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Educational policy analysis archives
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Educational policy analysis archives.
n Vol. 12, no. 23 (May 31, 2004).
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c May 31, 2004
Influence of school policy and practice on mathematics achievement during transitional periods / Janet K. Holt [and] Cynthia Campbell.
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1 of 22 A peer-reviewed scholarly journal Editor: Gene V Glass College of Education Arizona State University Copyright is retained by the first or sole author, who grants right of first publication to the EDUCATION POLICY ANALYSIS ARCHIVES EPAA is a project of the Education Policy Studies Laboratory. Articles appearing in EPAA are abstracted in the Current Index to Journals in Education by the ERIC Clearinghouse on Assessment and Evaluation and are permanently archived in Resources in Education Volume 12 Number 23May 31, 2004ISSN 1068-2341The Influence of School Policy and Practice on Mathematics Achievement During Transitional Periods Janet K. Holt Northern Illinois University Cynthia Campbell Northern Illinois UniversityCitation: Holt, J., & Campbell, C., (2004, May 31). The influence of school policy and practice on mathematics achievement during transitional periods Education Policy Analysis Archives, 12 (23). Retrieved [Date] from 23/.Abstract In this study, the effects of school policies and p ractices on math achievement growth, as students transitioned from m iddle to high school, were examined while controlling for school contextual variables. A pattern of accelerated growth in mathe matics achievement from grades 8 to 12 occurred, in which higher achieving students in mathematics at grade eight ac celerated more than lower achieving students in mathematics g rowth during the transition from middle to high school. Controll ing for school context, school policy promoting parent involvement and academic counseling had significant positive impact s on the acceleration in growth during this period. The impl ications of using multilevel growth models to study growth duri ng transition periods are discussed.


2 of 22 The goal of this line of research is to determine h ow school policy and school context interplay to influence a child’s success in mathematics. Past research has typically focused on variables influencing math success, as measured by achievement on mathematics standardized tests at de signated grade levels. Yet, little is known about changes in mathematics a chievement over time (i.e., growth), especially at critical developmental phase s. Further, contributions to this field that distinguish the influence of school policies and practices from school context would be particularly useful.The general purpose of this research was to investi gate the effects of school policies and practices in moderating the changes in achievement that occurs during key transition periods. Specifically, we wer e interested in examining (a) the growth patterns in math achievement, including both the instantaneous rate of change at grade 8 (i.e., linear growth), as well as the change in growth rate from grades 8 to 12 (i.e., acceleration or decelera tion) and (b) school policy, practice, and context variables associated with the se growth patterns. In the present study, “school policy” refers to int ernal rules of operation established by the institution. Such policies are d eveloped primarily by officials of the institution as are decisions of maintaining such policies. The term “school practice” refers to the institution’s implementatio n or enforcement of such policies. “School context” describes environmental variables characteristic of a school, but that are typically exogenous to the pol icies and practices of its school administrators and teachers. In our explorat ory analyses of the data, particular policy and context variables associated with math achievement growth were identified. Consequently, the scope of the following literature review is limited to studies examining variables re levant to this study. School Policy and Math AchievementRecent studies have found math performance to be po sitively related to school policies intended to create a safe school community (Borman & Rachuba, 2001). Through effective discipline practices (Clar k, 2000; Freiberg, Connell, & Lorentz, 2001), parental involvement (Brown, 1996; Ford, Follmer, & Litz, 1998), and in-school counseling programs (Bleuer & Walz, 1 993; Lapan, Gysbers, & Sun 1997; Shoffner & Vacc, 1999), schools can culti vate an overall atmosphere conducive to student learning. Collectively, resear ch seems to suggest that policies which make good use of in-school time have greater potential for improving achievement for all learners, thereby clo sing the achievement gap between racial majority and minority students.School policy: Effective disciplinary practices. The overall goal of school disciplinary policies is to maintain an orderly env ironment so that teachers are better able to teach and students are better able t o learn. Barton, Coley, and Wenglinsky (1998) found that student disorder inter rupted not only school safety, but decreased student achievement as well. To ensure institutional order, some principals have elected to implement to ugh discipline responses such as “zero tolerance policies,” reporting that s trict consequences are absolutely necessary for maintaining school safety (Holloway, 2001/2002). Similarly, Echlelbarger and colleagues (1999) found that when misconduct is


3 of 22 not confronted, misbehaving students are likely to infer that such behavior will be tolerated. The researchers concluded that zero t olerance policies may send a clearer message to students about the consequence s associated with actions that do not comply with school policy, thereby sett ing standards for expected behavior.Conversely, Van Acker (2002) argues that although d iscipline policies are intended to curtail undesirable behavior, such effo rts may sometimes reinforce the very action they are intended to suppress. Inst ead, shifting discipline from reducing negative incidents to promoting positive f unctioning is recommended. Others also have advocated for disciplinary practic es that provide guidance for desired behaviors as opposed to merely enforcing pu nitive consequences (Shingles & Lopez-Reyna, 2002).School policy: Involving parents. Most would agree that parental involvement in their child’s education has many advantages (Brown, 1996; Ford, et al., 1998; Jones, 2001; Littman, 2001; Mulhall, Flowers, & Mer tens, 2002). Such benefits have been found in research using National Educatio n Longitudinal Study (NELS) data where parental aspirations (Fan, 2001; Fan & Chen, 2001; Thomas, 1998) and involvement (Brown, 2000, Ma & Kl inger, 2000) contributed significantly to students’ mathematics test scores.Consistent with literature citing positive effects of parental involvement on mathematics achievement, school policy supporting p arental involvement programs has been shown to promote student gains in overall achievement and application of mathematical concepts. In particular differing levels of parental involvement (high vs. low) counterbalanced effects of gender and socioeconomic status (SES) on math achievement (Sha ver & Walls, 1998). These studies highlight the importance of school-su pported programs that include parental involvement in students’ education al progress. School policy: In-school counseling programs. Effective school counseling programs have the potential to contribute to school improvement by en hancing school climate and raising student achievement (Bleuer & Walz, 1993; L apan et al., 1997; Shoffner & Vacc, 1999). Although this connection ma y seem intuitively obvious, empirical studies supporting this link are limited. One study by Fouad (1995) tested this connection by examining urban inner-cit y middle school students’ math achievement following a 1-year intervention pr ogram. An experimental/control method was employed to test th e efficacy of school counseling program interventions. In experimental c lassrooms, a 6-week math and science career awareness model was infused into the 8th grade curriculum. In addition to curricular enhancements, field trips illustrative activities, and guest speakers were utilized to increase students’ occupational knowledge. In addition, math achievement was analyzed and compare d between the two groups. Students exposed to career-linking activiti es significantly outperformed their control-group peers on mathematics homework a nd tests (although the achievement was not linear). Moreover, by compariso n, students in the experimental group showed greater effort and class participation, had better attendance, and were more likely to take additional math classes (particularly minority students) than students who did not partic ipate in school counseling intervention programs. Similarly, Lopez (2001) foun d that for at-risk Latino high school students, counseling interventions related t o higher math grades for


4 of 22 students in college preparation courses, but not fo r students in the remedial track.School policy and math achievement growth Providing students with academic counseling and assistance in coursework selection c ould have direct implications for both principals and counselors whe n adopting school policy. In particular, research shows that prior success in ma thematics increases the likelihood of future mathematics achievement. Schne ider, Swanson, and Riegle-Crumb (1997) investigated the relationship b etween school policy requiring course sequencing and math performance. E xamining data from NELS: 88-94, the researchers found course sequencin g in 10th grade to be the greatest predictor of mathematics coursework in 12t h grade. Moreover, high school students who participated in advanced mathem atics classes showed greater gains in mathematics achievement than their peers who did not take additional math courses beyond graduation requireme nts. In contrast, however, Hoffer (1997) found school policy requiring an addi tional math course did not significantly help or hurt mathematics achievement scores.Math Achievement and School Context VariablesThe relationship between school context and mathema tics achievement is well documented (Demery, 2000; Ma & Klinger, 2000; Patto n, 2001; Roscigno, 2000; Thomas, 1998). Defined as environment charact eristics generally not under the control of school policy (e.g., percentag e minority, free and reduced lunch, single family households), school context is an important variable to consider when evaluating educational effectiveness and student learning. Selected research investigating these variables is highlighted below. School context: Percentage minority enrollment, sch ool crime, and SES. Although National Assessment of Educational Progres s (NAEP) data indicate general gains in mathematics and reading performanc e, racial difference in mathematical performance is well documented (Hall, Davis, & Bolen, 1999; Lockhead, Thorpe, Brooks-Gunn, Casserly, & McAloon, 1985). For example, since 1990, NAEP score differences between AfricanAmerican and Caucasian students have widened (Hoff, 2000; Lubienski, 2002) Despite controlling for socioeconomic status (SES; i.e., as measured by par ticipation in free or reduced school lunch programs) White students still outperformed black students in mathematics (Rugutt, 2001).The relationship between criminal activity (e.g., g ang affliliation, drug abuse) and drop out rates is also evident (Arfaniarromo, 2 001; Belitz & Valdez, 1994). Looking at school context variables, Roscigno (2000 ) found racial inequalities in school enrollment, social class composition, and sc hool crime to negatively mediate mathematics achievement during late element ary and beginning middle school years. Similarly, Battin-Pearson, Newcomb, a nd Abbott (2000) found poor academic performance and dropping-out behavior related to general deviance, SES, and bonding to antisocial peers.School context: Single-parent families. Investigating the connection between single-parent homes and academic performance, Pong (1997) found schools with a higher percentage of students from single-pa rent families have lower


5 of 22 achievement scores in comparison to schools compris ed predominately of two parent households. The researcher did note, however that when strong social relations with a parent are controlled for, the neg ative achievement gap among students from single-parent and step families is re duced significantly. School context and math achievement growth Most of the work in math achievement has focused on variables related to mat h achievement; however, some authors have extended the realm of study to in clude math achievement growth (Muthn, 1997). Muthn determined that there is non-linear math achievement growth from grade 8 to grade 10; howeve r, he was not able to identify factors related to that change. Using NELS :88 data, Muller (1998) found that the gender gap in mathematics performance, par ticularly achievement gains between grades 8 and 10, were only found when parental involvement was not controlled for. As a school context variabl e, SES related positively to achievement growth over time, particularly between grades 1 and 6 (Jimerson, Egeland, & Teo, 1999).As described, there is a strong literature base lin king school policies and practices to mathematics achievement. Yet, it is no t clear if these same factors account for mathematics achievement growth. As stud ents transition from middle to high school, there is the potential for t he achievement gap to widen significantly due to unequal math achievement growt h. Consequently, the goal of this study is to build a model for predicting ma th achievement growth based on the prior literature on effective school policie s and practices and to test this model using random coefficients growth modeling.MethodsIn order to assess school context, Raudenbush and W illms’ (1995) definition for Type B school effects will serve as the guiding fra mework – the difference between a student’s performance in one school and t he performance that would have been expected had that student attended anothe r school with identical context, but with a practice of average effectivene ss. In other words, Type B school effects control for school contextual variab les (e.g., percent free and reduced lunch), while examining the effects of scho ol policy and practice variables (e.g., school disciplinary policies). As Raudenbush and Willms (1995) point out, Type B effects are most important for ev aluation studies of school effectiveness. Keeping within this framework, the i nfluence of school policies and practices on math achievement growth were exami ned while controlling for school contextual variables. Moreover, the effects of school policies and practices in moderating the changes in achievement growth that occurred as students transitioned from middle to high school we re investigated.Data SourceData from the National Educational Longitudinal Sur vey of 1988 (NELS:88) was used in this study. The NELS:88 survey was designed to assess educational transitions from middle school through early adulth ood, by assessing educational achievement and student, parent, teache r, and school variables that may be related to educational achievement. Thi s nationally representative survey has been conducted for the twelve-year perio d from 1988 to 2000,


6 of 22 tracking students initially in 8th grade through hi gh school and college and into the workforce. During the years 1988 to 1992, stude nts were tracked through the transition from middle school into high school and to high school completion. Participants were surveyed three times during this period: 1988, 1990, and 1992. For this study, only students who participate d in all three of these survey years ( n = 16,489) were selected. These students were from 1,011 different schools,Math AchievementMath achievement was assessed by the IRT-scaled mat hematics achievement score. The math test used in the NELS:88 assessed b asic math computational skills, as well as more advanced skills of problem solving and comprehension. This score was vertically scaled to enable measurem ent of change in achievement during the survey period.Variables Related to Math AchievementAll of the control and explanatory variables used i n this study came from the school administrator questionnaire. This questionna ire was administered to the building principal, headmaster, or another knowledg eable administrator and was designed to collect information about the overall a cademic climate of the school. Variables were selected from the administra tor questionnaire data that would relate to the study purpose; to investigate v ariables related to mathematics achievement growth to determine how sch ool context and policy interplay to influence mathematics achievement duri ng key transition periods. The school contextual effects explored in this stud y are listed in Table 1. These variables were selected based on their expected rel ationship to math achievement growth and their lack of multicollinear ity ( r < .7). Initially the school climate variables ( k = 10 for base year and k = 11 for first follow-up) were correlated with achievement as individual indicator s in the exploratory phase, as previous reports have indicated that although compo site school climate variables were not related to achievement, individu al variables were related to achievement (Peng, 1995). In contrast to Peng’s fin dings, the individual school climate variables used in this study had two distin ct correlation patterns with the growth parameters; one for the attendance school cl imate variables and the other for the illegal activities school climate var iables. Hence, for purposes of this analysis, two school climate composite variabl es were created for both base year and first follow-up. The first consisted of th e three attendance-related items: tardiness, absenteeism, and class cutting an d the second consisted of seven (base year) to eight (first follow-up) seriou s and/or illegal activities (i.e., physical conflict, robbery or theft, vandalism, alc ohol use, use of weapons, gang activity, physical abuse of teachers, and verbal ab use of teachers). Table 1 Potential School-Level Predictors of Math Achieveme nt Growth Contextual VariablesPolicy and Practice Variables


7 of 22 Base Year Percentage HispanicTeacher base salaryPercentage African-AmericanNumber of teachers with graduate degree Percentage single-parentStandardized tests to assig n students to assign 8th graders to high school courses Student emphasis on learningCounselors influence as signing high school courses Teacher moraleTeachers influence assigning high sch ool courses School absenteeism school climate composite Parents influence assigning high schoolcourses School violence school climate composite Tests influence assigning high school courses Students face competition for grades Math club available to 8th graders Discipline is emphasized at the school School environment is flexible Academic counseling exists for students Behavioral counseling exists for students Vocational counseling exists for students Student-teacher ratioFirst Follow-up Percent of 10th graders who dropped-out Middle school and high school administratorsmeet School absenteeism school climate composite Math ability grouping School violence school climate composite Senior graduation exam Percent on free and reduced lunch Number of math teachers Graduation requirements for math Number of higher-level math courses offered


8 of 22 Number college advanced math courses offered Second Follow-up Percent receiving remedial math Major new curricular programs established Grouping students by ability changed School-wide changes in instructional methods The school-level policy and practice variables exam ined are listed in Table 1. The criteria that were used to select these variabl es were a lack of multicollinearity among variables ( r < .7) and a theoretical expectation that they would correlate with math achievement growth, and r elate to the contextual variables – achievement relationships.Data Analysis ProceduresTraditional approaches for analyzing longitudinal s urvey data utilize repeated measures ANOVA or MANOVA techniques. These methods have severe constraints on the form of the data. Perhaps the tw o biggest problems in longitudinal research are that all subjects must ha ve an equal number of data points and the data points must have equal spacing. Inevitably data cannot be collected for all participants at each time period resulting in increased attrition rates as data collection progresses. In traditional data analytic approaches using listwise deletion, participants without full data for all time points are discarded. This often results in a data set that is greatly reduced, biased, and unrepresentative of the original sampled population To overcome these limitations, this study employed a multilevel, rand om coefficients growth modeling technique, which does not require full dat a or equal spacing of data and allows for random variation in growth curve coe fficients (Raudenbush & Bryk, 2002; Muthn & Curran, 1997). Using this meth od, data were not listwise deleted when data were missing on some waves of the study, but rather all data points were used in the estimation of the growth pa rameters. We took advantage of these growth modeling techniques to en able us to more accurately model the transition from middle school to high school in terms of mathematics achievement.Multilevel Growth ModelsIn this study, growth was not assumed to be linearl y related to time; that is growth was allowed to accelerate or decelerate as t ime increased (quadratic growth). When students’ cognitive changes coincide with transitions across developmental stages or transitions in learning env ironments, achievement growth patterns would be expected to change and thi s change would not be detected with methods employed to assess linear gro wth. Because transition in growth was of particular interest in this study, mu ltilevel, polynomial growth models were used to measure the acceleration or dec eleration in math


9 of 22 achievement growth rate that occurred across this l earning environment transition. Key features present in the multilevel model used in this study include: (a) observations are nested in individuals allowing for different number and spacing of observations across individuals; (b) an acceleration/deceleration parameter is explicitly added to the linear growth model; (c). average achievement, linear growth, and rate of change in g rowth rates are allowed to vary across schools; and (d) conditional models are formed at the school level, to determine variables of the school that are relat ed to average achievement, linear growth, and acceleration/deceleration.Missing data were imputed for the school-level vari ables using mean imputation procedures in order to have complete data for analy ses using the algorithm HLM3 (Raudenbush, Bryk, Cheong, & Congdon, 2000). A lthough, missing data can be tolerated at lower levels of analysis in HLM 3, complete data is needed at the highest level of analysis, in this case the sch ool level. The amount of imputed missing data ranged from 1.8% to 20.8% with an average of 9.1% across the 15 school-level variables used in the hi erarchical linear models (HLM). However, missing data were still present on the math achievement measures for individual students. The time series v ariable, grade, was centered at grade eight for interpretability. Therefore, ave rage achievement and the instantaneous growth rate at grade eight were estim ated. Additionally, the acceleration or deceleration in growth was estimate d from grades 8 to grade 12. The data analysis proceeded in three phases. In Pha se I, unconditional growth models were examined to determine if math achieveme nt growth was linear or curvilinear. During this phase, empirical Bayes (EB ) residuals of linear and quadratic growth estimates were also generated for the exploratory phase. In the exploratory phase, Phase II, these EB residuals were correlated with potential school-level predictor variables (see Tab le 1) to determine where strong and weak relationships with math achievement growth existed. These results, along with theoretical-based decision-maki ng, were used to determine potential predictors of math achievement growth. In Phase III, conditional models of growth were formulated using the variable s determined in Phase II. The relationships of these variables to linear and quadratic growth were tested with multilevel polynomial growth models.Results Phase IUnconditional models of both linear and quadratic g rowth were tested using multilevel modeling. It was necessary to constrain student-level linear and quadratic growth estimates in order for the maximum likelihood estimates to reach convergence using the HLM3 algorithm (Raudenb ush et al., 2000). The deviance statistic was statistically significantly different when the quadratic term was added to the model, chi-square = 2173.009, df = 4, p < .001, indicating that the quadratic model provided a better fit to the da ta than the linear model. Further, the coefficients (denoted by g for both linear and quadratic growth were positive ( g100 = 2.471 and g200 = 0.5950), indicating that both math achievement and the change in math growth increased as students progressed in grade level. As shown in Table 2, the correlatio ns between the residuals for


10 of 22 linear growth were negatively correlated with both average achievement and quadratic growth, whereas average achievement and q uadratic growth were positively related. This indicated that schools wit h higher average achievement had flatter linear growth rates but steeper acceler ation from grades 8 to 12 than schools with lower average achievement. Empirical B ayes (EB) residuals for average achievement, linear growth, and quadratic g rowth were outputted for further analysis. Table 2 Intercorrelations Among Random School-level Slopes and Intercept ParameterLinear Slope ( b10) Quadratic Slope ( b20) Schools ( n = 1011) Intercept ( b00) -.662.449 Linear Slope ( b10) -.933Phase IISchool-level contextual and policy and practice var iables were correlated with the empirical Bayes residuals from the school-level model to identify potential correlates of math achievement and growth (Raudenbu sh & Bryk, 2002, p. 268). The empirical Bayes residuals for the average achie vement at grade 8, linear growth in achievement at grade 8, and acceleration/ deceleration in growth from grades 8 to 12 were each correlated with the potent ial school-level predictors of math achievement. These variables are summarized in Table 1. Those with significant relationships to the residuals or with a strong theoretical basis for predicting math achievement growth were retained fo r Phase III (see Table 3). Table 3 Predictors of Math Achievement Growth from School-l evel Policy, Practice, and Contextual Variables VariableCoefficient SE Mean Achievement at Grade 846.352***0.285Base year attendance school composite-1.234*0.619Base year illegal activity School composite-0.7681. 241 Base year disciplinary policy-0.4900.303Base year academic counseling offered0.7050.953Base year behavioral counseling offered1.0590.964Base year vocational counseling offered-1.1270.593


11 of 22 VariableCoefficient SE Base year percent Hispanic-0.062***0.016Base year percent Black-0.070**0.019Base year percent single parent households0.0040.01 7 Mean growth rate at Grade 82.478***0.309Base year attendance school composite-0.6210.679Base year illegal activity School composite3.081**1 .147 Base year disciplinary policy0.0090.346Base year academic counseling offered-1.6801.095Base year behavioral counseling offered0.8431.098Base year vocational counseling offered-0.6870.687Base year percent Hispanic0.0160.022Base year percent Black0.0270.026Base year percent single parent households-0.0360.0 19 Mean change in growth rate0.593***0.073Base year attendance school composite0.1830.165Base year illegal activity School composite-0.724** 0.254 Base year disciplinary policy0.0340.084Base year academic counseling offered0.563*0.268Base year behavioral counseling offered-0.2210.284Base year vocational counseling offered0.1320.165Base year percent Hispanic0.0010.006Base year percent Black-0.0020.007Base year percent single parent households0.010*0.0 05 First follow-up school promotes parent involvement0 .094***0.023 First follow-up disciplinary policy-0.105**0.030First follow-up attendance school climate composite 0.0440.076 First follow-up illegal activity School climate com posite-0.0170.037


12 of 22 VariableCoefficient SE First follow-up percent drop-out in 10th grade0.000 50.002 First follow-up percent on free and reduced lunch-0 .005**0.002 p < .05; ** p < .01, *** p < .001Phase IIIThe variables retained from Phase II were used to m odel math achievement, math achievement growth, and acceleration/decelerat ion in growth in a three-level hierarchical model. The contextual vari ables used as predictors of level-one average achievement at grade 8, growth ra te at grade 8, and the acceleration from grades 8 to 12 included: the scho ol climate absenteeism composite, the school climate illegal activities co mposite, percent African-American, percent Hispanic, and percent sin gle parent. Additionally, the first follow-up absenteeism composite, the school c limate illegal activities composite, the percent of 10th graders who dropped out, and the percent on free and reduced lunch were used as predictors of q uadratic growth from grades 8 to 12.The selected base year policy and practice variable s that were entered as predictors of level-one average achievement and lin ear growth at grade 8, and quadratic growth from grades 8 to 12 included base year disciplinary policy, academic counseling, vocational counseling, and beh avioral counseling. Additionally, first follow-up disciplinary policy a nd whether the school promotes parent involvement were added as predictors of quad ratic growth from grades 8 to 12.As presented in Table 3, there were several statist ically significant predictors of both average school achievement and growth. Of part icular interest in this investigation were the predictors of growth. None o f the base year policy and practice variables were significant predictors of l inear growth at grade 8, although base year participation in illegal activit ies was positively associated with linear growth g102 = 3.081, p < .01. The contextual variables that statistically significantly predicted acceleration in math achievement included: the first follow-up attendance school climate compo site, g202 = -.1054, p < .01; the base year illegal activity school climate compo site, g204 = -.7236, p < .01; base year percentage of single-parent households, g2014 = .0099, p < .05; and percentage on free and reduced lunch in the first f ollow-up, g2015 = -.0051, p < .01. The school policy and practice variables that contributed to acceleration in growth, controlling for the contextual effects, inc luded whether academic counseling was offered in the base year, g208 = .5927, p < .05; whether the school promoted parent involvement at the first fol low-up, g201 = .0940, p < .001; and whether discipline was emphasized in the school at the first follow-up, g202 = -.1054, p < .01. Adding the school policy and practice varia bles accounted for a significant amount of the unexplain ed variance in math achievement and growth beyond that explained by the school context variables, (increment in chi-square) = 56.72, df = 14, p < .001.


13 of 22 DiscussionThe average school achievement growth trajectory ac celerated during the transition from middle to high school and the varia nce in acceleration was related to contextual variables and school policies and practices. This is particularly relevant for schools considering strat egies for improving mathematics achievement growth by countervailing ne gative influences of SES and other contextual variables.School crime (i.e., physical conflicts, robbery, va ndalism, alcohol use, possession of weapons, physical and verbal abuse of teachers) was positively related to math achievement growth at grade 8 but n egatively related to acceleration patterns in mathematics achievement. A lthough, these results may seem counter-intuitive, they are consistent with th e negative correlation between linear and quadratic growth. That is, schoo ls with lower math achievement had steeper math growth at grade 8, but less acceleration in growth over time, and these schools also had more s chool crime. Although, these schools with high crime have more potential, as seen by their steeper growth rate in grade 8, this growth tapers off as s tudents progress across the transition from middle to high school. This is cons istent with previous research reporting the severe consequence of lowered academi c performance in schools with high levels of crime (Roscigno, 2000). However these results contrast with Peng’s (1995) findings of no relationship between s chool climate variables and measures of achievement. It is important to note th at Peng defined school climate very broadly, including both contextual and policy variables. In this study, however, we constructed school climate compo sites that were comprised of more homogenous items thereby measuring more wel l-defined constructs. The percentage of single parent households with chi ldren attending the school in the base year was positively related to accelera tion. Although contrary to previous research and as noted by Pong (1997), it i s possible that the schools that had positive effects of single parenting also had strong parent-child relations, thereby reducing the potential negative impact of single parent households. The percentage of households in the school qualifyi ng for free and reduced lunch in the first follow-up was negatively related to acceleration. In other words, schools with families from lower SES strata had les s acceleration in math achievement from grades 8 to 12 than schools with f amilies from higher SES strata. This finding is consistent with prior resea rch demonstrating the inverse relationship between SES and achievement growth in mathematics over time (Jimerson, Egeland, & Teo, 1999; Rugutt, 2001).It appears that during these transition periods, in equity gaps are increased due to the higher acceleration rate for students from h igher SES strata. Therefore, our findings suggest that policies directed toward closing the mathematics achievement gap between high and low SES groups wou ld be more effective if implemented prior to the transition from middle sch ool to high school. School policy and practice variables were also rela ted to acceleration in math


14 of 22 achievement, controlling for school context. School s with policies emphasizing parental involvement were found to have greater acc eleration in mathematics achievement than schools without such an emphasis. This finding supports earlier research documenting the importance of a st able home environment and parental involvement in their children’s academic s uccess (Brown, 2000, Ma & Klinger, 2000; Pong, 1997). Moreover, school polici es that emphasize parental involvement could offset the negative effects of SE S on mathematics achievement as noted by Shaver and Walls (1998). It is critical that school policy makers, particularly in schools with large n umbers of students from low SES backgrounds, plan courses of action that draw u pon the positive effects of parental involvement when developing models of best practice in education. Effectiveness of educational policies is likely to be strengthened when common goals are acknowledged in both home and school. Mor eover, a holistic view of school policy can aid in buffering the negative inf luences of poverty that threaten the academic success of students at risk.This study also confirmed the importance of academi c counseling, in that school policies supporting academic counseling had greater accelerated growth trajectories in mathematics from 8th to 12th grade. This likely occurs through individualized advisement, whereby school counselor s and students collaborate on course selection and career planning. This is co nsistent with previous work in which school counseling programs were associated with a better school climate and higher achievement levels (Bleuer & Wal z, 1993; Lapan et al., 1997; Shoffner & Vacc, 1999). This finding is parti cularly important for economically poorer schools where low mathematics t est scores are more common. Schools with policies supporting fully deve loped counseling intervention programs showed greater achievement re gardless of socioeconomic level. This suggests that schools tha t support academic counseling may be able to offset the negative effec ts of SES through promotion of activities leading to academic success, thereby facilitating acceleration in students’ academic growth during critical phases in their educational experiences.Moreover, disciplinary policy was negatively relate d to acceleration in math achievement. This was likely not strictly due to th e effects of disciplinary policies, but rather the school atmosphere that req uires more disciplinary policies. Although school climate related to attend ance problems and illegal activities was controlled for in this study, there might be other school climate variables that were not assessed in NELS that might require disciplinary policies, such as negative or discriminatory attitu des among students that could result in school procedures to maintain control.Analysis of growth trajectories in this study indic ates that there is a positive association between average math achievement in the school and acceleration in growth. Hence, we can surmise that schools that emphasize parental involvement and provide academic counseling can pro duce dramatic effects in math achievement growth for high achieving students because these variables increase the acceleration in academic growth that o ccurred during the transition from middle school to high school.This study also demonstrates the effectiveness of p olynomial growth models to


15 of 22 study variables related to transitional periods in which growth rate changes. These transitional periods may be due to developmen tal transitions or to changes in the environment, as was the case in this investigation. In the example provided here, students were transitioning from middle to high school and during this time their growth rate changed. The polynomial growth model was sensitive to this change in growth that occurre d as a result of the school transition. By using multilevel modeling, the growt h trajectories were allowed to vary across schools. The variance in growth could t hen be modeled by school-level variables, a strength of multilevel mo deling. By controlling for contextual effects and investigating the effects of policy and practice variables through the use of Type B effects (Raudenbush & Wil lms, 1995), we determined the effects of school policies and pract ices in schools with similar contexts during these transitional periods. This ha s particular importance in the study of growth periods that have significant accel eration, because the rate of growth is actually increasing. Therefore, any schoo l policy or practice initiated at this time, which affects acceleration can have dram atic effects on achievement since this is a period of rapid growth.With the availability of increasingly sophisticated analytic procedures that allow the modeling of growth trajectories, there is the o pportunity to reframe questions about educational success to study the variables re lated to rate of change and acceleration in rate of change. School effects need not center around differences in mean achievement level among schools but rather around the differences in achievement growth rates and acceler ation across schools. Targeting achievement growth, rather than average a chievement may significantly improve current understanding of cogn itive changes during key transition periods.NoteBoth authors contributed equally to the research an d writing of this article.ReferencesArfaniarromo, A. (2001). Toward a psychosocial and sociocultural understanding of achievement motivation among Latino gang members in U.S. school s. Journal of Instructional Psychology, 28 (3), 123-136. Barton, P., Coley, R., & Wenglinsky, H. (1998). Ord er in the classroom: Violence, discipline, and school achievement. Princeton, NJ: Educational Test ing Service. Battin-Pearson, S., Newcomb, M. D., & Abbott, R. D. (2000). Predictors of early high school dropout: A test of five theories. Journal of Educational Psychology, 92 (3), 568-582. Belitz, J., & Valdez, D. (1994). Clinical issues in the treatment of Chicano male gang youth. Hispanic Journal of Behavioral Sciences, 16 (1), 57-74. Bleuer, J. C., & Walz, G. R. (1993). Striving for e xcellence: Counselor strategies for contributing to the national education goals. (ERIC Document Reprod uction Service No. ED357317. Borman, G.D., & Rachuba, L.T. (2001) Academic success among poor and minority students: An analysis of competing models of school effects (ERIC Document Reproduction Service No. ED451281. Brown, J. D. (2000). The relationships between the dimensions of self-concept and the dimensions of parental involvement. Dissertation Abstracts International, 61 (3-B), 1669.


16 of 22 Brown, J. R. (1996). A superintendent’s perspective on mathematics and school improvement. Thrust for Educational Leadership, 25, 6-9. Clark, P. (2000). Equity: How can we use effective teaching methods to boost student achievement [and] Equity: How can we enhance conditions for lea rning [and] Equity: What can we do to enhance school climate? (ERIC Document Reproduction Service No. ED457315. Demery, J. (2000). The relationship between teacher s’ perceptions of school climate, racial composition, socioeconomic status, and student achi evement in reading and mathematics. Dissertation Abstracts International, 61 (3-A), 957. Fan, X. (2001). Parental involvement and students’ academic achievement: A growth modeling analysis. The Journal of Experimental Education, 70 (1), 27-61. Fan, X., & Chen, M. J. (2001). Parental involvement and students’ academic achievement: A meta-analysis. Educational Psychology Review, 13 (1), 1-22. Ford, M. S., Follmer, R., & Litz, K. K. (1998). Sch ool-family partnerships: Parents, children, and teachers benefit! Teaching Children Mathematics, 4, 310-312. Fouad, N. A. (1995). Career linking: An interventio n to promote math and science career awareness. Journal of Counseling and Development, 73 (5), 527-534. Freiberg, H. J., Connell, M. L., & Lorentz, J. (200 1). Effects of Consistency Management on student mathematics achievement in seven chapter I elementary schools, Journal of Education for Students Placed at Risk, 6 (3), 249-270. Hall, C. W., Davis, N. B., Bolen, L. M. (1999). Gen der and racial differences in mathematical performance. The Journal of Social Psychology, 139 (6), 677-689. Hoff, D. J. (2000). Gap widens between black and wh ite students on NAEP. Education Week, 20 (1), 6-7. Hoffer, T. B. (1997). High school graduation requir ements: Effects on dropping out and student achievement. Teachers College Record, 98 (4), 584-607. Holloway, J. H. (2001/2002). The dilemma of zero to lerance. Educational Leadership, 59 (4), 84-85. Jimerson, S., Egeland, B., & Teo, A. (1999). A long itudinal study of achievement trajectories: Factors associated with change. Journal of Educational Psychology, 91( 1), 116-126. Jones, R. (2001). Involving parents is a whole new game: Be sure to win!. The Education Digest, 67 (3), 36-43. Lapan, R. T., Gysbers, N. C., & Sun, Y. (1997). The impact of more fully implemented guidance programs on the school experiences of high school s tudents: A statewide evaluation study. Journal of Counseling and Development, 75, 292-302. Littman, C. B. (2001). The effects of child-centere d and school-centered parent involvement on children’s achievement: Implications for family int eractions and school policy. Dissertation Abstracts International, 61 (7-A), 2655. Lockhead, M., Thorpe, M., Brooks-Gunn, J., Casserly P., & McAloon, A. (1985). Sex and ethnic differences in middle school mathematics, science, and computer science: What do we know? Princeton, NJ: Educational Testing Service. Lopez, E. M. (2001). Guidance of Latino high school students in mathematics and career identity development. Hispanic Journal of Behavioral Sciences, 23 (2), 189-207. Lubienski, S. T. (2002). Are we achieving “mathemat ical power for all?” A decade of national data on instruction and achievement. (ERIC Document Reprodu ction Service No. ED463166). Ma, X., & Klinger, D. A. (2000). Hierarchical linea r modeling of student and school effects on academic achievement. Canadian Journal of Education, 25 (1), 41-55. Mulhall, P. F., Flowers, N., & Mertens, S. B. (2002 ). Understanding indicators related to academic


17 of 22 performance. Middle School Journal, 34 (2), 56-61. Muller, C. (1998). Gender differences in parental i nvolvement and adolescents’ mathematics achievement. Sociology of Education, 71 (4), 336-356. Muthn, B.O. (1997). Latent variable modeling of lo ngitudinal and multilevel data. In A. E. Rafferty (Ed.), Sociological methodology (pp. 453-480). Washington, DC: Blackwell. Muthn, B.O., & Curran, P.J. (1997). General longit udinal modeling of individual differences in experimental designs: A latent variable framework f or analysis and power estimation. Psychological Methods, 2, 371-402. Patton, D. K. (2001). Demographic and education-rel ated factors that influence student behavior. Dissertation Abstracts International, 61 (12-A), 4632. Peng, S. (1995). Empirical evaluation of social psychological, and e ducational construct variables used in NCES surveys (NCES Working Paper No. 95-14). Washington, DC: U .S. Department of Education. Pong, S. L. (1997). Family structure, school contex t and eighth-grade math and reading achievement. Journal of Marriage and Family, 59 (3), 734-746. Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical linear models: Applications and data a nalysis methods (2nd ed.). Newbury Park, CA: Sage. Raudenbush, S.W., Bryk, A.S., Cheong, Y.F., & Congd on, R. (2000). HLM 5. Chicago: Scientific Software International. Raudenbush, S. W., & Willms, J. D. (1995). The esti mation of school effects. Journal of Educational and Behavioral Statistics, 20, 307-335. Roscigno, V. (2000). Family/school inequality and A frican-American/Hispanic Achievement. Social Problems, 47 (2), 266-290. Rugutt, J. K. (2001). A study of student academic c hange in mathematics and language achievement: A multilevel structural equation model (MSEM) approach. Planning and Changing, 32 (3 & 4), 226-246. Schneider, B., Swanson, C. B., & Riegle-Crumb, C. ( 1997). Opportunities for learning: Course sequences and positional advantages. Social Psychology of Education, 2 (1), 25-53. Shaver, A. V., & Walls, R. T. (1998). Effect of Tit le I parent involvement on student reading and mathematics achievement. Journal of Research and Development in Education, 3 1 (2), 90-97. Shingles, B., Lopez-Reyna, N. (2002). Cultural sens itivity in the implementation of discipline policie s and practices. (ERIC Document Reproduction Service No. ED466867). Shoffner, M. F., Vacc, N. N. (1999). Careers in the mathematical sciences: The role of the school counselor. (ERIC Document Reproduction Service No. ED435950). Thomas, J. P. (1998). Productivity and mathematics achievement and attitudes among African-Americans: Testing Walburg’s model. Dissertation Abstracts International, 61 (3-A), 882. Van Acker, R. (2002). Establishing and monitoring a school and classroom climate that promotes desired behavior and academic achievement. (ERIC Do cument Reproduction Service No. ED466862).About the AuthorsJanet K. Holt is an Associate Professor in the Department of Educ ational Technology, Research and Assessment at Northern Ill inois University. She teaches statistics and research methods and her res earch interests include statistical modeling methods for measuring growth d uring critical transitions and factors related to success in math and science. Ema il:


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