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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 2 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 3 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 4 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 5 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 Bibliography Aber, J., Brown, J., & Henrich, C. (1999). 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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: S1M1 -0.31*** (0.03) Path: S1S2 0.59*** (0.10) Path: M1S2 -0.64*** (0.08) Path: M1M2 0.85*** (0.03) Path: S2M2 -0.05*** (0.01) Path: S2DS 0.34*** (0.06) Path: M2DS -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