ability grouping.

Conclusions: Students’ ability group placements in the early grades evolve into divergent educational paths that grow further apart with multiple years of grouping. These findings provide the first longitudinal evidence linking ability grouping to the reproduction of educational inequalities.

Since the passage of the No Child Left Behind¹ legislation over a decade ago, national and state policies have sought to improve literacy via a flurry of school reforms, school restructuring, redesigned professional development, and new instructional methods. In the midst of these reforms, ability grouping has remained firmly entrenched in U.S. schools. In fact, its use has been steadily increasing since the mid-1990s (Loveless, 2013). This resurgence is quite surprising given the long-standing criticism regarding the effectiveness of this instructional practice and the vocal condemnation of its use. Proponents, however, argue that ability grouping is the best response to student variation in talent because it encourages all students to realize their full potential by customizing content and pace of instruction to their diverse needs (Glass, 2002; Hallinan, 2003). Indeed, some scholars advocate its use over newer instructional practices for ungrouped classes, such as differentiated instruction, unleashing a new round of heated debates among educational scholars and practitioners (Delisle, 2015; Tomlinson, 2015). Critics answer that ability grouping places students in divergent educational paths, which, over the course of schooling, widens achievement gaps among them (Condron, 2008; Duckworth, Akerman, Guttman, & Vorhaus, 2009; Ireson, Hallam, Hack, Clark, & Plewis, 2002; National Education Association, 1990; Tach & Farkas, 2006). With socioeconomically advantaged students overrepresented in high-ability groups, critics claim that ability grouping allows children from advantaged families to follow a separate and superior educational track than less advantaged students. Thus, the concern of many of its critics has long been that ability grouping is not only an ineffective practice for educating a diverse population of students but also a mechanism reproducing educational and, ultimately, social inequalities (Barr & Dreeben, 1983; Duckworth et al., 2009; Hallinan, 2003; Ireson et al., 2002; Oakes, 1985).

Despite the contested nature of ability grouping, researchers have not been able to produce reliable evidence to evaluate critics charge that ability grouping creates divergent educational paths (Glass, 2002; Kulik, 2004; Schofield, 2010). One of the main reasons for this lack of evidence has been the limited availability of national longitudinal studies tracking the academic progress of students over long periods of time. Our research seeks to fill this void by using data from the Early Childhood Longitudinal StudyKindergarten Cohort (ECLSK 1998), the only U.S. national longitudinal study to date that follows the same students from kindergarten to the eighth grade. We investigate potential consequences of ability grouping in the early grades for students academic careers in the middle grades. We focus on the early grades as a likely time for ability grouping to have long-term consequences because this is when students establish their educational foundations (Ready, LoGerfo, Burkam, & Lee, 2005). Using data from students who were followed from the early grades until the eighth grade, we examine the degree to which exposure to within-class grouping for reading instruction from kindergarten to third grade is predictive of their academic performance in the eighth grade, a critical juncture in students educational careers. Our analyses seek to answer the following question: Is exposure to within-class ability grouping in the early elementary grades predictive of reading test scores and English coursework in the middle grades? We formulate multivariate models, which include both student characteristics and school features, and compare the fifth- and eighth-grade test scores as well as the eighth-grade English coursework of students who were in grouped versus ungrouped classrooms during kindergarten and first and third grades.

BACKGROUND

TYPES OF ABILITY GROUPING IN U.S. SCHOOLS

Homogeneous ability grouping is widely used in many countries around the world (LeTendre, Hofer, & Shimizu, 2003; Schofield, 2010). The term encompasses a wide range of instructional practices that assign students to different educational contexts based on their IQ, grades, achievement tests, or even their preferences (Kulik, 2004; Schofield, 2010). Schools adopt such grouping practices to cope with variation in students skills and abilities, and, as such, they are most often associated with a differentiated curriculum designed to match the skills and learning potential of students in different ability groups (Hallinan, 2003; Kulik, 2004). Although the term ability grouping is widely used, it does not perfectly reflect grouping by innate mental capacity as implied by the word ability. Students abilities and skills, as well as their social characteristics (e.g., socioeconomic status [SES], racial/ethnic background, gender, or classroom behaviors) and school or classroom composition and organization, play a role in group placements (Attewell & Domina, 2008; Catsambis, Mulkey, Buttaro, Steelman, & Koch, 2012; Gamoran, 1992; Hallinan & Sorensen, 1986; Oakes, 1985; Oakes & Guiton, 1995; Pallas, Entwisle, Alexander, & Stulka, 1994; Schofield, 2010). In addition, average levels of achievement and homogeneity of student skills vary considerably within ability groups, depending on school and classroom characteristics (Barr & Dreeben, 1983; Hallinan & Sorensen, 1986).

Ability grouping can involve the organization of students within or between classes and schools. In the United States, distinct types of ability grouping are employed at different levels of schooling. In the elementary grades, grouping primarily occurs within the classroom, where teachers divide the class into smaller groups according to each students achievement and instruct each group separately (Kulik, 2004; Loveless, 2013). As soon as they enter school, students are divided into such homogeneous groups, primarily for the purpose of reading instruction (Loveless, 2013). Within-class ability groups differentiate high-, average-, and low-achieving students. Some researchers have reported these groups to be fairly large in size and stable over the school year (Entwisle, Alexander, & Olson, 1997; Hallinan & Sorensen, 1986). However, because the groups are within-class and are often decided by one teacher, they can be more flexible than the between-class ability groups found in higher grades. Within-class grouping offers opportunities for students to be regrouped during the school year or across years to reflect changes in their performance. The most common alternative to within-class grouping is whole-class instruction, with all students in the class receiving the same instruction either as one group or in smaller mixed-ability groups (Loveless, 2013).

Vocal criticism of ability grouping led to a gradual decline in the use of all forms such grouping, including within-class, and by the mid-1990s, the majority of teachers in U.S. elementary schools used whole-class instruction as their main instructional method (Loveless, 2013). More recent U.S. national data, however, reveal a dramatic upsurge in use of within-class grouping; the percentage of fourth graders grouped for reading instruction increased from 28% in 1998 to 71% in 2009 (Loveless, 2013).

In U.S. middle schools, which typically encompass Grades 5 or 6 through 8,² use of between-class grouping becomes prevalent. In this form of grouping, students are separated into classes with differentiated curricula for specific achievement levels. They are often grouped for English and mathematics instruction and return to heterogeneous classes for their remaining subjects (Kulik, 2004). Students may also enroll in classes designated as special education, advanced placement, honors, and others (Loveless, 1998; Worthy, 2010). Assignment of students in these differentiated classes is based on previous grades, teacher recommendations, placement tests, or, sometimes, parental preferences (Gamoran, 1992; Loveless, 1998). In U.S. high schools, ability grouping can take the form of differentiated curricula, often called tracking, where students enroll in a series of courses whose curricula are defined as college preparatory, general, or vocational (Loveless, 1998). Although use of tracking has declined, ability grouping practices that differentiate classes by achievement are quite common in both middle and high schools (Gamoran, 1992; Loveless, 1998, 2013; Lucas, 1999; Worthy, 2010). Over the past two decades, about three fourths of U.S. eighth graders attended tracked math classes, although ability-grouped classes in subjects such as English and history declined somewhat (Loveless, 2013).

RATIONALE AND CONTROVERSY OVER THE CONSEQUENCES OF ABILITY GROUPING IN U.S. SCHOOLS

Ability grouping is intended to foster cognitive growth among students of all achievement levels (Hallinan, 1994a, 1994b, 1994c). According to its proponents, students learn best if they are grouped with other students who have similar levels of skill, allowing teachers to tailor the content and pace of instruction to each groups needs (Glass, 2002; Pallas et al., 1994). Ideally, a good fit between a students ability and the level of instruction will maximize the effectiveness and efficiency of this instructional practice (Hallinan, 1994a; Kulik, 2004). Benefits of the practice are expected to outweigh costs and thus account for its widespread usage in American schools (Hallinan & Sorensen, 1986).

Despite the prevalence of ability-grouping practices, little evidence suggests that they actually work as well as supporters would claim. Extensive research on this subject, conducted over decades, has produced inconsistent results, largely because of methodological limitations and the large number of ability-grouping configurations that have been implemented (Kulik, 2004). Results vary not only by grade, subject matter, and type of grouping considered (Kulik, 2004) but also by type of school and instructional conditions within the classroom (Hong, Corter, Hong, & Pelletier, 2012; Nomi, 2010). The most extensive research of ability grouping practices in the United States has been conducted on secondary school tracking and between-class grouping. For over 20 years, research reported that these forms of grouping influence students achievement; they widen the achievement gap by undermining the achievement of low-achieving students and increasing gains among high-performing students (Callahan, 2005; Carbonaro & Gamoran, 2002; Gamoran & Berrends, 1987; Hallinan, 2003; Hallinan & Kubitschek, 1999).

International studies also support the U.S. findings showing that tracking and between-class grouping widen the achievement gap among secondary school students. Studies from a number of different countries reported that use of various ability groupings within and between schools increased educational inequalities among social groups, given that immigrant, minority, and low-SES students are disproportionately overrepresented in low-ability groups (Duckworth et al., 2009; Ireson et al., 2002; Schofield, 2010). Thus, both U.S. and international studies support the concerns of many scholars and educators regarding the consequences of ability grouping practices for students in low-ability groups (Glass, 2002; Hallinan, 2003; National Education Association, 1990). Critics also point to research findings that show inequalities in learning opportunities, with students in low-ability groups receiving poorer quality of instruction compared with their peers in high-ability groups. Low-ability groups are often taught by teachers who are less experienced, who hold lower expectations for students, and who spend more time in non-instructional activities (Chorzempa & Graham, 2006; Eder, 1981; Gamoran, 1986; Gamoran, Nystrand, Berends, & LePore, 1995; Hallinan, 2003; Oakes, 1985; Page, 1991; Worthy, 2010). Exposure to less challenging and interesting curricula discourages students in low-ability groups and lowers their academic expectations and motivation to learn (Gamoran, 1986; Gamoran et al., 1995; Hallinan, 2003; Ireson et al., 2002; Lucas & Berends, 2002).

The above conclusions regarding the negative consequences of ability grouping are derived mostly from studies on ability-grouping practices in middle and secondary schools. Classic meta-analyses by Slavin (1987) and Kulik (2004), as well as a more recent work by Puzio and Colby (2010), reported positive effects for within-class grouping, which is the norm in U.S. elementary schools (Loveless, 2013). These scholars concluded that within-class grouping has positive effects for elementary school students, especially when they are grouped for specific subjects and when ability groups are small. They also emphasized the importance of adapting instruction to the needs of the group (Kulik, 2004; Slavin, 1987). Based on experimental and quasiexperimental studies, the meta-analyses conducted by Kulik (2004), Slavin (1987), and Puzio and Colby (2010) have so far provided the most robust evidence on the positive effects of within-class grouping. Differential effects for high-, average-, and low-ability students remained inconclusive, however, and most of the studies reviewed were conducted on small samples with limited generalizability (Condron, 2008). Until recently, researchers were not able to reproduce these results with data that include the full variation of schools and students across the United States. The release of the ECLSK 1998, together with recent methodological advances in multilevel modeling and propensity score matching, allowed for more precise estimations and valid inferences on the effectiveness of ability grouping than prior research. Data from the ECLSK reveal that nearly two thirds of students in the United States are being placed into reading groups of different achievement levels as early as kindergarten (Buttaro, Catsambis, Mulkey, & Steelman, 2010). This form of grouping is most often used in schools with diverse student populations, many of them low-performing public schools that serve minority and disadvantaged students (Buttaro et al., 2010; Nomi, 2010). Studies that used data from the ECLSK have investigated the effectiveness of within-class grouping for reading instruction. Their findings reveal positive results only for specific types of students and under specific conditions: low-achieving students in private, socially advantaged schools (Nomi, 2010); low- and middle-achieving students when grouping size is small and students receive ample instruction in reading (Hong et al., 2012); and high-achieving students participating in a gifted program in kindergarten (Adelson & Carpenter, 2011). However, studies that focus on trends for the whole sample of students reveal that, overall, students in high reading groups learn more during the course of a school year than comparable ungrouped students. By contrast, students in low reading groups learn less than their ungrouped counterparts (Condron, 2008; Lleras & Rangel, 2008; Tach & Farkas, 2006). These findings are similar to those found in studies of ability grouping in middle and secondary schools. Thus, variations in the effectiveness of ability grouping in both elementary and secondary education may limit learning opportunities for disadvantaged students, who are overrepresented in low-ability groups (Condron, 2008; Dreeben & Barr, 1988; Hallinan, 2003; Hallinan & Sorensen, 1983; Kubitschek & Hallinan, 1996; Oakes, 1990). These conclusions further support critics concerns that use of ability grouping practices leaves low-achieving students further behind and thus widens initial achievement gaps among social groups (Glass, 2002).

LONG-TERM CONSEQUENCES OF ABILITY GROUPING FOR ACHIEVEMENT AND EDUCATIONAL EQUITY

Despite efforts to improve the academic achievement of all students in the United States, educational inequality still persists. Achievement gaps among students of different social backgrounds exist before kindergarten and widen throughout the elementary and secondary school years (Alexander & Entwisle, 1996; Jencks & Phillips, 1998; Lee & Burkam, 2002). How students fare in school depends strongly on the differential resources they bring to school and on the degree to which schools can structure the learning environment to compensate for initial inequalities in school readiness. Homogeneous ability grouping is one of the key methods used in schools to tailor the pace and content of instructions to students educational needs. Yet, as noted earlier, critics raise the concern that in the long run, this instructional practice constitutes a key mechanism reproducing educational inequality (Glass, 2002; National Education Association, 1990; Oakes, 1990). Recent studies that used nationally representative data indicate that ability grouping in the elementary grades may contribute to cumulative advantages or disadvantages that develop during students educational careers (Condron, 2008; Lleras & Rangel, 2008; Tach & Farkas, 2006). Given their methodological rigor, the recent studies of within-class grouping that show differential effects for students in high- and low-ability groups are especially important. These results prompted scholars to conclude that the effects of ability grouping in the early elementary grades will grow over the years, exacerbating inequality in academic skills and across social groups (Condron, 2008; Tach & Farkas, 2006).

This emerging picture of the effects of within-class ability grouping needs further examination, however, because existing studies are based only on one-year snapshots of childrens academic gains, without considering students reading group experiences over multiple years. The mentioned studies estimated achievement gaps of grouped versus ungrouped children over a one-year period. Then, they estimated this gap again for the next year, but on a different set of children because the number of grouped children and their group placements changed from one grade to the other (Condron, 2008; Lleras & Rangel, 2008; Tach & Farkas, 2006). Although stringing discrete one-year snapshots of achievement growth together indicates growing inequality, it might be making the inequality process seem more additive and stable than it is. It is not clear that the effects of early ability grouping will not fade away over the years, especially given that the effects of ability grouping may vary for different types of students and according to school or classroom organization (Adelson & Carpenter, 2011; Hong et al., 2012; Nomi, 2010). As students move from one grade to another, low achievers may encounter new opportunities for catching up through different configurations of ability groups and teachers using different instructional practices, while high achievers may hit a ceiling in their academic growth. Thus, concluding that ability grouping has long-term consequences for students achievement is premature. One-year snapshots of achievement growth leave unanswered questions about students ability group placements across years and about the long-term persistence of the effects of early ability grouping.

Extrapolating one-year results into a long-term picture of achievement growth seems reasonable (Condron, 2008; Tach & Farkas, 2006) under the assumption that children are locked into their ability groups year after year. This assumption is supported by some early studies reporting that once students were assigned to a lower group, they usually would not move upward (Kerckhoff & Glennie, 1999; Rosenbaum, 1976). Yet, these studies did not use national data and focused only on upper grades. The degree to which students are locked into specific ability groups with clearly defined educational trajectories across the elementary grades has not been examined. It is possible that pronounced movement across ability groups occurs in the early grades, because as students enter school, they may adjust to the demands of the school environment at different rates (Loveless, 2013). Indeed, our preliminary analyses revealed that students may experience varied educational paths composed of combinations of exposure to achievement grouped or ungrouped classrooms or placements in different achievement groups from one grade to another. It is still not known if this complexity of instructional grouping across grades has long-term consequences for students education in later years. Do the effects of ability grouping in the early grades fade over the years? And do the effects of placement in different ability groups depend on how many years students are placed in these groups? Answers to such questions require tracing the academic achievement of the same students across multiple grades.

THE CURRENT STUDY

Our analyses seek to elucidate potential consequences of within-class ability grouping in the early grades for students subsequent educational careers. To this aim, we use national longitudinal data that allow us to follow the same students from their first year of school, in kindergarten, until the end of middle school, in eighth grade. To date, no research has considered this totality of ability-grouping experiences in investigating whether ability grouping serves as an agency of differential educational outcomes.

Underpinning our analytic approach is a well-established theoretical perspective positing that the effects of ability grouping are mediated via instructional, social, and institutional pathways (Lucas, 1999; Pallas et al., 1994). The instructional pathway considers variations in the pace and content of instruction for groups of different ability levels, which should academically benefit those in the high-ability groups (Hallinan, 1994a; Oakes, 1985). The social pathway suggests that students are organized into groups of different status and prestige, which can impact their self-concept. Placement in lower ability groups is seen as psychologically hurtful compared with placement into high-ability groups that convey greater prestige. Finally, the institutional pathway is understood as a status marker by parents, teachers, and others who are closely tied to students. Placement in ability groups conveys a message about students aptitudes regardless of actual performance level, affecting the actions of students and school personnel (Pallas et al., 1994). Thus, students in high-ability groups who experience more instructional input, higher self-expectations, and higher expectations from significant others should outperform their ungrouped counterparts and those in lower ability groups (Pallas et al., 1994).

Taken together, these three pathways may explicate when and how ability grouping matters. Following this reasoning, we examine two types of potential educational outcomes that may be associated with students exposure to ability grouping in the early grades. We first consider students history of ability group placements to be associated with their achievement growth as measured by reading test scores. We expect that test scores will be susceptible to the effects of early ability grouping primarily through instructional pathways. If ability grouping has long-term consequences due to differences in instructional quality, then a direct relationship between exposure to ability grouping in the early grades and reading test scores in later grades will be observed. We also consider the predictive ability of early grouping for the new forms of ability grouping in the middle grades. During this level of schooling, ability grouping takes the form of differentiated coursework, with students enrolling in general, honors, or below-grade-level courses. We reason that the institutional and social pathways may especially affect course enrollments, whereby students prior histories of placement will inform their level of eighth-grade coursework. This is because students enrollments may be affected both by teachers who may harbor differential performance expectations based on students prior grouping history and by students themselves, who may live up to their labels as high or low achievers.

Following these expectations, we investigate three research questions focusing on students reading achievement across grades and level of English coursework by the eighth grade: (1) How stable is exposure to different within-class ability groups across the early elementary grades? (2) Does the degree of exposure to specific reading ability groups across K3 grades predict variation in students learning trajectories up to the end of eighth grade? (3) Does the degree of exposure to specific reading ability groups across K3 grades predict ability group placements in eighth-grade English classes?

We will return and articulate more thoroughly these research questions when presenting the analytic strategy.

DATA

We use data from the ECLSK, which is a nationally representative panel study of the 1998 U.S. kindergarten cohort sponsored by the National Center for Education Statistics, U.S. Department of Education (Tourangeau, Nord, Lê, Sorongon, & Najarian, 2009). Approximately 21,000 children from about 1,000 schools were sampled across the country during the first round of data collection, in the fall of kindergarten. Quantitative data were collected from children, parents, teachers, and school administrators through the use of structured interviews and professional observations of students. Data for the full sample of students were collected in the fall of kindergarten and again in the spring of kindergarten and first, third, fifth, and eighth grades.³ Our analyses are based on the subsample of 7,800 students with valid data from all the previously mentioned six waves of data collection. However, because of our specific hypotheses, we curtailed the sample to include only students who met the following criteria: (1) they remained in the same school through third grade (to avoid confounding change in ability grouping across grades with change in schools), and (2) they had complete data on the reading test score in eighth grade.⁴ This resulted in a longitudinal subsample of 6,476 students.

Dependent Variables

Students reading Item Response Theory (IRT) scale scores are based on assessment tests administered at each wave of data collection to measure various reading skills at each grade. IRT scores estimate what students scores would be on a test of infinite questions, based on their pattern of answers to a small set of routed questions. IRT scores can be compared across grades and are designed to minimize floor and ceiling effects (Tourangeau et al., 2009). Our analyses use students IRT reading test scores at six time points (fall and spring of kindergarten, and spring of first, third, fifth, and eighth grades).

English course level, spring eighth grade is based on English teachers reports on sampled students English class and is coded into three categories: instruction for students performing below grade level; regular; and honors, enrichment, or gifted and talented (hereafter referred to as honors classes).

Main Independent Variables

Time in months between reading assessment dates represented the chronological distance among the dates when the cognitive tests were administered to students in each wave of data collection. This variable is used in our achievement growth models. We used month as the unit of measure (as opposed to a simple count for each round of data collection, or the number of school years) to account more accurately for the unequal spacing that exists across the six waves of data (Singer & Willett, 2003). Considering the assessment dates at fall kindergarten and spring eighth grade as starting and ending points of the time window considered in our study, this variable ranges from 0 to 104.7 months. We obtained five different versions of this measure by successively centering it at the end of each grade (i.e., at the spring test dates of kindergarten and first, third, fifth, and eighth grades). The centering operation consisted of a linear transformation of the time variable by subtracting the number of months between first reading assessment (i.e., fall kindergarten) and each one of the successive reading tests. In this way, each test date (after the beginning of schooling) played the role of initial time (i.e. time_t = 0 months). For example, when we centered time at spring kindergarten (time_{Spring K}), we subtracted the number of months that occurred between the test administered at fall and the one at spring of kindergarten, and we obtained a new version of this variable with the range −8.6 to 98.5. On this new time_{Spring K}, the value of 0 months corresponds to the date at the end of kindergarten, when the second test was administered to students. From this new initial time, the first test, at the beginning of kindergarten, happened in the pastwhich is indicated by a negative number of months (see the lower limit of the range). Later test dates are indicated by a positive number of months, with the assessment at the end of eighth grade occurring, at the latest, 98.5 months after the spring kindergarten test. Analogously, to center time at the end of first grade (time_{Spring 1st}), we subtracted the number of months that occurred between the first test (in fall kindergarten) and the third test (spring first grade), resulting in a new version of this measure ranging between −21.2 and 86.8. For this time_{Spring 1st} variable, 0 months refers to the date when the third test was administered; however, both first and second tests now are indicated by a negative number of months, whereas the assessments at the waves after spring first grade are indicated by a positive number of months. We applied this transformation at each wave of data up to the end of middle school, when Time& centered at spring eighth grade (time_{Spring 8th}) ranged between −104.7 and 0; this looks exactly like the reverse of the original version, with initial time coinciding with fall kindergarten.

Years of exposure to grouping in K–3 refers to four variables that indicate the number of academic years students were exposed to groups of different ability levels (ungrouped, low, average, and high). We created these variables in three steps. We first determined each students placement status in reading ability groups (i.e., ungrouped or in a low, average, or high group) for each of the three grades K3 by using teacher reports. In each wave, teachers were asked whether they used achievement groups for reading instruction, and, if so, (a) how many groups there were, and (b) in which group each child was placed.⁵ To ensure comparability across classes and grades, students placed in the lowest reading group of the class were coded as being in the low ability group; students placed in the highest reading group were coded as being in the high ability group; and all others were considered as placed in the average group. We imputed missing cases on these variables (see our discussion on strategy for dealing with missing information) and then created four additive variables indicating how many of the three years (kindergarten and first and third grades) students were ungrouped or placed in low, average, or high groups.

Class ability level, spring fifth grade is used as an indicator of between-class ability grouping that occurs in this grade. It is derived from teacher reports of the reading ability level of the sampled students classes relative to the children in their schoolwidely mixed ability, primarily low ability, primarily average ability, or primarily high ability. Although our analysis focused on ability grouping in the early grades, use of this variable provided a more complete picture of students academic experiences. We kept this variable separate from the one previously mentionedindicating years of ability groupingbecause between-class grouping represents a different instructional method than within-class grouping.

Control Variables

Informed by existing literature on variables associated with student achievement, we selected a series of control variables, which we divided into time-varying and time-invariant.

Time-varying control variables. For each round of data collection, we used the following variables: single-parent family; number of siblings living in household; SES; level of welfare assistance (sum of three items indicating whether the family/child had received, in the previous 12 months, AFDC/TANF, food stamps, free or reduced price lunch [for fall of kindergarten, this last item was replaced by WIC benefits for the child]); parental highest level of education; parental educational expectation for child; school region (Northeast, Midwest, South, West); school locality (urban, suburban, rural); private school; school size; and school minority concentration.

Time-invariant control variables. We used the following variables: childs sex; race/ethnicity (White, Black/African American, Hispanic, Asian, and other racial/ethnic background); student age in months (computed between the childs date of birth and the assessment date at each time point); mothers age in years at fall of kindergarten; and moved to a different reading group during the academic year or not (three variables, one for each grade, K3).

Our strategy for dealing with missing information due to item nonresponse was broken down into two stages, taking advantage of both the longitudinal nature of the ECLSK survey and its rich availability of data. In the first stage, we sought to lower the amount of missing information by retrieving (as opposed to estimating) valid information from values on other observed variables. To this end, we replaced, when appropriate, part of the missing data with information from the repeated version of the measure(s) collected in previous and/or following waves of data collection. For example, for school region, we examined whether the child had moved residence between each of two consecutive waves (going backward), and for those who did not move, we replaced part of the missing data with the value they had after their last residential move. In the second stage, we predicted the remaining missing data using multiple imputation of 10 data sets (the maximum allowed by the hierarchical linear modeling software we used for our multilevel modeling). Considering the repeated measures as separate items, out of a total of 95 variables (time-varying, time-invariant, dependent, and independent), only seven measures had an amount of missing data higher than 5%; the variable with the highest number of missing data being level of welfare assistance at spring of eighth grade, with less than 11% of missing information.⁶

All analyses were weighted and adjusted by the appropriate longitudinal sampling design effects available in the data set. Further details about all the variables and their descriptive statistics are provided in the appendix.

ANALYTIC STRATEGY

We conducted descriptive statistics to answer our first research question pertaining to the stability of exposure to within-class ability groups across grades. These descriptive statistics were based on our full longitudinal sample of students followed from kindergarten to Grade 8 and refer to the eighth graders past ability grouping experiences in K3 grades. We ran bivariate analyses, followed by two different multivariate techniques to answer our second and third research questions. Our multivariate analysis for our second research question, regarding the degree to which ability grouping across K3 grades predicts students learning trajectories, entailed five three-level achievement growth models. We included one model predicting students reading test scores for each round of data collectionthat is, fall and spring of kindergarten and first, third, fifth, and eighth grades. For the analytic sample of eighth graders, the first model provides information on student skills before any potential schooling effects by predicting reading school readiness in the fall of kindergarten. The subsequent models predict reading learning growth at the end of each specific grade (spring of kindergarten through eighth grade), the main focus being the contribution of ability grouping in K3 grades to achievement across grades. In all the models, level 1 represents the repeated measures of test scores of the six rounds of data collection nested within students, which are the level 2 units. Because software for multilevel modeling did not allow adjustment for survey design effects and their relative clustering, we added a third level to our models representing the sampling strata. We ran different baseline models, conditional (only) on time at level 1, to assess the most appropriate functional form for the growth and the type of random effects to be estimated. We obtained optimal results⁷ with a quadratic growth model that includes random intercept (π_0ij), random slope of time (π_1ij), and fixed slope of quadratic time across students (π_2ij)⁸ (Raudenbush & Bryk, 2002). The following equations represent this baseline model:

Level 1 equation:

Y_tij = π_0ij + π_1ij * (Time in Months_{Fall K})_tij + π_2ij * (Time in Months_{Fall K})_tij ² + e_tij.

Level 2 equations:

π_0jk = b_00j + r_0ij ,

π_1jk = b_10j + r_1ij

Level 3 equation:

b_00j = g₀₀₀ + u_00j

The interpretation of each of these three parameters depends on the specific centering adopted for the time measure (see previously mentioned Time &). For example, for our model, where the time measure is centered at spring kindergarten (i.e., time_{Spring K} = 0), the intercept (π_0ij) represents the average student achievement at spring of kindergarten, the slope of time (π_1ij), the instantaneous growth rate at spring of kindergarten, and the slope of quadratic time (π_2ij), the curvature of the growth (i.e., how much the change over time changes). If time is centered at another time point—for example, spring of first grade—the meaning (and the estimate) of the curvature does not change, but π_0ij and π_1ij stand now, respectively, for the status (i.e., average reading achievement) and instantaneous growth rate at spring of first grade. For our final model, we centered the time predictor at the date of the eighth-grade assessment so that the intercept of the multilevel model represents the final status, or average reading IRT score in eighth grade (Singer & Willett, 2003). Thus, by centering time differently for each growth model, we were able to estimate parameters specific to each grade. Variation in centering allows parameter estimates to change accordingly because, with the passing of time, not only does the average reading score become progressively higher, but the average inclination of the learning curve changes as well (slopes of the tangents to different points on the learning curve are different). In our study, the peak of the growth function falls outside the time frame considered (fall K to spring eighth grade). This means that the magnitude of the curvature (deceleration in the present case) is not large enough to allow the growth curve to reach the turning point where the growth changes from increasing to decreasing (Singer & Willett, 2003).

The above strategy of centering time at each time point allowed for a more dynamic picture of the pattern(s) of association between K3 grouping and the overall learning growth in reading during the first eight grades of school. In other words, at each grade, we can see the achievement differences between students who were grouped in specific ability groups for a certain number of years and those who were never ability grouped. In later grades, we can compare between the associations of within-class ability grouping (K3) and other forms of grouping implemented in fifth and eighth grades. Across grades, we can discern how the strength of those associations changes and the degree to which ability grouping in the early grades has long-term consequences on academic achievement, placing students on different learning trajectories.

Within the series of models predicting achievement growth, the first predicts average reading test score at spring kindergarten; in the equation that follows (TVCs: time-varying controls; TICs: time-invariant controls):

Level 1 equation:

Y_tij = π_0ij + π_1ij * (Time in Months_{Spring K})_tij + π_2ij * (Time in Months_{Spring K})_tij ² + π_3–16ij * (TVCs)_tij + e_tij

Level 2 equations:

π_0jk = b_00j + β_01–03j * (Low/Average/High Grouped_{K Grade})_ij + β_04–011j * (TICs)_ij + r_0ij ,

π_1jk = b_10j + r_1ij

Level 3 equation

b_00j = g₀₀₀ + u_00j

Models for the first and third grades included ability-grouping variables with increasing counts (range 02 years for first grade, 03 years for third, fifth, and eighth grades). The model for kindergarten included, at level 2, the (time-invariant) control moved group during kindergarten, whereas the model for the first grade added moved group during first grade, and the models from third to eighth grade added moved group during third grade. By controlling for these variables in the level 2 equations (they are part of TICs), our models compare the achievement of students who remained in a specific ability group during an entire school year with similar students who were never grouped.

The level 3 equation remains the same as the one presented earlier, whereas the level 1 and level 2 equations for Grades 13 are:

Level 1 equation:

Y_tij = π_0ij + π_1ij * (Time in Months_{Spring 1st or Spring 3rd})_tij + π_2ij * (Time in Months_{Spring 1st or Spring 3rd Grades})_tij ² + π_3–16ij * (TVCs)_tij + e_tij

Level 2 equations:

π_0jk = b_00j + β_01–03j * (Num. Years Low/Average/High Grouped_{K–1st or K–3rd})_ij + β_{04–12j or 04–013j} * (TICs)_ij + r_0ij ,

π_1jk = b_10j + r_1ij

The model for fifth grade adds at level 2 a new variable for between-class ability grouping in this grade, whereas the final model for eighth grade also adds at level 2 students’ ability group placement in the eighth grade (English course level).

In all models, we grand-mean-centered all the continuous predictors and left unaltered both count and dummy variables. This centering strategy yields intercepts representing the mean reading test score (achieved at each specific grade) of a student who had a value of zero on all count variables (i.e., always ungrouped K3, no siblings and no welfare assistance in eighth grade) and all dummy variables (i.e., did not change reading ability groups during a school year, enrolled in a regular English class in eighth grade, placed in mixed-ability fifth-grade class, female, White, from a non-single-parent family in eighth grade, attending a public, urban school in the Northeast region), and average characteristics as measured by the continuous variables (SES and other social background, educational expectations, school features). Based on the parameter estimates of the previously presented models, we also calculated, for each grade, the change in test scores associated with years of exposure to low, average, or high grouping expressed as a percentage of the average student test score of ungrouped students (i.e., the intercept). These percent changes in test scores for each grade reveal how their learning trajectories may have developed over time by showing the weight that within-class ability grouping may have at specific points in students academic careers.

Comparing parameters of ability grouping across grades we can evaluate (a) the contribution of within-class grouping to student reading test scores at the end of kindergarten when the grouped children have experienced it for the first time; (b) its contribution to student test scores at the end of first and third grades, after potentially two or three years of exposure⁹; and (c) its contribution to students test scores in later grades (fifth and eighth grades),¹⁰ when it can potentially result in further consequences for students career paths.

Our multivariate analysis for the third research questionregarding the degree to which ability grouping in K3 grades predicts placements in eighth-grade English classesconsisted of two multinomial logistic regression models (Agresti, 2002). The models predict students likelihood of placement in a below-grade-level or honors class, as opposed to a regular English class in eighth grade. In the first model, we entered the predictors indicating the number of school years of exposure to various ability-grouping levels (i.e., low, average, high) in K3 grades. We omitted the number of years being ungrouped which, by construction, was redundant with the previously mentioned three variables. We also entered the ability level of students fifth-grade class (with mixed-ability class as reference category) and fifth-grade reading test score. In the second model, we added all other controls. Using the link function  where m in the numerator refers to either 1 = below grade level or 3 = honors, whereas M in the denominator represents the reference category (i.e., 2 = regular class), the multinomial logistic equation of the full model is:

_(m) =

α_(m) + β_1–3(m) * (Num. Years Low/Average/High Grouped_K–3rd) + β_4–6(m) * (Low/Average/High Ability Class_5th–Grade) + β_7–28(m) * (Controls)

In these models, we adopted the same centering strategy used in the multilevel models so that we obtain a pair of intercepts representing the adjusted mean log odds of enrollment in the below-grade-level class (relative to regular class) and honors class (relative to regular class) of an average student (in terms of continuous predictors) who had a value of zero on all count and dichotomous variables.

RESULTS

We reconstruct eighth graders experiences in within-class ability group placements from kindergarten entry and up to the third grade. Contrary to long-standing expectations within the ability-grouping literature, students do not seem to be locked into their respective reading ability groups across grades. There is considerable variation in students ability grouping placements from one grade to the next; the majority of students experience a particular ability-group level only once (Figure 1). This is especially the case for placement into low-reading-ability groups (Figure 1, top right quadrant). Although the majority of students were never placed in the low group, more than 70% of those who experienced low grouping were placed into this group for only one year. Only 3.2% of all students who experienced low-ability grouping were placed there in all three grades. The highest proportion of students who experienced the same level of group placement in all three grades is composed of those who were never grouped (14.0%), followed by those placed in the high-ability groups (7.1%). These findings show that as students go through elementary school, they experience a variety of ability-grouping paths with combinations of exposure to ability-grouped or ungrouped classrooms and placements in different ability groups from one grade to another.

Figure 1. Number of academic years from kindergarten through third grade that eighth graders have spent in specific reading ability groups.

We follow our analysis by considering whether this complexity of instructional grouping across grades is associated with students academic experiences in later years. We examine bivariate associations between exposure to within-class ability grouping in K3 grades and student outcomes at the end point of data collection, the eighth grade, to determine the possibility of such long-term associations.

We find striking bivariate associations between years of exposure to reading groups of different ability levels in the early grades and reading test scores in the eighth grade (Figure 2). The association between number of years previously ungrouped and eighth-grade reading test scores is slightly positive, whereas there is practically no association between prior years in an average reading group and eighth-grade test scores. When considering exposure to low- or high-ability reading groups, we find an opposite pattern of association with eighth-grade test scores (Figure 2, top and bottom right quadrants). Each additional year of exposure to a low-ability group in K3 is associated with an average lower reading test score in the eighth grade (students low-grouped for one, two, and three years had average eighth-grade test scores of 155, 141, and 135, respectively). Students exposed to high-ability groups show instead a consistent higher average reading test score for each additional year spent at this level (those high-grouped for one, two, and three years had average eighth-grade test scores of 172, 182, and 186, respectively). We also notice that there is a smaller dispersion in the test scores of high-grouped students compared with the test score dispersion of their low-grouped peers. We further explore the degree to which the totality of ability grouping experiences across the early grades may serve as an agency of differential educational outcomes in multivariate models that follow our bivariate analyses.

Figure 2. Means and standard deviations of eighth-grade IRT reading test scores by eighth graders histories of ability group placement in K3 grades

Continuing with bivariate analyses (Figure 3), we observe students English course level in the eighth grade to be associated with their prior exposure to different levels of ability grouping in the early elementary grades. Students with different years of exposure to classrooms that did not group for reading instruction are somewhat more evenly distributed in eighth-grade English classes. The pattern of eighth-grade course enrollments of students who were ungrouped in the early grades looks quite similar to that of students placed in the average group (Figure 3, top and bottom left quadrants). Exposure to low- or high-ability reading groups in the early grades, however, shows strong patterns of association with English course enrollments in the eighth grade. These associations between years of placement in the low- or high-ability reading groups and eighth-grade coursework enrollments are linear, but in the opposite direction. The more years students are exposed to low K3 reading groups, the more likely they are to enroll in below-grade-level English classes in eighth grade (and less likely to enroll in regular classes, and even less likely to enroll in honors classes). The more years students are exposed to high K3 reading groups, the more likely they are to enroll in honors English classes in eighth grade (and less likely to enroll in regular classes, and even less likely to enroll in below-grade-level classes). More than one third of students who were placed in a low group for two years and almost 42% of those placed in a low group for three years enrolled in below-grade-level English classes in the eighth grade. By contrast, a little less than 33% of the students who were in high-ability reading groups for two years and close to 45% of those in high groups for three years were enrolled in honors English classes in the eighth grade (Figure 3, top and bottom right quadrants).

Figure 3. Eight graders histories of ability group placement in K­3 grades by English course placement in eighth grade

We continue our analysis with multivariate models investigating the contribution of within-class ability grouping in the early grades to differences in students reading achievement in each grade. We present our results for the fully conditional achievement growth models in Table 1. We first refer to the bottom panel of Table 1 (i.e., Random Effects) to examine the percent of the intercept variance (r₀) reproduced by our ability-grouping variables in the model for each grade. At first glance, we see that the intercept variance reproduced by the grouping variables reaches its peak at the first and third grades, with 31.4% and 32.1%, respectively. This signifies that ability grouping makes a substantial contribution to student achievement in the early grades. Even in the eighth grade, exposure to within-class ability grouping in K3 grades reproduces 18% of variation in average student achievement. In the eighth grade, subsequent ability-grouping experiences reproduce additional variation in student achievement by about 3% for fifth-grade between-class grouping and a further 5% for level of English coursework. These results indicate that all forms of ability grouping across grades are significant predictors of students achievement. We proceed by examining the specific parameter estimates for placement in different ability groups in each model. At school entry, before any exposure to within-class ability grouping, after adjusting for all controls (at both level 1 and level 2), students average initial status is less than 38 points, with an instantaneous rate of change of 2.76 and deceleration of −0.01 for each month of schooling.¹¹ At the end of kindergarten, the average achievement of ungrouped students is close to 53 points, but the average achievement of those students who have experienced low-ability grouping is 6.90 points lower. Those in the average groups receive a penalty of about 2 points, whereas those in the high reading groups have a spurt of more than 9 points. A similar pattern emerges in first and third grades in which students may have experienced up to a maximum of two and three years of within-class grouping, respectively.  We mentioned earlier that the peak of the growth curve falls outside the time frame investigated, which means that the average reading test score will be progressively higher at each time point. Parameter estimates of ability group placements from kindergarten to the eighth grade show every additional year of exposure to low grouping to be associated with a lower average reading test score, and every additional year of exposure to high grouping to be associated with a higher average reading test core. These parameters estimate test score differences between students placed in a specific ability group level and similar but ungrouped students. Comparing parameter estimates of the same ability group across grades shows the test score boost of high-ability grouping to fade faster than the penalty associated with low-ability grouping. The parameter estimate of high ability grouping drops from 9.20 in the spring of kindergarten to 6.03 in the spring of eighth grade (Model 1), while the parameter estimate of low-ability grouping drops from −6.90 to −4.89 during the same time period.  Students in average ability groups have only a slight but stable disadvantage in comparison with similar ungrouped students (parameter estimate of −2.06 in kindergarten to −.97 in the eighth grade).

We also observe that even in our most conservative models (Model 2 of fifth grade and Model 3 of eighth grade), the parameters of years in ability group placements remain statistically significant, and their magnitude is only slightly reduced despite the stringent controls of fifth-grade between-class grouping and eighth-grade English course. For example, in our final model estimating eighth-grade test scores, the parameter estimate for years in low-ability K3 grouping is reduced from −4.89 to −4.35, and the estimate for years in high-ability K–3 grouping is reduced from 6.03 to 5.25.

Table 1. Three-Level Achievement Growth Models^a Predicting Eighth Graders’ Reading IRT Scores From Fall Kindergarten to Spring Eighth Grade With Different Centering of the Time Measure^b (N_Level1 = 38,856, N_Level2 = 6,476, N_Level3 = 88)

Fixed Effects	Fall Kinder.	Spring Kinder.	Spring 1st Grade	Spring 3rd Grade	Spring 5th Grade		Spring 8th Grade
					Model 1	Model 2	Model 1	Model 2	Model 3
Mean Reading IRT, π0i (b00)	37.87	52.92	81.02	126.34	155.80	155.45	170.27	170.00	169.73
Number of Years Being Placed Inc:
Low Reading Group, b01	–	-6.90	-5.79	-4.96	-5.03	-4.79	-4.89	-4.67	-4.35
Average Reading Group, b02	–	-2.06	-0.79	-0.96	-0.97	-0.97	-0.97	-0.98	-0.95
High Reading Group, b03		9.20	7.18	5.93	6.04	5.72	6.03	5.73	5.25
Reading Class Ability Level, Spr. 5th Grade
Primarily Low Ability, b04						-4.46		-4.35	-3.98
Primarily Average Ability, b05						0.05ns		0.07ns	-0.05ns
Primarily High Ability, b06						3.37		3.16	2.51
English Course Level, Spr. 8th Grade
Below Grade Level, b07									-4.35
Honors Class, b08									5.00
Instantaneous Growth Rate, π1i (b10)	2.76	2.58	2.25	1.58	0.92	0.92	-0.10	-0.10	-0.10
Mean Deceleration, π2i	-0.01	-0.01	-0.01	-0.01	-0.01	-0.01	-0.01	-0.01	-0.01
Random Effects: Level 1 and Level 2 Variance Components and Percentage of Intercept Variation Reproducedd
Mean Reading IRT, r0	96.8	87.4	88.2	140.2	242.3	228.0	481.1	460.0	430.8
Instantaneous Growth Rate, r1	0.037	0.037	0.037	0.038	0.038	0.038	0.038	0.038	0.038
Level 1 Error, e0	147.3	147.2	147.1	147.1	147.0	146.9	147.1	147.0	146.9
Percentage of r0 Reproduced		16.6%	31.4%	32.1%	25.4%	29.8%	18.0%	21.6%	26.6%

Table 1. cont.d	Fall Kinder.	Spring Kinder.	Spring 1st Grade	Spring 3rd Grade	Spring 5th Grade		Spring 8th Grade
					Model 1	Model 2	Model 1	Model 2	Model 3
Reliability of the Level1 Regression Coefficients Estimates
Mean Reading IRT, π0i	.64	.66	.73	.85	.87	.86	.83	.82	.81
Mean Growth Rate, π1i	.66	.66	.66	.66	.66	.66	.66	.66	.66
Deviance (across Imputations) (df)	323,202 (31)	322,428 (35)	321,518 (36)	321,150 (37)	321,279 (37)	321,040 (40)	321,121 (37)	320,898 (40)	320,597 (42)
ΔDeviancede (Δdf)	–	805     (4)	1,764     (5)	2,175     (6)	2,201     (6)	2,440     (9)	2,204     (6)	2,427     (9)	2,728     (11)

^a All estimates are statistically significant at least at p < .05 unless noted as ns (not significant).

^b All models include the same set of control variables, some of which are calibrated/included according to the centering of the time measure and the relative prediction (i.e., students age and moved group). The model with time centered at fifth grade adds the variable between-class ability grouping in fifth grade; the model with time centered at eighth grade adds fifth-grade grouping and eighth-grade English course placement.

^c At school entry, these predictors are equal to 0; at spring of kindergarten, their range is 01; at spring of first grade, their range is 02; from spring of third grade forward, their range is 03. At spring of kindergarten, the full model controls also for moved group in kindergarten; at spring of first grade, the full model controls for moved group during kindergarten and moved group during first grade; from spring of third to eighth grades, all level 2 models include moved group during kindergarten, moved group during first grade, and moved group during third grade.

^d Percentages and model-deviance differences are computed from the model (relative to each centering), which includes all control variables.

^e We used full maximum likelihood to estimate all models.

Although the parameter estimates of these models show overall trends across grades, their values are not directly comparable because the intercept values change substantially across grades. We obtain a better picture of the contribution of within-class ability grouping to students achievement by evaluating the weight that grouping has at specific points in students academic career. To do so, we convert these parameter estimates into a percent change from the average achievement of comparable ungrouped students at each grade (Table 2). For example, at spring of kindergarten, the parameter estimate of −6.90 for one year of low grouping represents a test score reduction of 13.0% when compared with the average score of 52.92 for similar ungrouped students. A parameter of −5.79 represents a test score reduction of 7.1% in the first grade, when the average test score of ungrouped students is 81.02 points. Comparing these percentages across grades, we observe first that the percent change in test scores associated with ability grouping reaches its peak in the first grade. For students placed in low-ability groups, two years of placement in this group by the first grade yields a 14.1% reduction in test scores, while three years of placement in the same group in the third grade yields a 11.8% test score reduction. For students placed in high-ability groups, two years of exposure in the first grade yields a test score boost of 17.8%, while three years of exposure in the third grade yields a test score boost of 14.1%. Despite its diminishing contribution across grades, however, ability grouping in the early grades continues to be an important predictor of students test scores even five years later, in the eighth grade. At this grade, those who were consistently in low-ability groups in K3 grades experience a decrease in test scores of 7.7%, compared with those of similar ungrouped students. By contrast, students who were consistently in high-ability groups in K3 grades show a 9.3% increase in test scores compared with those of their ungrouped counterparts.

Table 2. Percentage Change^a of Eighth Graders Average Reading Test Scores by Years of Exposure to Various Forms of Grouping Across School Years

	Spring Kinder.	Spring 1st Grade	Spring 3rd Grade	Spring 5th Grade	Spring 8th Grade
Mean Reading IRTb	52.92	81.02	126.34	155.45	169.73
Percentage Change for Years in Low Group
One Year	-13.0	-7.1	-3.9	-3.1	-2.6
Two Years		-14.1	-7.8	-6.2	-5.1
Three Years			-11.8	-9.3	-7.7
Percentage Change for Years in Average Group
One Year	-3.9	-0.9	-0.8	-0.6	-0.6
Two Years		-1.8	-1.5	-1.2	-1.1
Three Years			-2.3	-1.9	-1.7
Percentage Change for Years in High Group
One Year	17.4	8.9	4.7	3.7	3.1
Two Years		17.8	9.3	7.3	6.2
Three Years			14.1	11.0	9.3
Percentage Change for Between-Class Placement in 5th Grade
Primarily Low Ability				-2.9	-2.3
Primarily Average Ability				0.0ns	-0.0ns
Primarily High Ability				2.2	1.5
Percentage Change for English Course Placement in 8th Grade
Below Grade Level					-2.6
Honors Class					2.9

^a All percentage changes refer to estimates from Table 1 that are statistically significant at least at p < .05 unless noted as ns (not significant).

^b This intercept (see Table 1) refers to the reference group, that is, students who have always been ungrouped in K3 grades.

It is also interesting to note that the percent change in test scores associated with just one year of grouping in K3 grades is slightly larger than the change associated with the type of grouping experienced in fifth or eighth grades. One year spent in a low-ability group in the early grades is associated with a 2.6% reduction in the eighth-grade test score, but attending a primarily low-ability fifth-grade class and being enrolled in a below-grade-level English class in eighth grade are associated with an eighth-grade test score reduction of 2.3% and 2.6%, respectively. Similarly, one year of exposure to a high group in the early grades is associated with an eighth-grade test score increase of 3.1%, but attendance in a primarily high-ability fifth-grade class and enrollment in an honors class in eighth grade are associated with a test score increase of 1.5% and 2.9%, respectively. Based on these results, it seems plausible to argue that within-class ability grouping in the early grades shapes students learning trajectories.

We continue our investigation of students learning trajectories by examining the degree to which within-class ability grouping predicts students placements in eighth-grade English coursework. We conduct multinomial logistic regressions, adjusting the initial bivariate association found between years of exposure to various reading groups and eighth-grade English coursework for a host of control variables. The control variables indicate students prior achievement, including between-class ability-group placement in the fifth grade, social background and family characteristics, and characteristics of students middle schools. Even with these extensive controls, years of exposure to a low-ability reading group across K3 grades is highly predictive of enrollment in a below-grade English class. Compared with their ungrouped counterparts in the early grades, students likelihood of enrollment into a below-grade-level English class (as opposed to regular class) in the eighth grade increases by 44% for every additional year of exposure to a low reading group (Table 3, Below Grade Level, Model 2). Placement in a high reading group is also highly predictive of English class enrollment in later years. In fact, after including all the control variables, each additional year of exposure to a high-ability group in K3 grades increases students likelihood of enrollment in an honors English class (as opposed to a regular class) in the eighth grade by 22% (Table 3, Honors Class, Model 2). Students in average reading groups tend to have a similar likelihood of enrollment in the three types of English classes in eighth grade when compared with similar students who were ungrouped in the early grades.

Table 3. Multinomial Logistic Regression Relative Risk Ratios^a for English Course Level, Spring Eighth Grade (Coefficients in Parentheses) (N = 6,476)

Variable	Regular Class (Ref. Category)
	Below Grade Level		Honors Class
	Model 1	Model 2	Model 1	Model 2
Number of Years K3 Grade (Reference: Ungrouped)
Placed in Low Reading Group	1.45** (0.37)	1.44** (0.36)	1.01 (0.01)	0.87 (-0.13)
Placed in Average Reading Group	1.23 (0.20)	1.14 (0.13)	1.22 (0.20)	0.95 (-0.05)
Placed in High Reading Group	0.98 (-0.02)	0.92 (-0.09)	1.48*** (0.39)	1.22* (0.20)
Reading Class Ability Level, Spring 5th Grade (Reference: Mixed Ability)
Primarily Low Ability	1.35 (0.30)	1.29 (0.25)	0.99 (0.01)	1.03 (0.03)
Primarily Average Ability	0.66* (-0.41)	0.70* (-0.36)	0.95 (-0.06)	1.04 (0.04)
Primarily High Ability	0.56* (-0.58)	0.59* (-0.53)	1.78** (0.58)	1.71* (0.54)
Reading IRT Score, Spring 5th Grade (Mean Centered)	0.97*** (-0.03)	0.97*** (-0.03)	1.04*** (0.04)	1.03*** (0.03)
Male		1.06 (0.06)		0.77 (-0.26)
Race/Ethnicity (Reference: White)
Black		0.68 (-0.39)		0.51* (-0.66)
Hispanic		0.95 (-0.05)		0.82 (-0.20)
Asian		0.79 (-0.24)		1.04 (0.04)
Other Race/Ethnicity		1.08 (0.07)		0.33** (-1.12)
Student Age in Months, Spring 8th Grade (Mean Centered)		1.01 (0.01)		0.99 (-0.01)
Single-Parent Family, Spring 8th Grade		0.82 (-0.20)		0.85 (-0.16)
Number of Siblings, Spring 8th Grade		1.01 (0.01)		1.04 (0.04)
Mother Age in Years, Fall Kindergarten (Mean Centered)		0.99 (-0.01)		1.02 (0.02)
Socioeconomic Status, Fall Kindergarten (Mean Centered)		0.86 (-0.15)		1.29 (0.25)
Level of Welfare Assistance, Spring 8th Grade		1.10 (0.10)		0.87 (-0.14)
Parental Highest Level of Education (Mean Centered)		1.00 (-0.00)		1.04 (0.04)
Parental Educational Expectations (Mean Centered)		0.92 (-0.08)		1.16* (0.15)
School Region, Spring 8th Grade (Reference: Northeast)
Midwest		0.97 (-0.04)		1.48 (0.39)
South		0.98 (-0.02)		2.37*** (0.86)
West		1.45 (0.37)		1.50 (0.41)
School Urbanicity, Spring 8th Grade (Reference: Urban School)
Suburban School		1.02 (0.02)		0.91 (-0.09)
Rural School		0.65 (-0.43)		0.59* (-0.53)
Private School, Spring 8th Grade		0.26* (-1.33)		0.31*** (-1.16)
School Size Level, Spring 8th Grade (Mean Centered)		0.94 (-0.06)		0.98 (-0.02)
School Minority Level, Spring 8th Grade (Mean Centered)		1.04 (0.04)		1.35*** (0.30)
Constant	0.08*** (-2.47)	0.10*** (-2.31)	0.11*** (-2.21)	0.14*** (-1.94)
F test (df)	21.3***                (14)	12.7***                (56)	21.3***                (14)	12.7***                (56)

^a p < 0.1. ^*p < .05. ^** p < .01. ^*** p < .001.

Associations between the ability level of fifth-grade class and eighth-grade English course enrollments are also notable. Our multivariate analysis shows that students who were in average or above-average ability classes in fifth grade have a much lower likelihood of enrolling in below-grade English classes in the eighth grade when compared with students in mixed-ability fifth-grade classes who have similar achievement and other sociodemographic characteristics. Students who were placed in a high-ability fifth-grade class have a much higher probability of enrolling in an honors English class as compared with their mixed-ability fifth-grade counterparts. Overall, these results corroborate the concerns of ability grouping critics that this instructional practice place students in different instructional paths that are reproduced from one level of schooling to the next.

SUMMARY AND CONCLUSIONS

Ability grouping fell out of favor in the late 1980s because many scholars and educational practitioners considered it an ineffective and unfair educational practice. According to its critics, this instructional practice operates as a sorting mechanism, placing students in unequal educational paths that perpetuate or accentuate achievement differences over time (Glass, 2002; Hallinan, 2003; National Education Association, 1990; Oakes, 1985, 1990). In response, some scholars and educators have developed alternative instructional practices, such as flexible grouping and differentiated instruction, whereas others are still advocating for its reinstatement (Delisle, 2015; Tomlinson, 2015). Indeed, a closer look at national data shows use of ability grouping steadily increasing in U.S. schools (Loveless, 2013). To address potential apprehensions over this resurgence of ability grouping, we investigate the consequences of within-class ability grouping at the onset of schooling, when students establish their educational foundations. We provide the first longitudinal evidence informing the long-standing concerns held by many educational scholars, practitioners, and the public at large regarding the consequences of ability grouping for students educational paths. Using data from a national study that followed students from kindergarten through the eighth grade, we estimate the degree to which within-class ability grouping in the early grades predicts students subsequent educational achievements up to the end of their middle school years.

Our analyses provide evidence that partially supports critics argument. Our findings do not support critics expectations that grouping is inflexible, leaving students locked into ability groups from one grade to the other. Early studies of cross-grade placements reported that once students were assigned to a lower group, they usually would not move upward (Glass, 2002; Kerckhoff & Glennie, 1999; Rosenbaum 1976). Our findings show that during the early elementary grades, students actually experience a variety of ability grouping paths so that only a small proportion of students were in the same ability group in all of the three grades we examined. Among the students who were ability grouped in the early grades, the majority are placed in a particular ability group level for only one year, whereas in other years, they may be ungrouped or placed in different ability groups. This is especially the case for those students placed in low-ability groups. Only a small fraction of them were locked into low-ability groups from kindergarten through third grade. These findings support proponents of the practice who expect students to be moving into higher ability groups once they have achieved a certain level of mastery. As Loveless (2013) has noted, within-class grouping in the early elementary grades seems to be more flexible than other forms of ability grouping found in higher grades. Because within-class grouping is mostly decided by the teacher, students can be grouped at different levels, or not at all, from one grade to another. Also, ability group placements may vary from one grade to another because of variations in classroom size and composition (Dreeben & Barr, 1988; Hallinan & Sorensen, 1983).

In the long run, proponents expect ability grouping to narrow educational gaps because lower achieving students would be catapulted into average, or even higher, groups. This expectation, however, is not realized. Notwithstanding the significant variability in ability group placements across the early grades, our findings support the most important of critics concerns regarding its contribution to educational inequality. Even though students do not experience the same grouping across grades, they may not be immune to its effects. Placement for even one year in a particular ability group in the early grades predicts differences in students educational experiences years later, as they are about to finish middle school and enter high school. Compared with ungrouped students with similar social, demographic, and academic characteristics who attend similar schools, students who were placed in low-ability groups for at least one year from kindergarten through third grade have lower reading test scores in every grade up to the end of middle school and are also more likely to be enrolled in eighth-grade English courses that are below grade. By contrast, students placed in high-ability groups in the early grades continue to have higher reading test scores in every grade up to the end of middle school and are more likely to be enrolled in honors English classes in the eighth grade than their counterparts who were always ungrouped in these grades.

The differences in achievement growth associated with ability grouping contradict the findings of experimental studies that earlier meta-analyses reported (Kulik, 2004). These studies found positive effects of within-class ability grouping for elementary school students of all achievement levels. They also underscore, however, that positive effects are associated with intensive instruction in small achievement groups that successfully tailor the pace and content of instruction to the needs of each group (Hong et al., 2012; Kulik, 2004). Our findings, based on nationally representative data, indicate that such optimal conditions may exist only in a few elementary schools across the United States. Differences in implementation may explain the findings by Nomi (2010), who used the same ECLSK data as the present study and found positive effects for low-achieving students in socially advantaged private schools. The same national data, however, show that advantaged schools are less likely to adopt such grouping practices than low-performing public schools with high proportions of minority and low-SES student populations (Buttaro et al., 2010; Nomi, 2010). In disadvantaged schools, limited resources, less experienced staff, or a challenging academic climate may compromise the effectiveness of this instructional practice.

By examining within-class ability grouping through a longitudinal lens, the long-term consequences of ability grouping for educational inequality are revealed to be stronger than previously expected. The achievement gaps between grouped and ungrouped students in the early grades increase with every additional year of exposure to the same ability group. Similar achievement disparities are also associated with fifth- and eighth-grade ability grouping but to a somewhat lesser degree. These gaps in achievement growth can be expected to rise mainly due to differences in the pace and content of instruction students receive in the different ability groups (Pallas et al., 1994). In addition to the achievement gaps, strong differences in English course enrollments appeared, even when students prior reading test scores are accounted for. We expect such coursework differences to be due to status distinctions of prior group placements affecting teachers expectations or students own interests and academic self-concepts. Future research should focus on examining the specific mechanisms leading to differences in middle school coursework enrollments between previously grouped and ungrouped students.

Overall, our findings attest to the significance of the early grades for students educational development. Students first school experiences may leave an indelible mark that cannot be easily overcome by educational interventions in higher grades. In consequence, providing instructional methods in the early years of schooling to effectively address student variation in skills becomes paramount to achieving the national goal of narrowing achievement gaps. We caution, though, that our analyses cannot firmly establish a causal connection between early ability grouping and later achievement. To do so would require developing an achievement growth analysis within a causal inference framework for observational data (Robins & Hernán, 2009). Such a design requires the treatment (within-class ability grouping) to be present at all time points included in the achievement growth model, which unfortunately is not possible because information on this grouping is not available for fifth and eighth grades. Nevertheless, our results are supported by prior research that established short-term effects of within-class ability grouping using the same data set (Condron, 2008; Lleras & Rangel, 2008; Tach & Farkas, 2006). Particularly important are the findings of Condron (2008), who used propensity score matching techniques to approximate the results of an experimental design. Even with this more stringent estimation adjustment, Condron (2008) found that by the end of first and third grades, students in high-ability reading groups learned more, and students in low-ability reading groups learned less, than their matched ungrouped counterparts. These findingsin conjunction with ours, showing that such grouping predicts achievement in every grade from kindergarten to the eighth grademake a compelling argument for the long-term consequences of within-class ability grouping. Skeptics may still argue that because most students placed in low-ability groups were there for only one year, the potential harm derived from this practice is minimal; our data estimated only a 2% reduction in average eighth-grade test scores for these students. Still, a good number of students experienced low-ability grouping for more than one year and have much higher test score reductions.

Ability grouping may have additional consequences for students beyond test scores. Using propensity score matching methods with the ECLSK data, Catsambis and Buttaro (2012) reported social psychological effects during kindergarten, whereby children in low-ability groups showed slower development in attributes of school readiness, such as motivation to learn, social control, and interpersonal skills, and an increase in externalizing problem behaviors. Students placed in high-ability groups showed accelerated development in the mentioned three indicators of academic predisposition. The degree to which such social psychological effects persist over the years or have long-term consequences is still not known. However, our findings showing that students who were previously placed in low-ability groups have increased chances of enrolling in a below-grade-level English class in the eighth grade provide some clues of this potential. It is therefore reasonable to conclude that ability grouping in the early years of schooling places students on an educational trajectory that reinforces initial differences in academic achievement. As students progress through school, they follow divergent educational paths and grow further apart with multiple years of exposure to ability grouping. Because minority and socioeconomically disadvantaged students are overrepresented in low-ability groups (Glass, 2002; Hallinan, 2003), the evidence mounts in support of ability grouping critics who claim that this instructional practice contributes to educational stratification, ultimately reproducing social inequalities.

Notes

1. The federal No Child Left Behind (NCLB) legislation, enacted in 2002, sought to increase student achievement in the United States and to close the achievement gap between poor and minority students and their more advantaged peers by holding schools accountable for the academic progress of all students. Under the law, if a school missed annual achievement targets set by its state for two consecutive years, either for all students or for specific subgroups, it was subject to a series of increasingly serious sanctions (Klein, 2015).

2. The appendix provides the average age of students by grade.

3. Data collected in the fall of first grade refer only to a reduced number of students (a little more than one quarter of the original sample size) and thus were not used for this analysis.

4. This test score had the highest amount of complete data among all test scores collected.

5. Teachers who used reading groups reported anywhere between two to more than five of them. Most teachers had three or four groups, with three groups being the modal category.

6. Because of these sample characteristics, we ran the multivariate analysis under different conditions (e.g., using a listwise deletion of cases, increasing the number of imputed data sets). The results appear very robust in terms of statistical significance, with small changes in the magnitude of the estimated coefficients.

7. In terms of model convergence, correlations between parameters and reliability of random coefficients, statistical significance of both fixed and random effects, and deviance statistics for the overall model fit.

8. In the ECLSK data, strata reflect differences in minority concentration, size (intended as number of children representing the sampling pool), and income in the primary sampling unit. It is reasonable to expect coefficient variation at level 3. Therefore, we also left the level 2 intercept of the slope of time to vary across strata at level 3, which improved greatly the overall fit of the model.

9. We acknowledge that data on students reading group placements and achievement test scores were collected during a very close time frame, toward the end of the school year for K3 grades. This could potentially pose a problem when estimating the contribution of ability group placement to student achievement in each of these grades because the causes of ability grouping placement could be confused with its consequences (Gamoran, 1992). For this reason, we included a control variable indicating whether or not each student remained in the same ability group during the entire school year in each grade. Controlling for this variable establishes, as much as possible, a temporal sequence with ability-group placement preceding student test scores (collected in spring of K3 grades).

10. A similar problem of temporal sequence can occur in our model predicting eighth-grade achievement when type of eighth-grade English course is controlled for. For this reason, we estimated two models, one that includes this control variable and one that does not (Table 1). The model controlling for eighth-grade English course represents the more conservative estimate of the contribution of K3 ability grouping to eighth-grade achievement.

11. At face value, these parameters may appear to be of no importance considering their magnitude. However, these values reflect the choice of using month as the unit of measure for the time variable, chosen to better fit the growth curve given the unequal spacing of the measurement occasions.

Acknowledgement

The authors contributed equally to this publication. Their names are listed in alphabetical order. Support for this research was provided by the National Institutes of Health, National Institute of Child Health and Development branch (Grant No. 5R01HD45614).

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APPENDIX

Weighted Means, Standard Deviations, Ranges, and Description of Variables Used in the Analyses

Variable	N	Meana	SD	Range	Original ECLSK: Label (Name, MinMax)
Dependent Variables
Reading IRT Scale Score on:
Fall Kindergarten	6,047	35.5	9.57	21.1128.1	C1 RC4 Reading IRT Scale Score (C1R4RSCL = 21139)
Spring Kindergarten	6,213	46.7	13.51	22.7156.9	C2 RC4 Reading IRT Scale Score (C2R4RSCL = 22157)
Spring 1st Grade	6,374	78.1	23.25	27.7184.1	C4 RC4 Reading IRT Scale Score (C4R4RSCL = 24185)
Spring 3rd Grade	6,421	127.5	27.68	52.1200.8	C5 RC4 Reading IRT Scale Score (C5R4RSCL = 51201)
Spring 5th Grade	6,463	150.3	26.31	65.2203.2	C6 RC4 Reading IRT Scale Score (C6R4RSCL = 64204)
Spring 8th Grade	6,476	168.0	28.29	86.6208.9	C7 RC4 Reading IRT Scale Score (C7R4RSCL = 85209)
English Course Level, Spring 8th Grade:
Below Grade Level	6,149	0.117	0.32	01	English Course Level (G7LEVEL = 1)
Regular Class (Ref. Category)	6,149	0.706	0.46	01	English Course Level (G7LEVEL = 2)
Honors, Enrichment, Gifted/Talented	6,149	0.177	0.38	01	English Course Level (G7LEVEL = 3)
Time in Months Between Reading IRT Assessment Dates (Fall Kindergarten to Spring 8th Grade) With Different Centering
Time Centered at:
Fall Kindergarten (TimeFall–K)	38,856	–	–	0.0–104.7	Derived from Original Variables (see Data section)
Spring Kindergarten (TimeSpring–K)	38,856	–	–	−8.6–98.5	(as above)
Spring 1st Grade (TimeSpring–1st)	38,856	–	–	−21.2–86.8	(as above)
Spring 3rd Grade (TimeSpring–3rd)	38,856	–	–	−45.2–62.7	(as above)
Spring 5th Grade (TimeSpring–5th)	38,856	–	–	−68.2–39.6	(as above)
Spring 8th Grade (TimeSpring–8th)	38,856	–	–	−104.7–0.0	(as above)
Main Independent Variables
Number of Years K3 Grade Being:
Ungrouped (Ref. Variable)	6,476	1.2	0.94	03	Derived from Original Variables (see Data section)
Placed in Low Reading Group	6,476	0.3	0.62	03	(as above)
Placed in Average Reading Group	6,476	0.6	0.76	03	(as above)
Placed in High Reading Group	6,476	0.6	0.80	03	(as above)
Reading Class Ability Level, Spring 5th Grade
Widely Mixed Ability (Ref. Category)	6,181	0.173	0.38	01	G6 Reading Class Ability Level (G6ABILITY = 4)
Primarily Low Ability	6,181	0.138	0.34	01	G6 Reading Class Ability Level (G6ABILITY = 3)
Primarily Average Ability	6,181	0.506	0.50	01	G6 Reading Class Ability Level (G6ABILITY = 2)
Primarily High Ability	6,181	0.183	0.39	01	G6 Reading Class Ability Level (G6ABILITY = 1)
TimeVarying Control Variables
Single Parent Family on:
Fall Kindergarten	6,413	0.214	0.41	01	P1 Family Type (P1HFAMIL = 3, 4)
Spring Kindergarten	6,413	0.205	0.40	01	P2 Family Type (P2HFAMIL = 3, 4)
Spring 1st Grade	6,409	0.207	0.41	01	P4 Family Type (P4HFAMIL = 3, 4)
Spring 3rd Grade	6,380	0.215	0.41	01	P5 Family Type (P5HFAMIL = 3, 4)
Spring 5th Grade	6,378	0.232	0.42	01	P6 Family Type (P6HFAMIL = 3, 4)
Spring 8th Grade	5,906	0.215	0.41	01	P7 Family Type (P7HFAMIL = 3, 4)
Number of Siblings on:
Fall Kindergarten	6,413	1.4	1.11	011	P1 Number of Siblings in Household (P1NUMSIB = 011)
Spring Kindergarten	6,413	1.5	1.12	010	P2 Number of Siblings in Household (P2NUMSIB = 014)
Spring 1st Grade	6,402	1.5	1.12	010	P4 Number of Siblings in Household (P4NUMSIB = 011)
Spring 3rd Grade	6,328	1.5	1.11	011	P5 Number of Siblings in Household (P5NUMSIB = 011)
Spring 5th Grade	6,365	1.5	1.13	012	P6 Number of Siblings in Household (P6NUMSIB = 012)
Spring 8th Grade	5,906	1.5	1.13	012	P7 Number of Siblings in Household (P7NUMSIB = 012)
Socioeconomic Status on:
Fall Kindergarten	6,476	0.01	0.80	-4.752.75	WK Continuous SES Measure (WKSESL = −5–3)
Spring Kindergarten	6,476	0.01	0.80	-4.75–2.75	(as above)
Spring 1st Grade	6,476	-0.02	0.79	-4.18–2.88	W1 Continuous SES Measure (W1SESL = −3–3)
Spring 3rd Grade	6,476	-0.06	0.80	-4.18–2.58	W3 Continuous SES Measure (W3SESL = −3–3)
Spring 5th Grade	6,476	-0.04	0.80	-3.27–2.54	W5 Continuous SES Measure (W5SESL = −3–3)
Spring 8th Grade	6,476	-0.08	0.78	-4.75–2.42	W8 Continuous SES Measure (W8SESL = −3–3)
Level of Welfare Assistance Before:
Fall Kindergarten	6,407	0.7	0.92	03	Derived from Original Variables (see Data section)
Spring Kindergarten	6,407	0.5	0.81	03	(as above)
Spring 1st Grade	6,395	0.5	0.80	03	(as above)
Spring 3rd Grade	6,347	0.5	0.78	03	(as above)
Spring 5th Grade	6,340	0.5	0.80	03	(as above)
Spring 8th Grade	5,770	0.5	0.78	03	(as above)
Parental Highest Level of Education on:
Fall Kindergarten	6,476	4.7	1.92	19	WK Parent Highest Education Level (WKPARED = 1 [8thgrade or below] thru 9 [doctorate or professional degree])
Spring Kindergarten	6,476	4.7	1.92	19	(as above)
Spring 1st Grade	6,476	4.7	1.92	19	W1 Parent Highest Education Level (W1PARED = 1 [8thgrade or below] thru 9 [doctorate or professional degree])
Spring 3rd Grade	6,476	4.9	1.94	19	W3 Parent Highest Education Level (W5PARED = 1 [8thgrade or below] thru 9 [doctorate or professional degree])
Spring 5th Grade	6,476	5.0	1.94	19	W5 Parent Highest Education Level (W5PARED = 1 [8thgrade or below] thru 9 [doctorate or professional degree])
Spring 8th Grade	6,476	5.0	1.95	19	W8 Parent Highest Education Level (W8PARED = 1 [8thgrade or below] thru 9 [doctorate or professional degree])
Parental Educational Expectations on:
Fall Kindergarten	6,476	4.1	1.09	16	P1 What Degree Expected of Child (P1EXPECT = 1 [less than HS diploma] thru 6 [PhD, MD, or other higher degree])
Spring Kindergarten	6,476	4.1	1.09	16	(as above)
Spring 1st Grade	6,476	4.0	1.08	16	P4 What Degree Expected of Child (P4EXPECT = 1 [less than HS diploma] thru 6 [PhD, MD, or other higher degree])
Spring 3rd Grade	6,476	4.0	1.06	16	P5 What Degree Expected of Child (P5EXPECT = 1 [less than HS diploma] thru 6 [PhD, MD, or other higher degree])
Spring 5th Grade	6,476	4.0	1.06	16	P6 What Degree Expected of Child (P6EXPECT = 1 [less than HS diploma] thru 6 [PhD, MD, or other higher degree])
Spring 8th Grade	6,476	4.0	1.09	16	P7 What Degree Expected of Child (P7EXPECT = 1 [less than HS diploma] thru 6 [PhD, MD, or other higher degree])
School Region, K3 Gradeb:
Northeast (Ref. Category)	6,476	0.167	0.37	01	Census Region in Sample Frame (CREGION = 1)
Midwest	6,476	0.228	0.42	01	Census Region in Sample Frame (CREGION = 2)
South	6,476	0.394	0.49	01	Census Region in Sample Frame (CREGION = 3)
West	6,476	0.211	0.41	01	Census Region in Sample Frame (CREGION = 4)
School Region, Spring 5th Grade:
Northeast (Ref. Category)	6,476	0.162	0.37	01	R6 Census Region (R6REGION = 1)
Midwest	6,476	0.228	0.42	01	R6 Census Region (R6REGION = 2)
South	6,476	0.398	0.49	01	R6 Census Region (R6REGION = 3)
West	6,476	0.212	0.41	01	R6 Census Region (R6REGION = 4)
School Region, Spring 8th Grade:
Northeast (Ref. Category)	6,476	0.160	0.37	01	R7 Census Region (R7REGION = 1)
Midwest	6,476	0.230	0.42	01	R7 Census Region (R7REGION = 2)
South	6,476	0.400	0.49	01	R7 Census Region (R7REGION = 3)
West	6,476	0.210	0.41	01	R7 Census Region (R7REGION = 4)
School Urbanicity, K3 Gradeb:
Urban School (Ref. Category)	6,476	0.363	0.48	01	Location Type in Base Yr Sam. Frame Rev (KURBAN_R = 1)
Suburban School	6,476	0.409	0.49	01	Location Type in Base Yr Sam. Frame Rev (KURBAN_R = 2)
Rural School	6,476	0.228	0.42	01	Location Type in Base Yr Sam. Frame Rev (KURBAN_R = 3)
School Urbanicity, Spring 5th Grade:
Urban School (Ref. Category)	6,462	0.344	0.48	01	R6 Location Type (R6URBAN = 1)
Suburban School	6,462	0.424	0.49	01	R6 Location Type (R6URBAN = 2)
Rural School	6,462	0.232	0.42	01	R6 Location Type (R6URBAN = 3)
School Urbanicity, Spring 8th Grade:
Urban School (Ref. Category)	6,276	0.334	0.47	01	R7 Location Type (R7URBAN = 1)
Suburban School	6,276	0.426	0.49	01	R7 Location Type (R7URBAN = 2)
Rural School	6,276	0.240	0.43	01	R7 Location Type (R7URBAN = 3)
Private School on:
Fall Kindergarten	6,476	0.137	0.34	01	(see below)
Spring Kindergarten	6,476	0.137	0.34	01	S2 Public or Private School (S2PUPRI = 2)
Spring 1st Grade	6,476	0.136	0.34	01	S4 Public or Private School (S4PUPRI = 2)
Spring 3rd Grade	6,476	0.136	0.34	01	S5 Public or Private School (S5PUPRI = 2)
Spring 5th Grade	6,467	0.127	0.33	01	S6 Public or Private School (S6PUPRI = 2)
Spring 8th Grade	6,443	0.115	0.32	01	S7 Public or Private School (S7PUPRI = 2)
School Size Level on:
Fall Kindergarten	6,476	3.5	1.08	05	(see below)
Spring Kindergarten	6,476	3.5	1.08	05	S2 Total School Enrollment (S2ENRLS = 1 [0149 students] thru 5 [750 and above])
Spring 1st Grade	6,476	3.5	1.08	05	S4 Total School Enrollment (S4ENRLS = 1 [0149 students] thru 5 [750 and above])
Spring 3rd Grade	6,476	3.5	1.08	05	S5 Total School Enrollment (S5ENRLS = 1 [0149 students] thru 5 [750 and above])
Spring 5th Grade	6,448	3.5	1.04	05	S6 Total School Enrollment (S6ENRLS = 1 [0149 students] thru 5 [750 and above])
Spring 8th Grade	6,086	3.9	1.14	05	S7 Total School Enrollment (76ENRLS = 1 [0149 students] thru 5 [750 and above])
School Minority Concentration Level on:
Fall Kindergarten	6,476	2.7	1.53	05	(see below)
Spring Kindergarten	6,476	2.7	1.53	05	S2 Percent Minority Students (S2MINOR = 1 [less than 10%] thru 5 [75% or more])
Spring 1st Grade	6,476	2.7	1.56	05	S4 Percent Minority Students (S4MINOR = 1 [less than 10%] thru 5 [75% or more])
Spring 3rd Grade	6,476	2.8	1.56	05	S5 Percent Minority Students (S5MINOR = 1 [less than 10%] thru 5 [75% or more])
Spring 5th Grade	6,467	2.9	1.56	05	S6 Percent Minority Students (S6MINOR = 1 [less than 10%] thru 5 [75% or more])
Spring 8th Grade	6,443	2.9	1.50	05	S7 Percent Minority Students (S7MINOR = 1 [less than 10%] thru 5 [75% or more])
Time-Invariant Control Variables
Male	6,476	0.514	0.50	01	Child Composite Gender (GENDER = 1)
Race/Ethnicity:
White (Ref. Category)	6,476	0.589	0.49	01	Child Composite Race (RACE = 1)
Black	6,476	0.167	0.37	01	Child Composite Race (RACE = 2)
Hispanic	6,476	0.170	0.38	01	Child Composite Race (RACE = 3, 4)
Asian	6,476	0.031	0.17	01	Child Composite Race (RACE = 5)
Other Race/Ethnicity	6,476	0.044	0.21	01	Child Composite Race (RACE = 6, 7, 8)
Student Age in Months, Fall Kindergarten	6,476	67.4	4.04	57.582.3	Derived from Original Variables (see Data section)
Student Age in Months, Spring Kinderg.	6,476	73.5	4.04	63.388.5	(as above)
Student Age in Months, Spring 1st Grade	6,476	85.5	4.05	75.0100.2	(as above)
Student Age in Months, Spring 3rd Grade	6,476	109.3	4.08	98.8124.2	(as above)
Student Age in Months, Spring 5th Grade	6,476	132.6	4.11	122.1148.0	(as above)
Student Age in Months, Spring 8th Grade	6,476	168.8	4.11	158.5184.6	(as above)
Mother Age in Years, Fall Kindergarten	6,426	33.8	6.65	1880	Derived from Original Variables (see Data section)
Moved Reading Group in Kindergarten	6,298	0.145	0.35	01	T2 Moved to Higher/Lower/Same Group (T2GPMOBL = 12)
Moved Reading Group in 1st Grade	5,981	0.312	0.46	01	T4 Moved to Higher/Lower/Same Group (T4GPMOBL = 12)
Moved Reading Group in 3rd Grade	5,655	0.132	0.34	01	T5 Moved to Higher/Lower/Same Group (T5GPMOBL = 12)
Analytic Instruments
Student Level Longitudinal (Fall KindergartenSpring 8thGrade) Survey Design Effects Adjustments:
Probability Weights	6,476			2.47,295	C1C2C4C5C6C7 Child Panel Weight Full Sample (C1_7FC0 = 07,295)
Strata	6,476			188	C1C2C4C5C6C7 Child Panel Weight Taylor Series Sample Strata (C17FCSTR = 188)
Primary Sampling Units	6,476			165	C1C2C4C5C6C7 Child Panel Weight Taylor Series PSU (C17FCPSU = 165)

^a The number of decimal places varies in order to convey the substantive meaning of each variable, e.g.: when the mean expresses percentages the third decimal point, given the analytic sample size, signals a change of about 6 cases; for ordinal and count variables, one decimal point should suffice to indicate whether the average is closer to the lower or upper level, although this practice hides some of the changes occurring on the timevarying measures over time.

^b Only students who did not change school from fall of kindergarten to spring of first grade were selected (see Data section).

Cite This Article as: Teachers College Record Volume 121 Number 2, 2019, p. 1-50 https://www.tcrecord.org ID Number: 22574, Date Accessed: 10/9/2021 12:53:55 PM Purchase Reprint Rights for this article or review