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Running Head: THE PROCESS OF PUSHING OUT
1
Recent research has demonstrated that students who have been suspended in high school
have a higher risk of dropping out in the future (Skiba, Simmons, Staudinger, Rausch, Dow, &
Feggins 2003) and that students who have dropped out have a higher risk of being incarcerated in
the future (Christle, Jolivette, & Nelson, 2005). On the other hand, students who have
demonstrated high levels of math ability, affect, and attainment, have higher rates of attending
college, majoring in a STEM subject, and securing a STEM job (see Pajares & Miller, 1995,
Rose & Betts 2001, Tai, Liu, Maltese, & Fan, 2006). Thus, the school-to-prison (STP) pipeline
can be thought of as an increasing trajectory of exclusion—exclusion from classrooms
(suspension), formal education (dropping out), and society (incarceration), while the STEM
pipeline can be thought of as an increasing trajectory of inclusion—inclusion in selective STEM
classrooms, college majors, and career fields.
Nevertheless, despite the belief that the opposing pipelines of discipline and academics
are fundamentally related (Gregory, Skiba, & Noguera, 2010), these pipelines are often
researched as separate entities that are connected frequently in their outcomes, but rarely in their
processes. Thus, there is a tendency to view the impacts of discipline on academics—and vice
versa—as the unintentional outcomes of two unidirectional pipelines that occasionally intersect,
rather than the intentional processes of two bidirectional pipelines that continually interact. As a
result, our current understanding of complex phenomena that involves both discipline and
academics, such as dropping out, may be incomplete.
Theoretical Frameworks
Interactional Theories
An interactional theory of behavior was first put forth by Thornberry (1987), which
posited (a) that delinquency was subject to reciprocal effects of interrelated social factors, such
THE PROCESS OF PUSHING OUT
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as parents, peers, and schools; (b) that these reciprocal relationships continued to produce effects
on individuals over the life course; and (c) that these effects were not uniformly experienced
throughout the social structure; rather, race, gender, and class can impact starting locations—in
terms of the level of exposure to delinquency and the strength of the bonds to conventional
conformity—within the social structure. In doing so, interactional theory highlights the
importance of the interactive processes among multiple, interrelated pathways in producing
student outcomes.
Research Terms
This article defines “pipeline” as markers of persistence that are either negatively related
to discipline (the STP pipeline) or positively related to math (the STEM pipeline). Here, it is
important to note that the markers used to measure persistence in each respective pipeline are not
exhaustive indicators. Rather, these markers represent a facet of student persistence
opportunities—increased opportunities to persist in STEM and decreased opportunities to persist
in a formal learning environment.
Research Objectives
The primary objectives of this article is to understand the short term impact of
suspensions on math achievement, as well as the long-term interactions among the STP and
STEM pipeline in high school. By answering these questions, this research will add to
interactional theories by focusing on the sanction to misbehavior, rather than solely the
misbehavior. This will uniquely address the role of the school and in doing so uncover the
underlying structures of opportunity that impact the interactions among the STP and STEM
pipelines. Finally, this research will also add to the literature on both the STP and STEM
pipelines—demonstrating both their short-term cross-pipeline impacts, as well as their long-term
THE PROCESS OF PUSHING OUT
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cross-pipeline interactions, that are net of within-pipeline influences. In doing so, the process of
being pushed out, which is believed to be a result of both pipelines, will be better understood.
Data
The analyses in this paper utilized restricted-use data from High School Longitudinal
Study of 2009 (HSLS). The HSLS employed a stratified, two-stage random sampling design with
schools randomly selected at the first stage, followed by students randomly selected from these
schools at the second stage (Ingels, Pratt, Herget, Burns, Dever, Ottem, Rogers, Jin & Leinwand,
2011).
Study Variables
A latent construct of math achievement was created from the following variables: math
identity, norm-referenced standardized math score, and math course level. Suspension variables
consisted of parent reported binary measure of whether or not a their student had been suspended
prior to high school, as well as a student reported binary measure of whether or not he or she had
received an in-school suspension within the last 6 months. Finally, dropout (or “pushout”) status
was defined as students who had dropped out of high school during the spring semester of 12th
grade.
Methods and Results
This study employed a two-step process, which first used a confirmatory factor analysis
to test the validity of the latent construct of math achievement, and then used latent difference
score and structural equation models to test the relationships of these latent constructs of math
achievement to disciplinary variables.
Measurement Model
THE PROCESS OF PUSHING OUT
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The latent construct of math achievement—derived from math identity, test score, and
course level variables—can be described as a longitudinal, two-time-point factor with factor
loadings at time-point one correlated with factor loadings at time-point two. All factor loadings
were statistically significant and had standardized values above 0.4 (as recommended by
Stevens, 1992). Additionally, the model contained excellent fit statistics in term of RMSEA
(0.005) and CFI (1.0) values (as recommended by Hu and Bentler, 1999).
-- Insert Figure 1 here -Latent Difference Score Model
Developed from McArdle’s Latent Difference Score Approach (2001), Kenny (2014)
summarizes a method for modeling the difference of a latent construct that is caused by a
specific predictor. This approach will be used to model the difference of math achievement from
time-point one to time-point two that is caused by suspensions. In addition to correlating factor
loadings and constraining them to be equal at time points one and two, this approach calls for the
following model constraints (2014):
1. Y2 causes Y2, and constrain that causal effect to be 1.
2. The disturbance in Y2 represents change.
3. Correlate the disturbance of change with Y1.
4. Correlate X with Y1 and have it cause change.
In order to control for race, gender, and social class, MIMIC (Multiple Indicator Multiple
Cause) Modeling was used, which entails regressing the disturbance variable on race (Black or
Hispanic), gender (Female), and social class (lowest two quintiles of SES). Results indicate that
the overall model fit was excellent (RMSEA = .03; CFI = 0.97; DF = 23). Additionally, in order
to test the added influence of suspension, a null model, which only included race, gender, and
THE PROCESS OF PUSHING OUT
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social class, was run first. Results indicate that both poverty (STDY b = -0.13) and race (STDY b
= -0.07) significantly decrease math achievement, accounting for 3% of the variance explained in
the difference. When suspension was added to the model, it too, significantly decreased math
achievement (STDY b = -0.17). Additionally, the effect of both poverty (STDY b = -0.11) and
race (STDY b = -0.06) slightly decreased. Moreover, as the variance explained increased to 6%,
suspension can be seen as explaining an additional 3% in the variance of the outcome.
-- Insert Figure 2 here –
Continual Mediation in Structural Equation Modeling
In testing the interactions between the STP and STEM pipelines, a longitudinal mediation
model was constructed that represented 5 time points: (1) suspensions prior to high school; (2)
fall freshman year math achievement; (3) fall junior year suspensions; (4) spring junior year/fall
senior year math achievement; and (5) spring senior year dropout status. Here, fall freshman year
math achievement can be seen as mediating the relationship between pre-high school and fall
junior year suspensions, while fall junior year suspensions can be seen as mediating the
relationship time fall freshman year math achievement and spring junior year/fall senior year
math achievement. Additionally, spring junior year/fall senior year math achievement can be
seen as mediating the relationship between fall junior year suspensions and dropout status.
Similar to the latent difference score model, in order to control for race, gender, and
social class, a MIMIC modeling approach was employed, which regressed the endogenous
variables on these control variables. For the overall model, the standardized effect of pre-high
school suspension on freshman year math attainment was significant and negative (STDY b = 0.63), while the effect of pre-high school suspension on fall junior year suspension was
significant and positive (STDY b = 0.52). Similarly, standardized the effect of fall freshman year
THE PROCESS OF PUSHING OUT
6
math attainment on fall junior year suspensions was significant and negative (STDYX b= -0.28),
while the effect of fall freshman year math achievement on spring junior year/fall senior year
math achievement was significant and positive (STDYX b = 0.87). Additionally, standardized
the effect of fall junior year suspensions on fall junior year/spring senior year math achievement
was significant and negative (STDY b= -0.11), while the effect of fall junior year suspensions on
spring senior year dropout status was significant and positive (b = 0.29). Furthermore, the
standardized effect of spring junior year/fall senior year math achievement on spring senior year
dropout status was significant and negative (STDYX b = -0.48). Finally, the R-squared values
were 0.18 for fall freshman year math achievement; 0.88 for spring junior year/fall senior year
math achievement; 0.23 for fall junior year suspension, and 0.44 for spring senior year dropout
status.
Additionally, five tests of indirect effects were performed using the ‘MODEL
INDIRECT’ command from Mplus. The first indirect test involved the effect of pre-high school
suspension on spring senior year dropout status through all mediating variables, which was
positive, significant, and relatively small (STDY b = 0.01). The second indirect test involved the
effect of fall freshman year math achievement on spring senior year dropout status through fall
junior year suspensions and spring junior year/fall senior year math achievement, which was
negative, significant and relatively small (STDYX b = -0.02). The third indirect test involved the
effect of fall junior year suspension on spring senior year dropout status through spring junior
year/fall senior year math achievement, which was positive, significant and also small (STDY b
= 0.05). The fourth indirect test involved the effect of pre-high school suspension on spring
senior year dropout status through fall junior year suspension, which was positive, significant
and considerably larger (STDY b = 0.15) than previous indirect tests. The final indirect test
THE PROCESS OF PUSHING OUT
7
involved the effect of fall freshman year math achievement on spring senior year dropout status
through spring junior year/fall senior year math achievement, which was negative, significant
and considerably larger (STDYX b = -0.41) than previous indirect tests.
-- Insert Figure 3 here --- Insert Table 1 here --- Insert Table 2 here -Discussion and Conclusion
First, through the latent difference score model, the effect of being suspended on math
achievement was found to be similar to the effect of being from disadvantaged race and class
groups. This demonstrates the large effect of suspensions on math achievement that is net of both
race and class. Second, through testing the long term interaction among the STP and STEM
pipelines, it was found that parts of each pipeline significantly mediated the other pipeline, which
confirms the consistency between our data and our theoretical model.
More specifically, it was found that within-pipeline effects tended to be stronger than
cross-pipeline effects and that cross-pipeline effects resemble within-pipeline effects when
within-pipeline effects are absent. This demonstrates the need to include both when estimating
the relationships among discipline and academics. Furthermore, in terms of the outcome, it was
found that the effects of early pieces within each pipeline tended to weaken over time, especially
when they crossed pipelines. This demonstrates that pipelines can be altered despite early
influences, and that the early influences of each pipeline can be adequately altered with
interactions among other pipelines. Finally, it was found that pushouts are more impacted by the
STEM pipeline than the STP pipeline, which demonstrates the power of academics over
discipline in the process of pushing students out.
THE PROCESS OF PUSHING OUT
8
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THE PROCESS OF PUSHING OUT
Figure 1. CFA Model
15
Running Head: THE PROCESS OF PUSHING OUT
Figure 2. LDS Model
Note: Correlations among demographic controls not shown for the purpose of visual clarity.
1
THE PROCESS OF PUSHING OUT
Figure 3. SEM Model
Note: Demographic controls not shown for the purpose of visual clarity.
17
THE PROCESS OF PUSHING OUT
Table 1
Structural Equation Model Path Coefficients
Pre-HS HS
Drop. RMSEA
Susp.
Susp. Status / CFI
Non0.14
0.11
0.06
0.02
standardized
/ 0.96
(N = 16510)
STDYX
18
Path:
S1M1
-0.31***
(0.03)
Path:
S1S2
0.59***
(0.10)
Path:
M1S2
-0.64***
(0.08)
Path:
M1M2
0.85***
(0.03)
Path:
S2M2
-0.05***
(0.01)
Path:
S2DS
0.34***
(0.06)
Path:
M2DS
-1.31***
(0.12)
-0.22***
(0.02)
STDY
-0.63***
(0.05)
Note: Estimates followed by standard errors in parentheses
*p =/< .05
**p < .01
***p < .001
0.18***
(0.03)
0.52***
(0.09)
-0.28***
(0.03)
-0.28***
(0.03)
0.87***
(0.01)
0.87***
(0.01)
-0.11***
(0.03)
-0.11***
(0.03)
0.29***
(0.04)
0.29***
(0.04)
-0.48***
(0.03)
-0.48***
(0.03)
Table 2
Structural Equation Model Indirect Effects
Total
Medium Small
STP-only
Indirect
Ind.
Ind.
Ind.
Non0.01*** -0.04*** 0.06***
0.20***
standardized (0.003)
(0.01)
(0.02)
(0.05)
STDYX 0.003*** -0.02*** 0.05***
0.05***
(0.001)
(0.003)
(0.01)
(0.01)
STDY
0.01*** -0.02*** 0.05***
0.15***
(0.002)
(0.003)
(0.01)
(0.03)
Note: Estimates followed by standard errors in parentheses
*p =/< .05
**p < .01
***p < .001
STEM-only
Ind.
-1.12***
(0.10)
-0.41***
(0.03)
-0.41***
(0.03)
R-Square
HS Susp.
0.23
R-Square
Drop. Status
0.44
R-Square
Math 1
0.18
R-Square
Math 2
0.84
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