Navigating the Middle Grades (2012)

Working Paper

Navigating the Middle Grades: Evidence from New York City

Michael J. Kieffer William H. Marinell

April 2012

Navigating the Middle Grades: Evidence from New York City

Michael J. Keiffer Teachers College, Columbia University William H. Marinell The Research Alliance for New York City Schools
April 2012

© 2012 Research Alliance for New York City Schools. All rights reserved. You may make copies of and distribute this work for noncommercial educational and scholarly purposes. For any other uses, including the making of derivative works, permission must be obtained from the Research Alliance for New York City Schools, unless fair use exceptions to copyright law apply.

CONTENTS
I. II. Overview ................................................................................................................. 1 Analytic Approach .................................................................................................. 3

III. Data .......................................................................................................................... 4 IV. Findings .................................................................................................................. 5 ............................................................................... 5 What do students’ grade four-eight achievement and attendance trajectories look like? ............... 5 Does students’ grade four-eight achievement predict who’s on track in grade nine? .................... 7 Does students’ grade four-eight attendance predict who’s on track in grade nine? ...................... 8
Who’s on track to graduate and why? Do particular demographic groups of students demonstrate middle-grades trajectories that are associated with being off-track in grade nine? ................................................................... 12 Is middle grades performance equally predictive of later on-track status across ethnic and

....................................................................................................... 17 Do these patterns hold across schools? ........................................................................... 17
language groups?

V. Exploratory Analyses ........................................................................................... 20
How do high-growth and low-growth schools compare?

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VI. Conclusions & Implications................................................................................. 22 VII. Notes and References .......................................................................................... 23

I. OVERVIEW
Educators have long asserted that the middle grade years (typically, grades six through eight) are a time of both great importance and vulnerability in students’ K-12 schooling. Anecdotal and empirical evidence suggest that students encounter new social and emotional challenges, increased academic demands, and major developmental transitions during the middle grade years. 1 These questions have gained more prominence in New York City as the new Chancellor, Dennis M. Walcott, has made middle school reform a central priority for current efforts. 2 Despite the academic and developmental challenges associated with the middle grades transition, we know very little about whether changes in students’ achievement or attendance during this period can help us anticipate their progress toward graduation. The Research Alliance for New York City Schools has been investigating these topics in New York City through collaboration with principal researcher Michael Kieffer (Teachers College, Columbia University). The study is motivated by an interest in learning more about whether and when students struggle during the transitions into, through, and out of the middle grades, how early in their schooling vulnerable students can be identified, and whether the challenge of supporting students in the middle grades is prevalent across different demographic groups and across schools. In this study, we investigated whether and how students’ achievement and attendance change between grades four and eight and identified moments during this period when students’ achievement and attendance suggest that they will struggle to graduate from high school within four years. Our findings are as follows: • We can identify students who will struggle to graduate after four years of high school quite early in their schooling. Students’ grade four attendance rates and their scores on New York’s grade four math and English language arts (ELA) assessments all help predict the likelihood that students will graduate after four years of high school. Students’ performance on the grade four ELA and math assessments are particularly strong predictors of the likelihood that they will graduate on time. Despite these early grade four warning signs, it is also important to monitor students’ progress through the middle grades, as students whose attendance and achievement decline during this time period are less likely to graduate after four years of high school. In other words, the middle grades are not “too late to fail”: Even students who are performing reasonably well at the beginning of the middle grades can fall off-track during the middle grades, and these declines have consequences for students’ progress towards graduation.

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More specifically, students whose attendance falls during the middle grades are particularly at risk for not being able to graduate after four years of high school. While most students attend school regularly until the spring of grade six, their attendance begins to decline after this point, and falls quite rapidly between grades seven and eight. Many of the students whose attendance declines during this final middle grades year are on a similarly troubling trajectory at the end of grade nine, one year later. While slightly less portentous than attendance, students’ achievement during the middle grades also helps predicts which students will graduate after four years of high school. In particular, students whose math scores decline during the middle grades (relative to the scores of their peers) are particularly less likely to graduate after four years of high schools. These relationships are largely the same for students from different ethnic backgrounds and for English language learners. African-American, Native American, and Latino students are more likely than their White peers to demonstrate poor attendance and achievement during the middle grades, which in turn are associated with their lower probability of on-time graduation. English language learners demonstrate slightly better attendance but substantially lower achievement during the middle grades than their native English-speaking peers, whereas students who speak another language at home but are not designated as English language learners demonstrate consistently better attendance and achievement than native English speakers. These trends hold across schools in New York City. The vast majority of variation in students’ middle grades performance is between students attending the same schools and exploratory analyses with selected school variables (e.g., student demographics, teacher experience) suggested that substantial overlap in middle grades performance across schools with different characteristics. These results suggest that all schools need to be concerned about identifying and supporting those students who fall behind during the middle grades.

•

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These findings suggest that struggling students can be identified quite early in their schooling and that changes in students’ achievement and attendance during the middle grades can help us anticipate which students will struggle during high school in their progress towards graduation. The findings also point to some evidence of students’ resiliency in the middle grades, suggesting that interventions during the middle grades are not too late to prevent students from falling offtrack in their progress towards graduation. In the remainder of this report, we describe our analytic approach and the data sets that we use in these analyses, then we describe our findings in more detail and raise questions for future research. Readers who are interested in even more detail about our analyses are referred to the technical appendix to this report.

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II. ANALYTIC APPROACH
Previous research has demonstrated the importance of students’ performance in grade nine in predicting the likelihood of their graduating after four years of high school, which we refer to throughout this report as graduating “on time.” 3 These findings have prompted urban schools systems, such as those in Chicago and NYC, to develop “on-track indicators,” which identify vulnerable students in an attempt to help ensure that these students graduate on time and are prepared for post-secondary work or study. Following this precedent, our first set of analyses investigates the relationship between NYC students’ performance in grade nine and the likelihood of their graduating after four years of high school. Based on this analysis, we create a high school on-track indicator (i.e., a composite of student performance measures in grade nine) that maximizes our ability to predict students’ graduating on time. Subsequently, in our second set of analyses, we use this indicator as our new outcome, and we examine whether students’ performance between grades four and eight predicts their grade-nine indicator scores and, thus, their probability of graduating on time. In our third set of analyses, we investigate whether these predictive relationships hold across student groups and school. In particular, we investigate whether these relationships are the same for students from different ethnic backgrounds and for English language learners compared to native English speakers. We further investigate what proportion of the variation in middle grades performance is between children in the same schools and what proportion is between different schools, with the intent of describing the extent to which the patterns we detect are similar across the variety of schools in NYC. We end by providing exploratory descriptive analyses of some school characteristics for schools with high, medium, and low rates of average growth in attendance and achievement.

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III. DATA
These analyses draw on a number of student-level data files from the New York City Department of Education’s (DOE) archive. We use the DOE’s audited J-Form Register and Longitudinal Cohort files to identify first-time grade nine students and to monitor their progress through their high school graduation. The NY State ELA and Math Test Score file is the source of information on students’ English language arts and mathematics test scores in grades four and eight, and the student-level Regents file contains information about whether students attempted and passed Regents exams in grade nine. We obtain information about students’ grade nine course-taking, as well as the number of credits that they earned from these courses, from the Course Detail Records file, and information about attendance from the DOE’s official attendance system. In all analyses, our target population is all students in New York City schools, including English language learners and students with disabilities. For the first set of analyses, which predicts the probability of students graduating after four years of high school, we examine the progress of the cohort of students who were first-time ninth graders in the 2005-2006 school year. We begin with the 2005-2006 cohort because our data span the cohort’s progress from grade four through high school, including the cohort’s graduation in the spring of 2009. To examine whether the on-track indicators that we create for this cohort are robust across a different group of students, we conduct a series of parallel analyses for students who were first-time ninth graders during the 2000-2001 school year. For the second and third set of analyses, which examines students’ achievement and attendance patterns as they transition into and through the middle grades, we examine the progress of four cohorts of students who were first-time fourth graders between the 2000-2001 and 2003-2004 school years. Our data cover the former cohort’s progress through high school graduation and the latter cohort’s progress through grade nine. We focus this second set of analyses on the entire population of students who ever appear in these four cohorts (N = 303,845), although we also conducted additional analyses with the subset of students with complete data for the entire range of years and variables (see technical appendix). Results were largely the same for the entire population and the smaller subset.

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IV.
Who’s on track to graduate and why?

FINDINGS

The preliminary results from our first set of analyses suggest that indicators of students’ performance in grade nine are strong predictors of the likelihood that students will graduate after four years of high school. These grade-nine predictors include credits earned, courses failed, grade point average, attendance rate, whether a Regents exam was attempted, and whether a Regents exam was passed. These predictors remain strong when controlling for students’ grade eight test scores in English language arts and mathematics and for “school effects” – in other words, the role that schools play in influencing students’ performance. The single best predictor of students’ graduating on time is the number of credits students earn in grade nine. For both of cohorts that we studied, students who earned 11 or more credits in grade nine (i.e., one-quarter of the 44 credits needed to graduate) had a predicted graduation rate of 83 percent or higher, whereas students earning eight or fewer credits had a predicted graduation rate of 20 percent or lower. Using logistic regression to find the relative weights of each of the multiple predictors, we created a grade-nine “on-track” indicator that summarizes these predictive relationships into a single predicted probability of graduation for each student. The median predicted student graduation rate was 67 percent. Students with on-track indicator values in the top quartile had an average predicted graduation rate of about 92 percent, whereas those in the bottom quartile had an average predicted graduation rate of seven percent. Based on this analysis, we can also calculate the grade-nine indicator score for students who have yet to graduate, as long as we have their grade-nine performance, an approach that we use in the second set of analyses below. What do students’ grade four-eight achievement and attendance trajectories look like? In the second set of analyses, we describe how students’ achievement and attendance fluctuate between grades four and eight. This description serves as the basis for our investigation of the extent to which students’ performance during the middle grades predicts their grade-nine indicator score. Our preliminary results suggest that there is wide variation in both the levels of students’ attendance and achievement and in the extent to which these levels change during the middle grades. Attendance rates are generally high and stable across students from grades four through eight and then drop off steeply between grades seven and eight. Figure 1 illustrates this overall pattern by displaying growth trajectories in students’ attendance between fall of grade four and spring of grade eight for 20 students that we chose at random from the dataset. As Figure 1 depicts, most of the students have high attendance rates (above 90 percent of the days enrolled) until the spring of grade six, when they begin to fall steeply. In addition, some students’ 5

attendance rates fall much more dramatically than others during grades seven and eight. Moreover, students’ past attendance is not helpful in predicting which students will fall behind most in the later periods. Students’ grade four attendance does not correlate with their change in attendance in grade eight; in other words, the students who fell behind dramatically in grades seven and eight were equally likely to have high attendance as they were to have low attendance in earlier grades. The patterns that Figure 1 features also illustrate the general patterns across the entire dataset. Figure 1: Patterns of Change in Attendance between Fall Semester of Grade 4 and Spring Semester of Grade 8 for a Random Sample of 20 Students in New York City Schools

Grade

Note: Whole numbers indicate fall semester (e.g., 4 = fall of grade 4) while .5 indicates spring semester (e.g., 8.5 = spring of grade 8). Students’ achievement test scores are more stable than their attendance over time, with many students remaining at similar levels, relative to their peers, from grades four through eight. Figure 2 illustrates this general pattern by displaying the patterns of change in mathematics achievement for 20 students that we selected at random from the dataset. As shown, those students who have higher levels of achievement in grades four and six tend to be those who end up with higher achievement in grade eight, while only a few students move from above-average to below-average (or vice versa) over time. It is worth noting that these figures – like the analyses on which our overall findings are based – use z-scores, which categorize students’ 6

performance relative to other students in the same grade and have an average of zero in each grade. Thus, the flat nature of the overall trend is a result of our choice of measure and does not indicate that the average student’s mathematics performance is stagnant over time. Although the overall trend depicts stability across students’ relative performance, a minority of students fall substantially behind the bulk of New York City students, while others catch up with or surpass their peers. These patterns are largely similar for mathematics and for English language arts. Figure 2: Patterns of Change in Students’ Relative Rank-order in Mathematics Achievement for a Random Sub-sample of 20 Students in New York City Schools

Does students’ grade four-eight achievement predict who’s on track in grade nine? We find that students’ grade four achievement tells us a great deal about how they will perform in grade nine (i.e., predicts their grade-nine indicator score) and, thus, their likelihood of going on to graduate high school on time. However, changes in achievement during the middle grades also provide important information about how students will perform in grade nine. In particular, changes in students’ math scores between grades six and eight are much more predictive of their grade-nine indicator score than are changes between grades four and six grade—highlighting the importance of students’ performance in math during the middle grades for their eventual graduation. For reading scores, changes between grades six and eight are equally as predictive of students’ grade-nine indicator score as are changes in students’ reading scores between grades four and six. To illustrate these findings, Figure 3 displays achievement patterns and the associated ontrack indicator scores for four hypothetical students with prototypical performance. The left panel displays trends in students’ achievement between grades four and eight. As shown, the 7

student trajectory displayed in blue starts at the NYC average in mathematics achievement in grade four and remains at the average level through grade eight; the student trajectory in green starts at the NYC average but falls substantially behind in grades seven and eight (i.e., has a slope that is 1 SD below the sample mean slope); 4 the student trajectory in red starts substantially below-average in grade four 5 (i.e., with an initial level that is one SD below the sample mean) but maintains this level; and the student trajectory in purple starts substantially below-average in grade four (i.e., one SD below the mean) but falls even further behind (i.e., with a slope that is one SD below the mean slope). Given the relationships we find above, these differences in achievement patterns predict major differences in students’ grade-nine on-track indicator score and thus their probability of graduating on time. The right panel of Figure 3 displays the percent chance of being on-track for graduation for these same four prototypical students. As shown, only the student trajectory in blue is associated with a greater than 50 percent chance of later graduation. Most notably, a student who starts at an average level but falls behind during the middle grades (i.e., the student represented in green) has a less than 50 percent of graduating on time, which is only marginally better than a student who starts behind in grade four (i.e., the student represented in red). We found similar patterns, though to a somewhat lesser degree, for reading achievement. Does students’ grade four-eight attendance predict who’s on track in grade nine? As with our analyses of students’ achievement, students’ grade four attendance is an important predictor of whether students are on-track to graduate by the end of grade nine. Further, we find that students’ attendance during the middle grades may be an even more important source of information about their later success than their test scores. To illustrate these findings, Figure 4 displays attendance growth patterns and associated on-track indicator scores for four prototypical students. As the left panel shows, the blue and green trajectories both represent students who start with average attendance in grade four (i.e., attendance rates of roughly 94 percent); while the blue trajectory represents a student who maintains this level, the green trajectory represents a student who fall behinds sharply in attendance in grades seven and eighth (i.e., missing an additional 9 percent of days each year). This later drop represents a slope that is 1 SD below the sample mean. Similarly, the red and purple trajectories represent students who start with below-average attendance (i.e., attendance rates of roughly 87 percent or one SD below the mean); while the red trajectory represents a student who maintains this (relatively low) level, the purple trajectory represents a student who falls even further below (i.e., with a slope one SD below the sample mean). Our findings indicate that these differences in attendance patterns predict differences in students’ on-track indicator score and thus their chances of going on to graduate on time. As the right panel shows, a student who falls behind in the middle grades (i.e., the green trajectory) has only a 57 percent chance of going on to graduate, compared to the 75 percent chance for a student who maintains an average level of attendance. A student with a consistently low level of attendance (i.e., the red trajectory) 8

has only a 43 percent chance of graduating, while a student who low attendance in grade four who falls even further in grades seven and eight has only a 25 percent chance of going on to graduate.

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Figure 3: Fitted Trajectories for Four Prototypical Students with Average or Below-average Levels and Rates of Growth in Mathematics Achievement (Left Panel) with their Predicted Ninth-grade On-track Indicator Score, i.e., Percent Chance of Being On-track for Later Graduation (N = 303,845)

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Figure 4: Fitted Growth Trajectories in Attendance for Four Prototypical Students between Fourth and Eighth Grade (Left Panel) with their Predicted Ninth-grade On-track Indicator Score, i.e., Percent Chance of Being On-track for Later Graduation (N = 303,845)

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Do particular demographic groups of students demonstrate middle-grades trajectories that are associated with being off-track in grade nine? We find that Latino students, African-American students, and English language learners, on average, have lower attendance rates and achievement scores in the middle grades, as we might expect from other research. 6 For attendance, gaps between African-American and Latino students and their White and Asian counterparts begin in grade four, but grow most substantially between spring of grade six and spring of grade seven, as shown in Figure 5. Achievement test score gaps are large in grade four and remain so through grade eight, as shown in Figures 6 and 7.

Figure 5: Attendance Growth Trajectories Fitted by Ethnicity

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Figure 6: Mathematics Achievement Test Scores Fitted by Ethnicity

Figure 7: Reading Achievement Test Scores Fitted by Ethnicity

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These differences in middle grade performance by ethnic group are associated with substantially higher levels of risk for being off-track in grade nine for later high school graduation. For instance, students with middle-grade attendance and achievement at the average levels for White students have grade-nine on-track probabilities near .88, suggesting a high chance of going on to graduate, whereas students with middle-grade attendance and achievement at the average levels for Latino and African-American students have grade-nine on-track probabilities of .69 and .66, respectively indicating substantially lower probability of going on to graduate. It is worth noting that actual graduation rates are lower for all students and particularly for Latino and African-American students, in part because other factors beyond middle grades performance contribute to graduation. Students designated as English language learners when they enter grade four have mixed performance, with slightly higher attendance rates but much lower achievement, compared to their peers from native English-speaking backgrounds. Figure 8 displays attendance rates for three groups of students: native English speakers; students designated as English language learners in grade four; and language minority learners (i.e., students from homes in which English is not the primary language) who are not designated as English language learners. As shown in Figure 8, English language learners have consistently, if only slightly (approximately one percent) higher attendance rates across the middle grades, compared to native English speakers. Large and persistent achievement test score differences were also found between students designated as English language learners and native English speakers for both mathematics (Figure 9) and reading (Figure 10), though there is some evidence that English language learners narrow achievement gaps over time, as shown by the narrowing of the gap between the green and blue lines in the Figures 9 and 10. These differences in middle grade performance by language background are associated substantial differences in students’ probability of being on-track in grade nine. For instance, English language learners have an ontrack probability of approximately .62, compared to probabilities of .72 for native English speakers and .85 for language minority learners who are not designated as English language learners. In contrast, language minority learners who were not designated as English language learners in grade four have consistently better attendance rates and consistently higher achievement compared to native English speakers. This is consistent with research that suggests that language minority status, in and of itself, is not a substantial risk factor, that bilingualism can be a benefit. 7

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Figure 8: Attendance Rates by English Language Learner and Language Minority Status

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Figure 9: Mathematics Achievement over Time by English Language Learner and Language Minority Status

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Figure 10: Reading Achievement over Time by English Language Learner and Language Minority Status

Is middle grades performance equally predictive of later on-track status across ethnic and language groups? In addition to investigating whether ethnic and language groups have differing levels of middle grades performance, we also investigated whether the predictive relationships found between middle grades performance and later on-track status held across ethnic and language groups. We found that largely the same pattern of predictions held across groups. For each ethnic group, attendance levels and changes during the middle grades were robustly associated with on-track status in grade nine. Similarly, for each ethnic group, achievement levels and change during the middle grades were strongly associated with on-track status in grade nine (see Technical Appendix). Across groups, the overall pattern held, indicating that middle grades performance matters for all ethnic and language groups. Do these patterns hold across schools? We conducted analyses to investigate whether students’ levels and changes in attendance and achievement were associated with the schools that they attend. Specifically, we conducted analyses that allow us to partition the variation in performance into the portion that is associated 17

with differences between students attending the same school (within-school variation) and the portion that is associated with differences between students attending different schools (betweenschool variation). We partition this variation for both levels and rates of change for both achievement and attendance. We found that for both attendance and achievement, that vast majority of variation is associated with individual differences between students attending the same schools rather than due to differences between schools. In particular, the changes in attendance and achievement that we have noted and have found to be associated with later ontrack status appear to vary across students within schools. This suggests that some students in nearly every school serving the middle grades in NYC are declining substantially in achievement and attendance and that some students in nearly every school are maintaining or improving in achievement and attendance. Figure 11 displays the proportion of variation that is withinschools and between-schools for achievement and attendance levels (in grade six) and change (between grade six and grade eight). The importance of individual differences between students within the same schools holds particularly true for attendance. Only two percent to five percent of variation in attendance is associated with differences between schools. For achievement, a more substantial proportion of the variation in grade six level (27 percent) is associated with differences between schools; however, a much smaller proportion of variation in students’ changes in achievement between sixth and eighth grade (10 percent) is associated with differences between schools. Together, these findings suggest that the problem of students falling behind in attendance and achievement in the middle grades is not isolated to specific schools, but is a relatively universal phenomenon across schools in NYC. It also suggests that all schools have some students who are maintaining or recovering success in the middle grades.

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Figure 11: Proportion of Variance that is Associated with Differences between Students within Schools (in Blue) and between Different Schools (in Red) for Achievement and Attendance Levels and Slopes

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V. EXPLORATORY ANALYSES
How do high-growth and low-growth schools compare? To provide additional insight into how these patterns differ across schools, we conducted an exploratory analysis involving selected publically-available variables for school characteristics. Specifically, we identified which school students attended in grade six, then categorized schools based on their average estimated achievement and attendance growth into four quartiles. We next estimated the mean values for selected school characteristics for each quartile. Such an analysis has the value of looking beyond schools’ average levels of achievement and attendance to instead explore schools’ average rates of growth in achievement and attendance. These analyses suggested that the associations with demographic characteristics found for the student level (described above) largely hold at the school level as well (see technical appendix for details). For instance, schools which demonstrated higher rates of growth in attendance during the middle grades tended to have fewer African-American and Latino students. In addition, we found that schools with higher levels of growth in achievement and attendance tended to have much fewer students receiving free lunch, compared with schools with lower levels of growth in achievement and attendance. As shown in Figure 12, schools in the first quartile, whether the quartile was based on achievement or attendance growth, had much higher percentages of students receiving free lunch than schools in the fourth quartile. We also conducted exploratory analyses with teacher characteristics, including variables for teachers’ years of experience and the percent of core classes taught by “highly qualified” teachers (as defined by No Child Left Behind). However, these variables appeared to be relatively unrelated to school averages for achievement and attendance growth (see technical appendix). Schools classified as high-growth had similar proportions of relatively new and of more experienced teachers, compared to schools classified as low-growth, and this held whether the classification was based on achievement growth or attendance growth.

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Figure 12: Percent of Students Receiving Free Lunch for Schools, by Quartile based on School-average Achievement Growth between Grade 6 and 8, School-average Attendance Growth between Fall, Grade 6 and Spring, Grade 7, and Schoolaverage Attendance Growth between Spring 7 and Spring, Grade 8

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VI. CONCLUSIONS & IMPLICATIONS
Together, these results suggest several important discoveries. First, we have confirmed earlier research conducted in other contexts by finding that ninth grade performance provides strong information about whether students in NYC go on to graduate on time. Second, echoing research on the importance of early learning, 8 we find that NYC students’ attendance and achievement towards the end of the elementary grades tell us a lot about the likelihood that they will be on-track to graduate at the start of high school. Third, however, we find that the middle grades may not be too late to prevent declining attendance and stagnant achievement, given that changes during these years (not just prior levels in grade four) are predictive of students’ later success. Fourth, we found that these patterns largely hold across students of differing ethnic and language backgrounds and that students’ middle grade performance may explain much of the attainment gap in high school graduation. Fifth, we found that these patterns hold consistently across schools, such that little of the variation in attendance and achievement growth is associated with differences between schools. Sixth, we found that the aggregated demographic characteristics of schools, including concentration of students receiving free lunch, did appear to differentiate between schools in which students demonstrated more and less positive growth in attendance and achievement, but that teacher characteristics did not appear to differentiate between these schools. These findings suggest that initiatives to prevent declines in students’ attendance and achievement in the middle grades may well help accomplish their intended objectives. Our preliminary findings also suggest that focusing on students’ achievement alone may be misguided. While relative improvements or declines in students’ test scores are predictive of students’ progress towards graduation, changes in attendance during the middle grades are also equally, if not more, predictive of the likelihood that students will be on-track in grade nine to graduate from high school within four years. In finding similar relationships across demographic groups and across schools, these results suggest that attention to middle grades performance should cut across settings and groups. In light of Chancellor Walcott’s call for middle school reform, these findings suggest that such attention to the middle grades is warranted, although they cannot speak to the efficacy of particular strategies for such reform. These analyses also raise questions for future research. Most pressing for NYC educators, there are many open questions about how to intervene in the middle grades to promote positive trajectories in achievement and attendance. In that this analysis found relatively little existing variation between schools in these variables, such interventions may need to look beyond what is currently happening in New York City schools. In addition, such interventions will likely need to addresses gaps in achievement and attendance within schools of various kinds and configurations.

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VII. NOTES AND REFERENCES
1

Eccles, J. (fall, 1999). The Development of Children Ages 6 to 14. The Future of Children: When school is out, 9(2). Retrieved on February 17, 2011 from http://www.futureofchildren.org/futureofchildren/publications/docs/09_02_02.pdf Eccles, J., Midgley, C., & Adler, T. F. (1984). Grade-related changes in the school environment: Effects on achievement motivation. In J. G. Nicholls (Ed.) The development of achievement motivation (pp. 283-331). Greenwich, CT: JAI Press. National Middle School Association. (1995). This we believe: Developmentally responsive middle schools. Columbus, OH: Author. Seidman, E., Aber, J. L., & French, S. E. (2004). The organization of schooling and adolescent development. In K. Maton, C. Schellenbach, B. Leadbeater, & A. Solarz (Eds.), Investing in children, youth, families, and communities: Strengths-based research and policy (pp. 233–250). Washington, DC: American Psychological Association.

2

New York City Department of Education. In major policy address, Chancellor Dennis M. Walcott calls middle schools “ripe for opportunity,” lays out a bold strategy for success. News Release. Retrieved February 2, 2012 from http://schools.nyc.gov/Offices/mediarelations/NewsandSpeeches/2011-2012/msspeechatnyu92011.htm Allensworth, E. M., & Easton, J. Q. (2007). What matters for staying on-track and graduating in Chicago Public High Schools: A close look at course grades, failures, and attendance in freshman year. Retrieved on February 17, 2011 from http://ccsr.uchicago.edu/publications/07%20What%20Matters%20Final.pdf For all of these prototypical cases, a “major decline” is defined as one standard deviation below the sample mean for true rate of growth. For mathematics achievement during the sixth to eighth grade period, this is equivalent to approximately .2 z-score points. By substantially below average, we mean one standard deviation below the sample mean in true scores for fourth grade status. For mathematics achievement, this standard deviation is equivalent to approximately .92 z-score points.

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4

5

6

National Center for Educational Statistics (2009). Nation’s Report Card. Washington, DC: U.S. Department of education.

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E.g., Kieffer, M. J. (2011). Converging trajectories: Reading growth in language minority learners and their classmates, kindergarten to Grade 8. American Educational Research Journal, 48, 1157-1186. Balfanz, R. (2009). Putting middle grades students on the graduation path: A policy and practice brief. Retrieved on December 17, 2010 from: http://www2.kapoleims.k12.hi.us/campuslife/depts/electives/dance/Putting%20Middle%20Grades%20Studesnts% 20on%20the%20Graduation%20Path.%20%20A%20Policy%20and%20Practice%20Brief.%20%202009.pdf Balfanz, R., Herzog, L., & Mac Iver, D. J. (2007). Preventing student disengagement and keeping students on the graduation path in the urban middle-grades schools: Early identification and effective interventions. Educational Psychologist, 42(4), 223-235.

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The Research Alliance for New York City Schools conducts rigorous studies on topics that matter to the city’s public schools. We strive to advance equity and excellence in education by providing non-partisan evidence about policies and practices that promote students’ development and academic success.

Technical Appendix

Navigating the Middle Grades: Evidence from New York City

Michael J. Kieffer

April 2012

Navigating the Middle Grades: A Descriptive Analysis of the Middle Grades in New York City Technical Appendix

Michael J. Kieffer Teachers College, Columbia University

April 2012

© 2012 Research Alliance for New York City Schools. All rights reserved. You may make copies of and distribute this work for noncommercial educational and scholarly purposes. For any other uses, including the making of derivative works, permission must be obtained from the Research Alliance for New York City Schools, unless fair use exceptions to copyright law apply.

CONTENTS

I.

Methods ....................................................................................................... 1
Sample......................................................................................................... 1 Measures ...................................................................................................... 1

II.

Data Analysis and Results .................................................................... 3
Descriptives ............................................................................................................. 3 Who’s on track to graduate and why? Predicting High School Graduation based on Grade Nine Predictors ............................................................................................................... 4 What do students’ grade four-eight achievement and attendance trajectories look like? ........... 4 Does students’ grade four-eight achievement predict who’s on track in grade nine? ...............11 Does students’ grade four-eight attendance predict who’s on track in grade nine? .................14 Do particular demographic groups of students demonstrate middle-grades trajectories that are associated with being off-track in grade nine? ................................................................19 Is middle grades performance equally predictive of later on-track status across ethnic and language groups? ....................................................................................................29 Do these patterns hold across schools?

.......................................................................32

III.

Exploratory Analysis of School Characteristics .........................35

I.
Sample

METHODS

As noted in the main text, the analytic sample for the high school graduation analyses was the cohort of New York City students who were first-time ninth graders in the 2005-2006 school year. The analytic sample for the middle grades analyses included four cohorts of students who were first-time fourth graders between the 2000-2001 and 2003-2004 school years. Our data cover the former cohort’s progress through high school graduation and the latter cohort’s progress through grade nine. We identified first-time fourth graders by selected students who were in grade four in the appropriate school year for their cohort, but were not in grade four during the previous school year. We conduct the middle grades analyses primarily with the entire population of students who ever appear in these four cohorts (N = 303,845), using fullinformation maximum likelihood to account for data missing due to attrition or other causes. This sample thus included all students, including students classified as English language learners and students with disabilities. Descriptive statistics on the sample are displayed in Table 1 below. We also checked results against an analyses using the subset of students with complete data (n = 169, 953), i.e., those who do not enter or exit the district at any point between grades four and nine, who progress through each grade annually, and who have complete data on the variables of interest; results were largely similar when analyses were conducted with this subsample, so the results for the complete sample are reported here. Measures
High School Graduation.

Students’ on-time graduation in the fourth year after they enrolled as first-time ninth graders was drawn from the DOE’s Student Trackng System Dataset. Thus, graduation was defined as graduating within four years, so this variable equaled 0 for students who graduated later or completed a General Equivalency Diploma.
Performance in Grade Nine.

Measures of grade nine performance include credits earned over the course year, courses failed over the course of the year, and grade point average across the year, each drawn from the Course Detail Records file. Measures of grade nine performance also included the total attendance rate, as a percent of days enrolled, drawn from the DOE’s Student Tracking System Dataset. Measures also included a dummy variable for whether a Regents exam was attempted and one for whether a Regents test was passed in grade nine.
Achievement in Grades four-eight.

Achievement in the areas of mathematics and reading/English-language arts was assessed using the New York State tests, with scores drawn from the NY State ELA and Math Test Score
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file. Because the scale for these tests changed over the years of administration and were not vertically linked to be comparable across grade levels, scores were rescaled to be within-grade zscores, based on the district means and standard deviations. This approach is not ideal for growth modeling because it subtracts out the normative trajectory for growth and assumes homogeneity of variance across time. However, given the limitations of the scaling of the test scores, it is more appropriate than using the original scaled scores. It also has benefits over using proficiency levels, in that it preserves the continuous nature of achievement, as opposed to arbitrarily dividing the distribution into discrete categories. Tests were taken annually, yielding one score per year.
Attendance in Grades four-eight.

Attendance was measured as a percent of the days enrolled for each semester, yielding two attendance rate values for each year. Attendance data were drawn from the DOE’s Attendance System.

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II.
Descriptives

DATA ANALYSES AND RESULTS

Table 1: Means and standard deviations for achievement test scores, attendance along with demographics for the analytic sample (N = 303,845)
Mean Mathematics Achievement (within-grade zscores) Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Fall, Grade 4 Spring, Grade 4 Fall, Grade 5 Spring, Grade 5 Fall, Grade 6 Spring, Grade 6 Fall, Grade 7 Spring, Grade 7 Fall, Grade 8 Spring, Grade 8 African-American Asian Hispanic Native American White ELL in Grade 4 Language Minority Standard Deviation -0.02 1.01 -0.06 1.03 -0.08 1.04 -0.10 1.06 -0.15 1.09 -0.50 1.02 -0.07 1.03 -0.09 1.04 -0.09 1.05 -0.12 1.06 94.00 7.53 92.91 8.25 93.06 11.35 92.14 9.06 92.03 12.58 91.05 10.91 91.39 12.47 89.64 12.64 90.75 12.95 87.08 13.88 Percentage of Sample 33.3% 12.3% 39.1% 0.4% 14.8% 9.4% 41.4%

Reading Achievement (within-grade z-scores)

Attendance (Percent of Days Enrolled)

Race/ethnicity

Language Background

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Who’s on track to graduate and why? Predicting High School Graduation based on Grade Nine Predictors Logistic regression was used to determine whether the grade nine measures predicted ontime high school graduation. As shown in Table 1, credits earned, courses failed, GPA, attendance rate, whether a Regents test was attempted, and whether a Regents test was passed all predicted high school graduation. As mentioned in the main text, these predictors remain strong when controlling for students’ grade-eight test scores and for fixed effects of high school. These parameter estimates were used as relative weights for each measure in order to estimate a single “on-track” indicator that summarizes these predictive relationships for each student. These scores were then used in subsequent analyses. Table 2: Results of Logistic Regression Predicting On-time High School Graduation based on Grade (G) 9 Predictors Unstandardized Estimate Wald χ2 Intercept -7.12 1605.62*** G9 Credits Earned 0.31 3893.69*** G9 Courses Failed -0.09 235.93*** G9 Grade Point Average 0.03 211.09*** G9 Annual Attendance Rate 0.03 675.88*** G9 Regents’ Test Attempted 0.33 88.77*** G9 Regents’ Test Passed 0.94 543.00*** *** p < .001

What do students’ grade four-eight achievement and attendance trajectories look like? To address the question concerning the nature of students’ growth trajectories in achievement and attendance across grades four through eight, we fitted a series of piecewise unconditional growth models using latent growth modeling in a structural equation modeling (SEM) framework (Bollen & Curran, 2006). Piecewise models allow for nonlinear trajectories in which students demonstrate different rates of growth during different specified periods. They have the advantage of directly modeling true rates of growth (i.e., growth rates that are freed of occasion-specific measurement error) for each theoretically important period for which sufficient data points are available. Figure 1 displays a path diagram for the hypothesized unconditional piecewise growth model for attendance. As shown, students’ individual growth trajectories in attendance were specified to have an initial (Fall, grade four) status and four slopes representing growth in four distinct periods: Fall, grade four to Fall, grade five; Fall, grade five to Spring, grade six; Spring, grade six to Spring, grade seven; and Spring, grade seven to Spring, grade eight. Each slope was allowed to vary across children and the slopes were allowed to covary with one another and with
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students’ initial (Fall, grade four) status. Inspection of empirical growth plots (Singer & Willett, 2003) suggested that this piecewise model was appropriate to compare the population average growth trajectory as well as individual differences in the shape and elevation of students’ growth trajectories. Fitting of various unconditional models also indicated that this model was superior to other theoretically viable specifications. It is worth noting that the second period is longer due to the number of measurement occasions; with ten occasions, a four-slope piecewise model is only possible if one slope covers a longer period than the other three. Comparisons of alternate models indicated that this particular piecewise model, with a longer second period, fitted the data better than potential alternatives. As shown in Table 3, fitting the unconditional piecewise growth model for attendance provides insight into the average trajectory for attendance as well as individual variation around that trajectory. As shown in the second row of Table 3, students’ initial status, on average, was relatively high (approximately 94 percent of days enrolled) in the fall of grade four. As shown in the third through sixth rows of Table 2, each slope was negative, indicating declines in attendance on average, with the largest decline (a decline of 3 percent of days enrolled) occurring between spring of grade seven and spring of grade eight. The variance components displayed in the seventh through eleventh rows of Table 2 indicate that there was substantial variation in students’ initial status and each rate of growth, with the largest variance occurring again between spring of grade seven and spring of grade eight. Together, these two findings suggest that this period involves not only the largest declines in attendance for all students but also the widest variation in declines, with some students declining relative to other students to a much greater extent than in previous periods. In addition, this unconditional piecewise growth model provides insight into the relationship between early levels and later rates of growth in attendance. Correlations between students’ initial status and their rates of growth are displayed in the twelfth through fifteenth rows of the right column titled “Selected Standardized Estimates.” As shown, initial status had a moderately sized negative relationship with students’ rates of growth between fall, grade four and fall, grade five, but only trivially sized relationships with students’ rates of growth during later periods. This suggests that students’ levels of attendance prior to the middle grades provides little information for predicting the extent to which they will maintain or decline in attendance during the middle grades. Figure 2 displays a path diagram for the hypothesized unconditional piecewise growth model for mathematics achievement. As shown, students’ individual growth trajectories in mathematics achievement were specified to have an initial (grade four) status and two slopes representing growth in two distinct periods: grade four to grade six and grade six to grade eight. Each slope was allowed to vary across children and the slopes were allowed to covary with one another and with students’ initial (grade four) status. A parallel model with the same piecewise specification was fitted to reading/English-language arts achievement. Inspection of empirical growth plots suggested that this model was appropriate for both mathematics achievement and reading/English-language arts achievement. Fitting of various unconditional models also indicated that this model was superior to other theoretically viable specifications for both achievement outcomes. As shown in Table 4, fitting the unconditional piecewise growth model for mathematics and reading/English-language arts achievement provides insight into the levels and relative change in achievement for the average student in NYC schools. In interpreting these results, it is
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important to recall that within-grade z-scores were used, in the absence of a more absolute developmental scaled score, so change represents students’ relative movements within the rank order rather than growth in a traditional sense. As shown in the second through fourth rows of Table 4, estimates of initial status were close to the city average in grade four and average change was minimal, as we would expect given that the within-grade z-score scale eliminates average growth with increasing grade level. More interestingly, the variance components displayed in the fifth through seventh rows indicate much wider variation in initial (grade four) status (.86 within-grade SD) than in either rate of growth (.03 within-grade SD per year for both Slope 1 and Slope 2 in mathematics; .02 for both Slope 1 and Slope 2 in reading/Englishlanguage arts). This suggests that there is substantial stability in the rank-order of students’ achievement levels. For instance, a student with a high rate of growth in mathematics relative to the sample (i.e., 1 SD above the mean in Slope 1) would only change in the rank-order by 0.17 within-grade SD each year; a student with an analogously high rate of growth in reading/ELA would only change by 0.14 within-grade SD. These unconditional growth models of achievement also provide insight into the extent to which early levels of achievement predict later rates of growth, as shown in the eighth through eleventh rows and the fourth and sixth columns of Table 4. For both mathematics achievement, students’ initial (grade four) status had a trivially sized relationship with students’ later rates of growth (rs between -.01 and -.11). This should not be interpreted to mean that early levels do not strongly predict later levels of achievement; in fact, the previous findings above concerning stability of the rank-order suggests that they do. Rather, they suggest that growth trajectories are largely parallel, with students who start substantially higher in grade four demonstrating growth trajectories that neither increase nor decrease substantially than those of their peers.

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Figure 1: Path diagram for hypothesized piecewise linear growth model for attendance

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Figure 2: Path diagram for hypothesized piecewise linear growth model for mathematics achievement

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Table 3: Selected Results for Unconditional Piecewise Growth Model for Attendance (N = 303,845) Unstandardized Estimates Fixed Effects Initial (Fall, Grade 4) Status Slope 1 (Fall, Grade 4 – Fall, Grade 5) Slope 2 (Fall, Grade 5 – Spring, Grade 6) Slope 3 (Spring, Grade 6 – Spring, Grade 7) Slope 4 (Spring, Grade 7 – Spring, Grade 8) Initial Status 93.95*** -1.32*** -0.67*** -1.28*** -3.01*** 49.45*** Selected Standardized Estimates

Variance Components

Slope 1 40.44*** Slope 2 17.60*** Slope 3 45.84*** Slope 4 88.49*** Covariances Initial Status with Slope 1 -16.86*** -.38 Initial Status with Slope 2 0.36** .01 Initial Status with Slope 3 2.34*** .05 Initial Status with Slope 4 0.02 .00 Slope 1 with Slope 2 -9.20*** -.35 Slope 1 with Slope 3 -1.55*** -.04 Slope 1 with Slope 4 1.20*** .02 Slope 2 with Slope 3 1.76*** .06 Slope 2 with Slope 4 -2.12*** -.05 Slope 3 with Slope 4 -13.80*** -.22 Note: For the purposes of FIML, this model also included factors and indicates for mathematics and reading/ELA achievement and Grade 9 ontrack indicator score, which were allowed to covary with the latent growth factors for attendance. ** p < .01; *** p < .001

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Table 4: Selected Results for Unconditional Piecewise Growth Models for Mathematics and Reading Achievement (N = 303,845) Mathematics Achievement Unstandardized Selected Estimates Standardized Estimates -0.02*** Reading/ELA Achievement Unstandardized Selected Estimates Standardized Estimates -0.05***

Fixed Effects

Initial (Grade 4) Status Slope 1 (Grade 4 – -0.03*** -0.02*** Grade 6) Slope 2 (Grade 6 – -0.03*** -0.01*** Grade 8) Variance Initial Status 0.86*** 0.81*** Components Slope 1 0.03*** 0.02*** Slope 2 0.03*** 0.02*** Covariances Initial Status with -0.02*** -0.11 -0.01*** -.06 Slope 1 Initial Status with -0.01*** -0.07 -0.001 -.01 Slope 2 Slope 1 with Slope 2 0.003*** 0.12 -0.01*** -.29 Note: For the purposes of FIML, this model also included factors and indicates for attendance and Grade 9 ontrack indicator score, which were allowed to covary with the latent growth factors for mathematics and reading/ELA achievement. *** p < .001

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Does students’ grade four-eight achievement predict who’s on track in grade nine? Two SEM models were fitted to investigate whether variation in students’ levels and rates of relative change in achievement predict their grade nine indicator score. As shown in the path diagram in Figure 3, the grade nine ontrack indicator for students’ probability of on-time high school graduation was regressed on the growth terms for the piecewise growth model for mathematics achievement. A parallel model was fitted for reading/English-langauge arts achievement predicting the grade nine ontrack indicator. Table 5 displays the selected results of fitting this SEM model for mathematics achievement. As shown, initial status in mathematics has a strong relationship with the grade nine ontrack indicator. The two slopes in mathematics achievement also had moderate to large relationships with the grade nine ontrack indicator, with the stronger relationship demonstrated by the later growth term, representing growth between grade six and grade eight. Together, these findings suggest that initial (grade four) status in achievement provides substantial information for later probability of high school graduation, but also that the extent to which students change during the middle grades also provides valuable information. In particular, growth during the middle grades is substantially more predictive of later probability of high school graduation than growth during the upper-elementary grades. Table 6 displays the selected results of fitting a second, analogous SEM model for reading/English-language arts achievement. As shown, initial status in reading/ELA has a strong relationship with the grade nine on-track indicator. The two slopes in reading/ELA achievement also had moderate relationships with the grade nine on-track indicator that were approximately the same as each other. As with mathematics achievement, these findings suggest that grade four levels of reading/ELA achievement provide substantial information to predict probability of later high school graduation, but also that changes during the middle grades provide valuable information. However, unlike mathematics achievement, changes during the middle grades were similarly predictive of later graduation as change during the upper-elementary grades.

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Figure 4: Path diagram for hypothesized structural equation model in which latent growth in mathematics achievement predicts Grade 9 indicator for the probability of ontime high school graduation

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Table 5: Selected Results from Structural Equation Model with Initial Status and Rates of Growth in Mathematics Achievement Predicting Grade (G) 9 Ontrack Indicator Score (N = 303,845) Paths Unstandardized Estimates 1.63*** Standardized Estimates

Math Initial (Grade 4) Status  G9 Ontrack .51 Indicator Math Slope 1 (Grade 4 –Grade 6)  G9 Ontrack 3.70*** .21 Indicator Math Slope 2 (Grade 6 –Grade 8)  G9 Ontrack 6.62*** .39 Indicator Note: Model also included variances and intercepts for mathematics achievement initial status, slope 1, and slope 2 as well as residual variances for Grade 9 ontrack indicator score. For FIML purposes, model also included latent growth factors for reading/ELA and attendance which were allowed to covary with mathematics growth terms and Grade 9 ontrack indicator. *** p < .001

Table 6: Selected Results from Structural Equation Model with Initial Status and Rates of Growth in Reading/English-Language Arts (ELA) Achievement Predicting Grade (G) 9 Ontrack Indicator Score (N = 303,845) Paths Unstandardized Estimates 1.51*** Standardized Estimates .47

Reading/ELA Initial (Grade 4) Status  G9 Ontrack Indicator Reading/ELA Slope 1 (Grade 4 –Grade 6)  G9 Ontrack 5.79*** .28 Indicator Reading/ELA Slope 2 (Grade 6 –Grade 8)  G9 Ontrack 6.79*** .33 Indicator Note: Model also included variances and intercepts for reading/ELA achievement initial status, slope 1, and slope 2 as well as residual variances for Grade 9 ontrack indicator score. For FIML purposes, model also included latent growth factors for mathematics and attendance which were allowed to covary with reading/ELA growth terms and Grade 9 ontrack indicator. *** p < .001

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Does students’ grade four-eight attendance predict who’s on track in grade nine? A SEM model analogous to that fitted for the question above was fitted to investigate the extent to which levels and rates of growth in attendance predict students’ grade nine on-track probability of later high school graduation. As shown in Figure 4, grade nine on-track indicator score was regression on the intercept and four slope terms for the attendance growth model. Table 6 displays selected results for fitting this SEM model. As shown, students’ initial status in attendance had a strong relationship with their grade nine on-track indicator score and each of the four slope terms also had a moderate relationship with the grade nine on-track indicator. As with achievement, this finding indicates that students’ level of attendance in grade four provides information about whether they will be on track in grade nine for ultimately graduating from high school, but also that students’ growth or declines in attendance during the upper-elementary and middle grades provide additional information about whether they will be on track in grade nine. The magnitudes of the relationships between rates of growth and grade nine on-track indicator are largely similar across the different periods studied. To investigate the relative contributions of attendance and achievement during the middle grades to grade nine on-track indicator score, an additional SEM model that included regression paths between grade nine on-track indicator and the growth parameters for both attendance and achievement was fitted. This hypothesized model is displayed in Figure 5. Due to the high covariances among growth parameters for mathematics achievement and reading/ELA achievement, these were not modeled separately. Instead, a simple composite for achievement for each time point was estimated by averaging the z-scores for mathematics achievement and reading/ELA achievement; these then served as the indicators for a piecewise latent growth model for achievement as shown in Figure 5. Table 8 presents the results from fitting this model. As shown in the rightmost column, the standardized regression paths indicated that effects of both attendance and achievement initial levels and rates of growth remained robust when accounting for both simultaneously. These estimates are somewhat smaller than those presented in the attendance-only model in Table 7 and the achievement-only models in Tables 5 and 6, but remain non-trivial in magnitude. Moreover, the finding that growth in attendance and achievement during the middle grades adds information beyond that provide by students’ initial status in these predictors continues to hold when both predictors are accounted for simultaneously.

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Figure 4: Path diagram for hypothesized structural equation model for latent growth in attendance predicting Grade (G) 9 ontrack indicator for probability of high school graduation.

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Table 7: Selected Results from Structural Equation Model with Initial Status and Rates of Growth in Attendance Predicting Grade (G) 9 Ontrack Indicator Score (N = 303,845) Paths Unstandardized Estimates 0.195*** Standardized Estimates .47

Attendance Initial (Fall, G4) Status  G9 Ontrack Indicator Attendance Slope 1 (Fall, G4 –Fall, G5)  G9 0.175*** .38 Ontrack Indicator Attendance Slope 2 (Fall, G5 –Spring, G6)  G9 0.241*** .34 Ontrack Indicator Attendance Slope 3 (Spring, G6-Spring, G7) 0.137*** .31 G9 Ontrack Indicator Attendance Slope 4 (Spring, G7-Spring, G8) 0.085*** .27 G9 Ontrack Indicator Note: Model also included variances and intercepts for reading/ELA achievement initial status, slope 1, and slope 2 as well as residual variances for Grade 9 ontrack indicator score. For FIML purposes, model also included latent growth factors for mathematics and attendance which were allowed to covary with reading/ELA growth terms and Grade 9 ontrack indicator. *** p < .001

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Figure 5: Path diagram for hypothesized structural equation model in which latent growth in achievement (simple composite of mathematics and reading/ELA achievement) and attendance predicts Grade 9 on-track indicator

Note: Model also included measurement models for attendance as shown in Figure 1 and for achievement analogous to the model shown in Figure 2. Att = Attendance; Ach = Achievement Composite

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Table 8: Selected Results from Structural Equation Model with Initial Status and Rates of Growth in Both Attendance and Achievement Predicting Grade (G) 9 Ontrack Indicator Score (N = 303,805) Paths Unstandardized Standardized Estimates Estimates Attendance Initial (Fall, G4) Status  G9 0.13*** 0.30 Ontrack Indicator Attendance Slope 1 (Fall, G4 –Fall, G5)  G9 0.12*** 0.26 Ontrack Indicator Attendance Slope 2 (Fall, G5 –Spring, G6)  G9 0.16*** 0.22 Ontrack Indicator Attendance Slope 3 (Spring, G6-Spring, G7) 0.09*** 0.21 G9 Ontrack Indicator Attendance Slope 4 (Spring, G7-Spring, G8) 0.07*** 0.21 G9 Ontrack Indicator Achievement Composite Initial (G4) Status  G9 1.23*** 0.37 Ontrack Indicator Achievement Composite Slope 1 (G4-G6)  G9 3.42*** 0.17 Ontrack Indicator Achievement Composite Slope 2 (G6-G8)  G9 4.51*** 0.22 Ontrack Indicator Note: As shown in Figure 5, mnodel also included variances and intercepts for and covariances among all latent growth terms as well as a residual variance for Grade 9 ontrack indicator score. *** p < .001

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Do particular demographic groups of students demonstrate middle-grades trajectories that are associated with being off-track in grade nine? Given the relationships between middle-grades trajectories (level and growth) in attendance and achievement with the later grade nine on-track indicator, we next investigated whether particular demographic characteristics including race/ethnicity and language background predict students’ middle-grades trajectories. Table 9 presents descriptive statistics on achievement and attendance by race/ethnicity group while Table 10 presents descriptive statistics on achievement and attendance by language backgrounds. Specifically, we fitted a series of SEM models in which demographic characteristics predicted initial status and slopes for attendance and achievement. Figure 5 presents the SEM model for ethnicity (represented as a series of dummy variables with White specified as the reference category) predicting initial status and piecewise rates of growth in attendance, while Figure 6 presents the analogous SEM model for each achievement outcome. Analogous models were fitted for language background (represented as a series of two dummy variables for English language learner designated in grade four and Language Minority, non-ELL, with native English speakers specified as the reference category).

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Table 9: Means and standard deviations for achievement and attendance by race/ethnicity AfricanAsian (n Latino (n Native White American = 37,329) = 118,911) American (n (n = (n = = 1155) 44,871) 101,237) Mathematics Grade 4 -0.28 0.62 -0.21 -0.32 (0.98) 0.53 Achievement (0.90) (1.08) (0.91) (1.01) (within-grade zGrade 5 -0.34 0.66 -0.24 -0.40 (1.08) 0.50 scores) (0.94) (1.04) (0.93) (0.96) Grade 6 -0.37 0.70 -0.27 -0.40 (1.05) 0.42 (0.94) (1.06) (0.94) (0.97) Grade 7 -0.41 0.73 -0.29 -0.47 (1.15) 0.44 (0.96) (1.04) (0.94) (0.98) Grade 8 -0.46 0.88 -0.33 -0.49 (1.08) 0.34 (0.96) (1.10) (0.94) (1.01) Reading Grade 4 -0.20 0.41 -0.30 -0.30 (0.96) 0.53 Achievement (0.92) (1.08) (0.92) (1.08) (within-grade zGrade 5 -0.27 0.42 -0.29 -0.36 (0.99) 0.60 scores) (0.94) (1.01) (0.95) (1.06) Grade 6 -0.28 0.47 -0.30 -0.36 (1.02) 0.48 (0.94) (1.05) (0.96) (1.05) Grade 7 -0.29 0.48 -0.20 -0.38 (1.02) 0.49 (0.95) (1.03) (0.98) (1.05) Grade 8 -0.33 0.51 -0.32 -0.41 (0.98) 0.44 (0.93) (1.14) (0.93) (1.13) Attendance (Percent Fall, 93.29 96.76 93.51 92.75 (8.95) 94.62 of Days Enrolled) Grade 4 (8.55) (5.21) (7.49) (6.01) Spring, 91.90 96.40 92.43 91.61 (9.30) 93.63 Grade 4 (9.37) (5.57) (8.18) (6.55) Fall, 92.36 96.17 92.46 91.52 93.71 Grade 5 (12.03) (9.19) (11.58) (13.18) (10.04) Spring, 91.12 95.84 91.68 90.14 92.76 Grade 5 (10.14) (6.04) (8.97) (12.24) (7.49) Fall, 91.09 95.62 91.47 90.30 92.75 Grade 6 (13.39) (9.96) (12.48) (13.23) (12.14) Spring, 89.91 95.58 90.38 88.43 91.93 Grade 6 (12.08) (7.24) (10.72) (13.42) (9.36) Fall, 90.32 95.47 90.66 89.41 92.50 Grade 7 (13.38) (9.55) (12.51) (13.56) (11.22) Spring, 88.31 94.95 88.67 86.88 91.04 Grade 7 (13.81) (9.79) (12.58) (15.25) (10.77) Fall, 89.66 95.32 89.87 88.26 91.87 Grade 8 (14.00) (9.05) (13.14) (15.20) (11.40) Spring, 86.00 92.38 85.99 84.38 88.16 Grade 8 (15.01) (9.47) (14.13) (15.63) (12.01)
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Table 10: Means and standard deviations for achievement and attendance by language background Native English Speakers (n = 177,868) -0.04 (0.98) -0.11 (1.00) -0.15 (1.00) -0.18 (1.03) -0.25 (1.03) 0.00 (1.00) -0.04 (1.03) -0.07 (1.02) -0.08 (1.03) -0.12 (1.04) 93.41 (7.89) 92.03 (8.73) 92.50 (11.38) 91.27 (9.56) 91.37 (12.85) 90.12 (11.53) 90.66 (12.93) 88.63 (13.32) 89.99 (13.50 86.16 (14.52) Language Minority, Non-ELL (n = 98,083) 0.20 (0.98) 0.19 (1.00) 0.18 (1.03) 0.17 (1.05) 0.15 (1.11) 0.07 (0.97) 0.08 (0.96) 0.08 (0.99) 0.09 (1.00) 0.08 (1.04) 95.07 (6.60) 94.33 (7.04) 94.13 (10.89) 93.59 (7.78) 93.29 (11.90) 92.65 (9.52) 92.78 (11.36) 91.45 (11.12) 92.23 (11.67) 88.75 (12.48) ELLs in Grade 4 (n = 28,572)

Mathematics Achievement (withingrade z-scores)

Reading Achievement (within-grade z-scores)

Attendance (Percent of Days Enrolled)

Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Fall, Grade 4 Spring, Grade 4 Fall, Grade 5 Spring, Grade 5 Fall, Grade 6 Spring, Grade 6 Fall, Grade 7 Spring, Grade 7 Fall, Grade 8 Spring, Grade 8

-0.73 (0.99) -0.65 (1.07) -0.60 (1.08) -0.58 (1.08) -0.49 (1.06) -1.01 (0.89) -0.89 (0.97) -0.86 (0.98) -0.84 (1.04) -0.77 (0.96) 93.98 (7.77) 93.50 (8.21) 92.78 (12.39) 92.74 (8.90) 91.89 (12.71) 91.56 (10.26) 91.22 (12.61) 89.87 (12.16) 90.40 (13.09) 87.14 (13.68)

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Figure 5: Path diagram for hypothesized latent growth in attendance predicted by racial/ethnic group

Note: Model also included measurement model for attendance as shown in Figure 1. F= Fall, S = Spring, G = Grade

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Figure 6: Path diagram for latent growth in mathematics predicted by racial/ethnic group

Note: Model also included measurement model for achievement as shown in Figure 2. G = Grade

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Table 11 presents the results for attendance predicted by ethnic group while Table 12 presents the results for achievement. As shown in Table 11, Native American, Latino, and African-American students all have notably lower initial (grade four ) status in attendance, compared to White students, while Asian students have notably higher grade four status. African-American students demonstrate steeper declines in each of the first three periods, but a less steep decline in the last period, compared to White students. Latino and Native American students demonstrate steeper declines during the middle two periods, spanning grade five to grade seven. Asian students have less steep declines in each of the four periods. It is worth noting that the residual variance for the final measurement occasion was set to 0 to avoid convergence problems. As shown in Table 12, Native America, Latino, and African-American students had substantially lower mathematics and reading/ELA achievement in grade four than their White peers (nearly 1 SD in each case). These gaps persist through grade eight as shown by the relatively trivial differences in rates of growth demonstrated by these three ethnic groups. These results are also illustrated in Figures 5-7 in the main text. Table 13 presents the results for attendance predicted by language background and Table 14 presents the results for achievement. As shown in Table 9, ELLs had slightly higher attendance in grade four than their native English-speaking counterparts, and relatively similar rates of growth. In contrast, language minority learners who were not designated as ELLs had notably higher attendance rates in grade four and slightly less steep rates of decline, compared to native English speakers. As with the models for attendance by ethnicity, the residual variance for the final measurement occasion was set to 0 to avoid convergence problems in this model. In contrast, ELLs’ achievement was much slower than their counterparts, as shown in Table 14. As shown in the column marked Y-standardized estimates, the standardized difference between ELLs and their native English-speaking peers was ¾ of a SD for mathematics achievement and nearly 9/10ths of a SD for reading/ELA achievement in grade four. ELLs made notably improvements over time, as indicated by their more positive rates of growth in both the grade four-six and grade six-eight periods, but remain far below their peers as shown in Figures 9 and 10 in the main text. Language minority learners who were not designated as ELLs had somewhat higher achievement in grade four in both mathematics and reading/ELA as well as slightly higher rates of growth in both periods.

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Table 11: Selected Results for Piecewise Growth Model for Attendance Predicted by Race/Ethnicity (N = 303,699)
Unstandardized Estimates 94.59*** -1.89*** 2.18*** -1.12*** -1.36*** 0.13 -2.40*** -1.38*** -0.10 0.64*** 0.07 -0.14** 0.14 -1.45 -0.51*** -0.79*** 0.31*** -0.30*** -0.26*** -1.32* 0.81 -0.75*** -0.78* 0.31*** -0.89*** -0.82*** -0.83 -3.63* -3.27*** 0.16 0.40*** 0.10 0.38*** 2.23* 2.50 48.74*** Selected Y-Standardized Estimates

Fixed Effects

Initial (Fall, Grade 4) Status

Slope 1 (Fall, Grade 4 – Fall, Grade 5)

Slope 2 (Fall, Grade 5 – Spring, Grade 6)

Slope 3 (Spring, Grade 6 – Spring, Grade 7)

Slope 4 (Spring, Grade 7 – Spring, Grade 8)

Intercept (for White) Native American Asian Latino African-American Multiracial Unknown Intercept (for White) Native American Asian Latino African-American Multiracial Unknown Intercept (for White) Native American Asian Latino African-American Multiracial Unknown Intercept (for White) Native American Asian Latino African-American Multiracial Unknown Intercept (for White) Native American Asian Latino African-American Multiracial Unknown

-0.27 0.31 -0.16 -0.19 0.02 -0.34

-0.02 0.10 0.01 -0.02 0.02 -0.23

-0.19 0.07 -0.07 -0.06 -0.32 0.20

-0.12 0.05 -0.13 -0.12 -0.12 -0.53

0.02 0.04 0.01 0.04 0.24 0.27

Variance Components

Initial Status

Slope 1 41.54*** Slope 2 17.38*** Slope 3 46.08*** Slope 4 89.01*** Note: Model also included residual covariances among the latent growth terms as in the unconditional growth model. * p < .05; ** p < .01; *** p < .001

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Table 12: Selected Results for Piecewise Growth Model for Mathematics and Reading/English-language Arts Achievement Predicted by Race/Ethnicity (N = 303,699)
Mathematics (N = 296,323) Unstandardized Selected YEstimates Standardized Estimates 0.54*** Reading/ELA (N = 294,863) Unstandardized Selected YEstimates Standardized Estimates 0.56***

Fixed Effects

Initial (G4) Status

Intercept (for White) Native American Asian Latino AfricanAmerican Multiracial Unknown Intercept (for White) Native American Asian Latino AfricanAmerican Multiracial Unknown Intercept (for White) Native American Asian Latino AfricanAmerican Multiracial Unknown

-0.86*** 0.10*** -0.75*** -0.81*** -0.34*** -0.47*** -0.04***

-0.94 0.10 -0.81 -0.88 -0.37 -0.52

-0.86*** -0.13*** -0.83*** -0.76*** -0.25*** -0.44*** -0.02***

-0.96 -0.14 -0.93 -0.85 -0.28 -0.49

Slope 1 (G4 – G6)

0.01 0.08*** 0.02*** 0.003 0.05 -0.001 -0.03***

0.07 0.51 0.15 0.02 0.32 -0.01

0.004 0.05*** 0.02*** -0.01*** 0.008 0.003 -0.02***

0.03 0.33 0.17 -0.08 0.06 0.02

Slope 2 (G6 – G8)

0.00 0.09*** 0.005* -0.002 0.00 0.006 0.71***

-0.001 0.52 0.03 -0.01 0.04 -0.002 0.84***

0.01 0.05*** 0.01*** 0.01** 0.07* -0.06 0.68***

0.04 0.35 0.09 0.04 0.48 -0.39

Variance Components

Initial Status Slope 1 0.03*** 0.98*** 0.02*** Slope 2 0.03*** 0.97*** 0.02*** Note: Model also included residual covariances among the latent growth terms as in the unconditional growth model. * p < .05; ** p < .01; *** p < .001

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Table 13: Selected Results for Piecewise Growth Model for Attendance Predicted by Language Background (N = 303,622)
Fixed Effects Initial (Fall, G4) Status Intercept (for English-only) Language Minority non-ELL English language learner in G4 Intercept (for English-only) Language Minority non-ELL English language learner in G4 Intercept (for English-only) Language Minority non-ELL English language learner in G4 Intercept (for English-only) Language Minority non-ELL English language learner in G4 Intercept (for English-only) Language Minority non-ELL English language learner in G4 Unstandardized Estimates 93.35*** 1.70*** 0.63*** -1.52*** 0.44*** 0.60*** -0.72*** 0.11*** -0.03 -1.44*** 0.32*** -0.20*** -3.03*** -0.07 -0.03 49.52*** -0.01 -0.00 0.05 -0.03 0.03 -0.01 0.07 0.09 Selected YStandardized Estimates

0.24 0.09

Slope 1 (Fall, G4 – Fall, G5)

Slope 2 (Fall, G5 – Spring, G6)

Slope 3 (Spring, G6 – Spring, G7)

Slope 4 (Spring, G7 – Spring, G8)

Variance Components

Initial Status

Slope 1 41.60*** Slope 2 17.34*** Slope 3 46.19*** Slope 4 89.01*** Note: Model also included residual covariances among the latent growth terms as in the unconditional growth model. * p < .05; ** p < .01; *** p < .001

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Table 14: Selected Results for Piecewise Growth Model for Achievement Predicted by Language Background
Mathematics (N = 292,250) Unstandardized Selected YEstimates Standardized Estimates -0.03*** 0.24*** 0.26 Reading/ELA (N = 294,791) Unstandardized Selected YEstimates Standardized Estimates 0.01*** 0.08*** 0.27

Fixed Effects

Initial (G4) Status

Slope 1 (G4 – G6)

Slope 2 (G6 – G8)

Intercept (for English-only) Language Minority nonELL English language learner in G4 Intercept (for English-only) Language Minority nonELL English language learner in G4 Intercept (for English-only) Language Minority nonELL English language learner in G4

-0.67***

-0.73

-0.95***

-0.87

-0.04*** 0.04*** 0.26

-0.03*** 0.04*** 0.14

0.12***

0.73

0.10***

0.45

-0.04*** 0.03*** 0.19

-0.02*** 0.02*** 0.14

0.09***

0.57

0.06***

0.45

Initial 0.78*** 0.93 0.74*** 0.91 Status Slope 1 0.03*** 0.95 0.02*** 0.96 Slope 2 0.03*** 0.97 0.02*** 0.98 Note: Model also included residual covariances among the latent growth terms as in the unconditional growth model. *** p < .001

Variance Components

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Is middle grades performance equally predictive of later on-track status across ethnic and language groups? To investigate whether middle-grades performance is equally predictive of being on-track in grade nine for ultimate high school graduation, we fitted the model displayed in Figure 5 separately to sub-samples comprises of each ethnic group and of each language group. To investigate whether middle-grades performance is equally predictive of being on-track in grade nine across the different ethnic and language groups, we fitted the model displayed in Figure 5 separately to sub-samples comprises of each ethnic group and of each language group. As shown by the standardized estimates in Table 15, the relative predictive power of attendance and achievement levels and rates of growth appeared to be largely similar across ethnic groups, with some exceptions. For African-Americans, both initial status and Slope 1 in attendance had notably larger effects on grade nine “on-track” indicator score than for other groups. In addition, Slope 3 for White students was notably less predictive of grade nine “on-track” indicator score than for other groups. As shown in Table 16, predictive relationships were also largely similar across language backgrounds, with perhaps only one exception. Attendance Slope 3 was less predictive for language minority students not designated as ELLs compared to other groups.

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Table 15: Selected Results from Structural Equation Models with Initial Status and Rates of Growth in Both Attendance and Achievement Predicting Grade (G) 9 Ontrack Indicator Score, Fitted Separately for Each Ethnic Group Paths White (n = 44, 871) .29*** Standardized Estimates Asian (n = African-American (n 37, 327) = 101,237) .26*** .37***

Attendance Initial (Fall, G4) Status  G9 Ontrack Indicator Attendance Slope 1 (Fall, G4 –Fall, G5) .27*** .23*** .32*** .27***  G9 Ontrack Indicator Attendance Slope 2 (Fall, G5 –Spring, .30*** .23*** .31*** .26*** G6)  G9 Ontrack Indicator Attendance Slope 3 (Spring, G6-Spring, .03 .16*** .23*** .16*** G7) G9 Ontrack Indicator Attendance Slope 4 (Spring, G7-Spring, .39*** .35*** .28*** .31*** G8) G9 Ontrack Indicator Achievement Composite Initial (G4) .31*** .30*** .35*** .33*** Status  G9 Ontrack Indicator Achievement Composite Slope 1 (G4-G6) .11*** .12*** .17*** .18***  G9 Ontrack Indicator Achievement Composite Slope 2 (G6-G8) .17*** .19*** .19*** .21***  G9 Ontrack Indicator Note: As shown in Figure 5, mnodel also included variances and intercepts for and covariances among all latent growth terms as well as a residual variance for Grade 9 ontrack indicator score. *** p < .001

Latino (n = 118, 898) .31***

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Table 16: Selected Results from Structural Equation Models with Initial Status and Rates of Growth in Both Attendance and Achievement Predicting Grade (G) 9 Ontrack Indicator Score, Fitted Separately for Each Ethnic Group Standardized Estimates English Language Learners in G4 (n = 28, 567)

Attendance Initial (Fall, G4) Status  G9 Ontrack .30*** .29*** Indicator Attendance Slope 1 (Fall, G4 –Fall, G5)  G9 Ontrack .29*** .29*** .24*** Indicator Attendance Slope 2 (Fall, G5 –Spring, G6)  G9 .28*** .25*** .30*** Ontrack Indicator Attendance Slope 3 (Spring, G6-Spring, G7) G9 .21*** .20*** .03 Ontrack Indicator Attendance Slope 4 (Spring, G7-Spring, G8) G9 .28*** .27*** .38*** Ontrack Indicator Achievement Composite Initial (G4) Status  G9 .37*** .32*** .31*** Ontrack Indicator Achievement Composite Slope 1 (G4-G6)  G9 .17*** .18*** .14*** Ontrack Indicator Achievement Composite Slope 2 (G6-G8)  G9 .18*** .21*** .19*** Ontrack Indicator Note: As shown in Figure 5, mnodel also included variances and intercepts for and covariances among all latent growth terms as well as a residual variance for Grade 9 ontrack indicator score. *** p < .001

Native English Speakers (n = 177,842) .33***

Language Minority, Non-ELL (n = 98, 074)

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Do these patterns hold across schools? To investigate the extent to which these patterns hold across different school or are specific to certain schools, we used multilevel SEM modeling to partition the variance in the growth terms for attendance and achievement into within-school and between-school components. This approach provides insight into the extent to which middle schools influence these outcomes. In particular, we fitted models for individual growth nested within grade six school, including only those indicators for attendance and achievement between grade six and grade eight. Figure 7 presents the path diagram for the hypothesized two-level model, with both within-school and between-school components. Table 13 presents selected results from fitting this model. As shown by the interclass correlations (which represent the proportion of total variance that is between schools) for attendance in Table 17, only very small amounts of the variance in attendance initial (grade six) status (five percent) and slopes (two-three percent) are associated with differences between schools. As shown by the interclass correlations for achievement, larger but still relatively small percentages of the variance in achievement initial (grade six) status (27 percent) and slopes (10 percent) are associated with differences between schools. This is evidence to suggest that individual student differences within schools are much larger than differences between schools and that this is particularly the case for attendance.

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Figure 7: Path diagram for hypothesized multilevel latent growth model for attendance and achievement as nested within grade six school

Note: Model also included measurement models for attendance as shown in Figure 1 and for achievement analogous to the model shown in Figure 2. Att = Attendance; Ach = Achievement Composite; G = Grade

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Table 17: Selected Results for 3-Level Piecewise Growth Model for Unconditional Attendance Growth Nested within Grade 6 School (N = 266,450)
Fixed Effects Attendance Initial (Fall, G6) Status Attendance Slope 3 (Fall, G6 – Spring, G7) Attendance Slope 4 (Spring, G7 – Spring, G8) Achievement Initial (G6) Status Achievement Slope 2 (G6 –G8) Attendance Initial Status Intercept Intercept Intercept Intercept Intercept Within-school Between-school Interclass Correlation Within-school Between-school Interclass Correlation Within-school Between-school Interclass Correlation Within-school Between-school Interclass Correlation Within-school Between-school Interclass Correlation Estimates 91.98*** -1.23*** -2.39*** -0.09*** -0.02*** 115.35*** 6.06*** .05 34.51*** 0.66*** .02 35.93*** 1.22*** .03 0.62*** 0.22*** .27 0.03*** 0.003*** .10

Variance Components

Attendance Slope 3

Attendance Slope 4

Achievement Initial Status

Achievement Slope 2

Note: Model also included covariances among the latent growth terms.

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III.

EXPLORATORY ANALYSIS OF SCHOOL CHARACTERISTICS

To explore whether these patterns of achievement and attendance growth differ by observable school characteristics, we conducted some additional descriptive analyses. Specifically, we identified which school students were enrolled in for grade six. We then divided the schools into four quartiles based on three dimensions: 1) their students’ average growth rate in achievement between grade six and grade eight, 2) their students’ average growth rate in attendance between Fall, grade six and Spring, grade seven (i.e., attendance slope three in the original attendance growth models), and 3) their students’ average growth rate in attendance between Spring, grade seven and Spring grade eight (i.e., attendance slope four). We then estimated descriptive statistics (means and standard deviations) for several publically-available variables for school characteristics by achievement and attendance growth quartile. School-level variables were measured in the year in which the sampled students were in grade six; in most cases, this means that we had four values for the school-level variables corresponding to the four cohorts, which were then averaged. It is worth noting that this approach characterizes schools based not on their students’ levels of achievement and attendance (as might typically be done for accountability purposes), but rather on how their students change in achievement and attendance during the middle grades. Table 18 and 19 present the results of these exploratory analyses, with Table 18 presenting results for teacher characterized and Table 19 presenting results for student characteristics aggregated to the school level. When one compares the four quartiles in Table 18, it appears that the measured teacher characteristics, including experience and “highly qualified” status, were roughly the same across schools with substantially different achievement and attendance growth. In contrast, demographic variables do appear to be somewhat different across the schools, consistent with our previous student-level analyses of demographic predictors, as shown in Table 19. For instance, consistent with our previous results, schools which demonstrated higher average achievement growth in the middle grades had lower proportions of African-American students, compared with schools which demonstrated lower average achievement growth. Similarly, schools which demonstrated higher average attendance growth during the Fall, grade six to Spring, grade seven period had lower proportions of AfricanAmerican and Latino students, compared to schools which demonstrated lower average attendance growth. As described in the main text, schools with higher rates of achievement and attendance growth also tended to have much lower concentrations of students receiving free lunch. These exploratory analyses are not meant to support causal inferences about the school characteristics that matter most, but are rather intended to spur additional research into what schools can do to support more positive achievement and attendance trajectories during the middle grades.

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Table 18: Means for Teacher Characteristics for Schools Classified in the First through Fourth Quartile, based on Achievement and Attendance Growth
Percent of teachers with more than 2 years in this school School Average G6 - G8 Achievement Growth School Average F,G6 - S,G7 Attendance Growth Quartile 1 Quartile 2 Quartile 3 Quartile 4 Quartile 1 Quartile 2 Quartile 3 Quartile 4 Quartile 1 Quartile 2 Quartile 3 Quartile 4 67.31 63.96 66.63 64.19 65.48 64.58 66.39 65.65 66.61 65.83 64.69 65.95 Percent of teachers with more than 5 years experience anywhere 56.26 53.79 55.16 53.09 54.93 54.23 55.33 53.76 54.40 55.54 53.49 55.63 Percent of core classes taught by highly qualified teachers 88.38 85.61 88.64 87.59 85.28 86.02 87.99 91.19 88.28 87.48 87.11 87.57

School Average S,G7 - S, G8 Attendance Growth

Table 19: Means for Student Characteristics for Schools Classified in the First through Fourth Quartile, based on Achievement and Attendance Growth
Enrollment Total Percent of students receiving free lunch 72.30 75.01 67.70 64.21 84.38 78.91 67.37 46.73 71.21 67.74 70.15 70.78 Percent of students who are AfricanAmerican 40.97 42.45 31.89 23.22 46.49 42.39 31.80 19.91 29.21 34.56 35.82 40.81 Percent of students who are Latino 37.78 37.81 39.76 38.80 46.50 43.48 37.96 25.75 38.57 37.74 39.75 37.58 Percent of students who are ELLs 11.90 14.49 15.13 16.95 15.45 14.80 14.77 12.91 15.70 14.40 14.77 13.56 Percent of students in special education 18.09 20.86 14.96 12.28 24.72 19.00 13.32 10.20 13.89 19.80 18.18 12.30

School Average G6 - G8 Achievement Growth School Average F,G6 - S,G7 Attendance Growth School Average S,G7 - S, G8 Attendance Growth

Quartile 1 Quartile 2 Quartile 3 Quartile 4 Quartile 1 Quartile 2 Quartile 3 Quartile 4 Quartile 1 Quartile 2 Quartile 3 Quartile 4

695 689 738 804 654 676 782 790 898 703 671 715

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