Navigating the Middle Grades (2012)

8/13/2019 Navigating the Middle Grades (2012)

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Michael J. Kie

William H. Mari

Apri l

Navigating the Middle Grades:

Evidence from New York City

Working Paper


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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

2012Research Alliance for New York City Schools. All rights reserved. You may make copies of and distribute this work for non-

commercial 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.


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CONTENTS

I. Overview .................................................................................................................1

II. Analytic Approach ..................................................................................................3

III. Data ..........................................................................................................................4

IV. Findings ..................................................................................................................5

Whos on track to graduate and why? ............................................................................... 5

What do students grade four-eight achievement and attendance trajectories look like? ............... 5

Does students grade four-eight achievement predict whos on track in grade nine? .................... 7

Does students grade four-eight attendance predict whos on track in grade nine? ...................... 8Do particular demographic groups of students demonstrate middle-grades trajectories that are

associated with being off-track in grade nine? ................................................................... 12Is middle grades performance equally predictive of later on-track status across ethnic and

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

V. Exploratory Analyses ...........................................................................................20

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

VI. Conclusions & Implications ................................................................................. 22

VII. Notes and References ..........................................................................................23


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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 emotionalchallenges, 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

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 aboutwhether 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.

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.

Our findings are as follows:

We can identify students who will struggle to graduate after four years of high school quiteearly in their schooling. Students grade four attendance rates and their scores on New

Yorks 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 studentsprogress 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 particularlyat 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 middlegrades 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 andfor 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 instudents 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.

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 off-

track 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 thesepredictive 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 Educations (DOE) archive. We use the DOEs audited J-Form Register and

Longitudinal Cohortfiles to identify first-time grade nine students and to monitor their progress

through their high school graduation. TheNY State ELA and Math Test Scorefile is the source of

information on students English language arts and mathematics test scores in grades four and

eight, and the student-level Regentsfile 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 DOEs 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 cohorts progress from grade four through high school, including the cohorts

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 cohorts progress through high school

graduation and the latter cohorts 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. FINDINGS

Whos on track to graduate and why?

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


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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

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

Grade


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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 students 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 whos 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

gradehighlighting the importance of students performance in math during the middle grades

for their eventual graduation. For reading scores, changes between grades six and eight areequally 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 on-

track 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


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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);4the student trajectory in red starts substantially

below-average in grade four5

Does students grade four-eight attendance predict whos on track in grade nine?

(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.

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 whofalls 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)


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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 wi th 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 Predic ted 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 Latinostudents 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 Fit ted by Ethnici ty


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Figure 6:

Mathematics Achievement Test Scores Fitted by Ethnici ty

Figure 7:

Reading Achievement Test Scores Fitted by Ethnici ty


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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 languagelearners 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 on-

track 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 Engl ish Language Learner and Language Minori ty

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


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with differences between students attending the same school (within-school variation) and the

portion that is associated with differences between students attending different schools (between-

school 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 on-

track 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 within-

schools 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 holdsparticularly 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 inattendance 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 berelatively 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 School-

average 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

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 Walcotts 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.

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 demographiccharacteristics 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 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

1Eccles, 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. 233250). Washington, DC: American Psychological

Association.

2New 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 fromhttp://schools.nyc.gov/Offices/mediarelations/NewsandSpeeches/2011-2012/msspeechatnyu92011.htm

3 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

4For 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.

5By 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.

6National Center for Educational Statistics (2009).Nations Report Card. Washington, DC: U.S. Department of

education.

7E.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.

8Balfanz, 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. EducationalPsychologist, 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 citys 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.

285 Mercer Street, 3rd Floor | New York, New York 10003-9502

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[email protected] | www.steinhardt.nyu.edu/research_alliance


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Michael J. Kieffe

April 201


Evidence from New York City

Technical Appendix


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A Descriptive Analysis of the Middle Grades inNew 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 non-

commercial 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.


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CONTENTS

I. Methods .......................................................................................................1Sample .........................................................................................................1

Measures ......................................................................................................1

II. Data Analysis and Results .................................................................... 3

Descriptives .............................................................................................................3Whos 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? ........... 4Does students grade four-eight achievement predict whos on track in grade nine? ...............11Does students grade four-eight attendance predict whos 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? ................................................................19Is 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 Characterist ics .........................35


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I. METHODS

Sample

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 cohorts progress through high school graduation and the latter

cohorts 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 full-

information 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 learnersand 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 sub-

sample, so the results for the complete sample are reported here.

MeasuresHigh School Graduation.

Students on-time graduation in the fourth year after they enrolled as first-time ninth

graders was drawn from the DOEs 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 Recordsfile. Measures of grade nine performance also included the total

attendance rate, as a percent of days enrolled, drawn from the DOEs Student Tracking SystemDataset. 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 theNY 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 z-

scores, 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 DOEs

Attendance System.


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II. DATA ANALYSES AND RESULTSDescriptives

Table 1:Means and standard deviat ions for ach ievement test sco res, attendance along

with d emograph ics for th e analytic samp le (N = 303,845)

Mean StandardDeviation

Mathematics Achievement (within-gradez-scores)

Grade 4 -0.02 1.01Grade 5 -0.06 1.03Grade 6 -0.08 1.04Grade 7 -0.10 1.06

Grade 8 -0.15 1.09Reading Achievement (within-gradez-scores) Grade 4 -0.50 1.02

Grade 5 -0.07 1.03Grade 6 -0.09 1.04Grade 7 -0.09 1.05

Grade 8 -0.12 1.06Attendance (Percent of Days Enrolled) Fall, Grade 4 94.00 7.53

Spring, Grade 4 92.91 8.25Fall, Grade 5 93.06 11.35

Spring, Grade 5 92.14 9.06Fall, Grade 6 92.03 12.58Spring, Grade 6 91.05 10.91Fall, Grade 7 91.39 12.47Spring, Grade 7 89.64 12.64

Fall, Grade 8 90.75 12.95

Spring, Grade 8 87.08 13.88Percentage of Sample

Race/ethnicity African-American 33.3%Asian 12.3%

Hispanic 39.1%Native American 0.4%White 14.8%

Language Background ELL in Grade 4 9.4%Language Minority 41.4%


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4

Whos 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 on-

time 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 allpredicted 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:

Resul ts of Log ist ic Regression Predict ing On-t ime High School Graduat ion based

on Grade (G) 9 PredictorsUnstandardized Estimate Wald

2

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 looklike?

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 fourdistinct 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 growthtrajectories. 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 isonly 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 attendanceprovides 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 inattendance 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 instudents 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 widestvariation 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 betweenstudents 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 duringlater 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 growthmodel 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 empiricalgrowth 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 bothachievement 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-gradez-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 ofTable 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 componentsdisplayed 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 SDper year for both

Slope 1 and Slope 2 in mathematics; .02 for both Slope 1 and Slope 2 in reading/English-

language arts). This suggests that there is substantial stability in the rank-order of studentsachievement levels. For instance, a student with a high rate of growth in mathematics relative to

the sample (i.e., 1 SDabove the mean in Slope 1) would only change in the rank-order by 0.17

within-grade SDeach year; a student with an analogously high rate of growth in reading/ELAwould 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 concerningstability 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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7

Figure 1:

Path diagram for hy pothesized piecewise l inear growth model for attendance


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8

Figure 2:

Path diagram for hypo thesized piecewise l inear grow th mo del for mathematics

achievement


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9

Table 3:

Selected Results for Unc ondit ion al Piecewis e Growth Mo del for Atten danc e (N = 303,845)

Unstandardized Estimates Selected Standardized

Estimates

FixedEffects

Initial (Fall, Grade 4) Status 93.95***

Slope 1 (Fall, Grade 4 Fall, Grade 5) -1.32***

Slope 2 (Fall, Grade 5 Spring, Grade 6) -0.67***

Slope 3 (Spring, Grade 6 Spring, Grade 7) -1.28***Slope 4 (Spring, Grade 7 Spring, Grade 8) -3.01***

Variance

Components

Initial Status 49.45***

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*** .05Initial Status with Slope 4 0.02 .00

Slope 1 with Slope 2 -9.20*** -.35

Slope 1 with Slope 3 -1.55*** -.04Slope 1 with Slope 4 1.20*** .02

Slope 2 with Slope 3 1.76*** .06



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 Resul ts for Unco ndi t ional Piecewise Growth Models for Mathematics and Reading

Ac hiev emen t (N = 303,845)

Mathematics Achievement Reading/ELA Achievement

UnstandardizedEstimates

SelectedStandardized

Estimates


SelectedStandardized

Estimates

FixedEffects

Initial (Grade 4)Status

-0.02*** -0.05***

Slope 1 (Grade 4

Grade 6)

-0.03*** -0.02***

Slope 2 (Grade 6

Grade 8)

-0.03*** -0.01***

VarianceComponents

Initial Status 0.86*** 0.81***Slope 1 0.03*** 0.02***

Slope 2 0.03*** 0.02***Covariances Initial Status with

Slope 1-0.02*** -0.11 -0.01*** -.06

Initial Status with

Slope 2

-0.01*** -0.07 -0.001 -.01

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 ontrac

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 whos on track in gradenine?

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 thepath 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 formathematics achievement. A parallel model was fitted for reading/English-langauge artsachievement 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 largerelationships 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 informationfor 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 approximatelythe 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 valuableinformation. 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 h ypothesized structural equat ion m odel in which latent grow th

in mathematics achievement predicts Grade 9 indicator for the pro babi l i ty of on-

t ime high sch ool g raduat ion


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Table 5:Selected Resul ts from Structural Equat ion Model wi th Ini t ia l Status and Rates of Growth in

Mathematics Ach ievement Pred icting Grade (G) 9 Ontrack Indicator Sc ore (N = 303,845)

Paths Unstandardized

Estimates

Standardized Estimates

Math Initial (Grade 4) Status G9 OntrackIndicator

1.63*** .51

Math Slope 1 (Grade 4 Grade 6) G9 Ontrack

Indicator

3.70*** .21

Math Slope 2 (Grade 6 Grade 8) G9 Ontrack

Indicator

6.62*** .39

Note: Model also included variances and intercepts for mathematics achievement initial status, slope 1, and slopeas well as residual variances for Grade 9 ontrack indicator score. For FIML purposes, model also included late

growth factors for reading/ELA and attendance which were allowed to covary with mathematics growth terms an

Grade 9 ontrack indicator.

***p < .001

Table 6:Selected Resul ts from Structural Equat ion Model wi th Ini t ia l Status and Rates of Growth in

Reading/Engl ish-Language A rts (ELA) Ach ievement Predict ing Grade (G) 9 Ontrack Indicator

Sco re (N = 303,845)

Paths UnstandardizedEstimates

StandardizedEstimates

Reading/ELA Initial (Grade 4) Status G9 Ontrack

Indicator

1.51*** .47

Reading/ELA Slope 1 (Grade 4 Grade 6) G9 Ontrack

Indicator

5.79*** .28

Reading/ELA Slope 2 (Grade 6 Grade 8) G9 Ontrack

Indicator

6.79*** .33

Note: Model also included variances and intercepts for reading/ELA achievement initial status, slope 1, and slop2 as well as residual variances for Grade 9 ontrack indicator score. For FIML purposes, model also included late

growth factors for mathematics and attendance which were allowed to covary with reading/ELA growth terms an

Grade 9 ontrack indicator.

***p < .001


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Does students grade four-eight attendance predict whos 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 thismodel. 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 Resul ts from Structural Equat ion Model w i th Ini t ial Status and Rates of

Grow th in Atten danc e Predictin g Grade (G) 9 Ontrack Indicator Sco re (N =

303,845)

Paths UnstandardizedEstimates StandardizedEstimates

Attendance Initial (Fall, G4) Status G9

Ontrack Indicator

0.195*** .47

Attendance Slope 1 (Fall, G4 Fall, G5) G9Ontrack Indicator

0.175*** .38

Attendance Slope 2 (Fall, G5 Spring, G6) G9

Ontrack Indicator

0.241*** .34

Attendance Slope 3 (Spring, G6-Spring, G7)G9 Ontrack Indicator

0.137*** .31


0.085*** .27

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 wereallowed to covary with reading/ELA growth terms and Grade 9 ontrack indicator.

***p < .001


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Figure 5:Path diagram for hy pothesized structural equat ion m odel in which latent grow th

in achievement (s imple comp osi te of m athematics 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 Resul ts from Structural Equat ion Model w i th Ini t ial Status and Rates of

Growth in Bo th Attendanc e and Ac hievement Predict ing Grade (G) 9 Ontrack

Indic ator Scor e (N = 303,805)

Paths Unstandardized

Estimates

Standardized

EstimatesAttendance Initial (Fall, G4) Status G9Ontrack Indicator

0.13*** 0.30

Attendance Slope 1 (Fall, G4 Fall, G5) G9

Ontrack Indicator

0.12*** 0.26

Attendance Slope 2 (Fall, G5 Spring, G6) G9

Ontrack Indicator

0.16*** 0.22


0.09*** 0.21


0.07*** 0.21

Achievement Composite Initial (G4) Status G9Ontrack Indicator 1.23*** 0.37

Achievement Composite Slope 1 (G4-G6) G9

Ontrack Indicator

3.42*** 0.17

Achievement Composite Slope 2 (G6-G8) G9

Ontrack Indicator

4.51*** 0.22

Note: As shown in Figure 5, mnodel also included variances and intercepts for and covariancesamong 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-gradestrajectories 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 investigatedwhether particular demographic characteristics including race/ethnicity and language background

predict students middle-grades trajectories. Table 9 presents descriptive statistics onachievement and attendance by race/ethnicity group while Table 10 presents descriptive statisticson 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 thereference 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 Englishlanguage 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 deviat ions for achievement and attendance by race/ethnic i ty

African-American

(n=

101,237)

Asian (n= 37,329)

Latino (n= 118,911)

NativeAmerican (n

= 1155)

White(n =

44,871)

MathematicsAchievement

(within-gradez-

scores)

Grade 4 -0.28(0.90)

0.62(1.08)

-0.21(0.91)

-0.32 (0.98) 0.53(1.01)

Grade 5 -0.34

(0.94)

0.66

(1.04)

-0.24

(0.93)

-0.40 (1.08) 0.50

(0.96)Grade 6 -0.37

(0.94)

0.70

(1.06)

-0.27

(0.94)

-0.40 (1.05) 0.42

(0.97)

Grade 7 -0.41(0.96)

0.73(1.04)

-0.29(0.94)

-0.47 (1.15) 0.44(0.98)

Grade 8 -0.46

(0.96)

0.88

(1.10)

-0.33

(0.94)

-0.49 (1.08) 0.34

(1.01)

ReadingAchievement(within-gradez-

scores)

Grade 4 -0.20(0.92) 0.41(1.08) -0.30(0.92) -0.30 (0.96) 0.53(1.08)Grade 5 -0.27

(0.94)

0.42

(1.01)

-0.29

(0.95)

-0.36 (0.99) 0.60

(1.06)Grade 6 -0.28

(0.94)

0.47

(1.05)

-0.30

(0.96)

-0.36 (1.02) 0.48

(1.05)

Grade 7 -0.29(0.95)

0.48(1.03)

-0.20(0.98)

-0.38 (1.02) 0.49(1.05)

Grade 8 -0.33

(0.93)

0.51

(1.14)

-0.32

(0.93)

-0.41 (0.98) 0.44

(1.13)

Attendance (Percent

of Days Enrolled)

Fall,

Grade 4

93.29

(8.55)

96.76

(5.21)

93.51

(7.49)

92.75 (8.95) 94.62

(6.01)Spring,

Grade 4

91.90

(9.37)

96.40

(5.57)

92.43

(8.18)

91.61 (9.30) 93.63

(6.55)Fall,

Grade 5

92.36

(12.03)

96.17

(9.19)

92.46

(11.58)

91.52

(13.18)

93.71

(10.04)

Spring,Grade 5

91.12(10.14)

95.84(6.04)

91.68(8.97)

90.14(12.24)

92.76(7.49)

Fall,

Grade 6

91.09

(13.39)

95.62

(9.96)

91.47

(12.48)

90.30

(13.23)

92.75

(12.14)

Spring,Grade 6

89.91(12.08)

95.58(7.24)

90.38(10.72)

88.43(13.42)

91.93(9.36)

Fall,Grade 7 90.32(13.38) 95.47(9.55) 90.66(12.51) 89.41(13.56) 92.50(11.22)Spring,

Grade 7

88.31

(13.81)

94.95

(9.79)

88.67

(12.58)

86.88

(15.25)

91.04

(10.77)

Fall,Grade 8

89.66(14.00)

95.32(9.05)

89.87(13.14)

88.26(15.20)

91.87(11.40)

Spring,

Grade 8

86.00

(15.01)

92.38

(9.47)

85.99

(14.13)

84.38

(15.63)

88.16

(12.01)


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Table 10:

Means and standard deviat ions for achievement and attendance by language

background

Native

EnglishSpeakers

(n= 177,868)

Language Minority,

Non-ELL (n=98,083)

ELLs in Grade

4 (n= 28,572)

Mathematics

Achievement (within-gradez-scores)

Grade 4 -0.04 (0.98) 0.20 (0.98) -0.73 (0.99)

Grade 5 -0.11 (1.00) 0.19 (1.00) -0.65 (1.07)Grade 6 -0.15 (1.00) 0.18 (1.03) -0.60 (1.08)

Grade 7 -0.18 (1.03) 0.17 (1.05) -0.58 (1.08)

Grade 8 -0.25 (1.03) 0.15 (1.11) -0.49 (1.06)Reading Achievement

(within-gradez-scores)

Grade 4 0.00 (1.00) 0.07 (0.97) -1.01 (0.89)

Grade 5 -0.04 (1.03) 0.08 (0.96) -0.89 (0.97)

Grade 6 -0.07 (1.02) 0.08 (0.99) -0.86 (0.98)

Grade 7 -0.08 (1.03) 0.09 (1.00) -0.84 (1.04)Grade 8 -0.12 (1.04) 0.08 (1.04) -0.77 (0.96)

Attendance (Percent of

Days Enrolled)

Fall,

Grade 4

93.41 (7.89) 95.07 (6.60) 93.98 (7.77)

Spring,

Grade 4

92.03 (8.73) 94.33 (7.04) 93.50 (8.21)

Fall,Grade 5

92.50 (11.38) 94.13 (10.89) 92.78 (12.39)

Spring,

Grade 5

91.27 (9.56) 93.59 (7.78) 92.74 (8.90)

Fall,

Grade 6

91.37 (12.85) 93.29 (11.90) 91.89 (12.71)

Spring,

Grade 6

90.12 (11.53) 92.65 (9.52) 91.56 (10.26)

Fall,

Grade 7

90.66 (12.93) 92.78 (11.36) 91.22 (12.61)

Spring,Grade 7

88.63 (13.32) 91.45 (11.12) 89.87 (12.16)

Fall,

Grade 8

89.99 (13.50 92.23 (11.67) 90.40 (13.09)

Spring,Grade 8

86.16 (14.52) 88.75 (12.48) 87.14 (13.68)


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Figure 5:

Path diagram fo r hypo thesized latent growth in attendance predicted by

racial /ethnic g roup

Note: Model also included measurement model for attendance as shown in Figure 1. F= Fa

S = Spring, G = Grade


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Figure 6:

Path diagram for latent grow th in m athematics p redicted by racial/ethnic grou p

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 SDin 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 of a SDfor mathematics achievement andnearly 9/10ths of a SDfor 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 Resul ts for Piecewise Growth Model for A ttendance Predicted b y

Race/Ethn icity (N = 303,699)


Selected Y-StandardizedEstimates

Fixed Effects Initial (Fall, Grade 4) Status Intercept (forWhite)

94.59***

Native American -1.89*** -0.27Asian 2.18*** 0.31

Latino -1.12*** -0.16

African-American -1.36*** -0.19

Multiracial 0.13 0.02

Unknown -2.40*** -0.34

Slope 1 (Fall, Grade 4 Fall, Grade 5) Intercept (for

White)

-1.38***

Native American -0.10 -0.02

Asian 0.64*** 0.10Latino 0.07 0.01

African-American -0.14** -0.02

Multiracial 0.14 0.02

Unknown -1.45 -0.23Slope 2 (Fall, Grade 5 Spring, Grade6)

Intercept (forWhite)

-0.51***

Native American -0.79*** -0.19

Asian 0.31*** 0.07

Latino -0.30*** -0.07


Multiracial -1.32* -0.32Unknown 0.81 0.20

Slope 3 (Spring, Grade 6 Spring,

Grade 7)

Intercept (for

White)

-0.75***

Native American -0.78* -0.12

Asian 0.31*** 0.05

Latino -0.89*** -0.13


Multiracial -0.83 -0.12Unknown -3.63* -0.53

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

Intercept (forWhite)

-3.27***

Native American 0.16 0.02

Asian 0.40*** 0.04

Latino 0.10 0.01

African-American 0.38*** 0.04

Multiracial 2.23* 0.24

Unknown 2.50 0.27VarianceComponents

Initial Status 48.74***

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 Resul ts for Piecewise Growth Model for Mathematics and

Reading/Engl ish- language Arts Ach ievement Predicted by Race/Ethnic i ty (N =

303,699)

Mathematics (N= 296,323) Reading/ELA (N= 294,863)

Unstandardized

Estimates

Selected Y-

Standardized

Estimates

Unstandardized

Estimates

Selected Y-

Standardized

Estimates

Fixed Effects Initial

(G4)

Status

Intercept (for

White)

0.54*** 0.56***

Native

American

-0.86*** -0.94 -0.86*** -0.96

Asian 0.10*** 0.10 -0.13*** -0.14

Latino -0.75*** -0.81 -0.83*** -0.93

African-American -0.81*** -0.88 -0.76*** -0.85

Multiracial -0.34*** -0.37 -0.25*** -0.28

Unknown -0.47*** -0.52 -0.44*** -0.49

Slope 1

(G4

G6)

Intercept (for

White)

-0.04*** -0.02***

Native

American

0.01 0.07 0.004 0.03

Asian 0.08*** 0.51 0.05*** 0.33

Latino 0.02*** 0.15 0.02*** 0.17

African-

American

0.003 0.02 -0.01*** -0.08

Multiracial 0.05 0.32 0.008 0.06

Unknown -0.001 -0.01 0.003 0.02Slope 2

(G6

G8)

Intercept (for

White)

-0.03*** -0.02***

Native

American

0.00 -0.001 0.01 0.04

Asian 0.09*** 0.52 0.05*** 0.35

Latino 0.005* 0.03 0.01*** 0.09

African-

American

-0.002 -0.01 0.01** 0.04

Multiracial 0.00 0.04 0.07* 0

Documents

Navigating the Middle Grades (2012)