The Influence of School Policy and Practice on
Mathematics Achievement During Transitional Periods
Janet K. Holt
Northern Illinois University
Cynthia Campbell
Northern Illinois University
Citation: 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
http://epaa.asu.edu/epaa/v12n23/.
Abstract
In this study, the effects of school policies and practices on
math achievement growth, as students transitioned from middle to
high school, were examined while controlling for school contextual
variables. A pattern of accelerated growth in mathematics
achievement from grades 8 to 12 occurred, in which higher
achieving students in mathematics at grade eight accelerated more
than lower achieving students in mathematics growth during the
transition from middle to high school. Controlling for school
context, school policy promoting parent involvement and academic
counseling had significant positive impacts on the acceleration in
growth during this period. The implications of using multilevel
growth models to study growth during transition periods are
discussed. |
The goal of this line of research is to determine how 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 designated grade levels. Yet,
little is known about changes in mathematics achievement over time
(i.e., growth), especially at critical developmental phases.
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 investigate the
effects of school policies and practices in moderating the changes
in achievement that occurs during key transition periods.
Specifically, we were 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
deceleration) and (b) school policy, practice, and context
variables associated with these growth patterns.
In the present study, “school policy” refers to
internal rules of operation established by the institution. Such
policies are developed primarily by officials of the institution
as are decisions of maintaining such policies. The term
“school practice” refers to the institution’s
implementation or enforcement of such policies. “School
context” describes environmental variables characteristic of
a school, but that are typically exogenous to the policies and
practices of its school administrators and teachers. In our
exploratory 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 relevant to this study.
School Policy and Math Achievement
Recent studies have found math performance to be positively
related to school policies intended to create a safe school
community (Borman & Rachuba, 2001). Through effective
discipline practices (Clark, 2000; Freiberg, Connell, &
Lorentz, 2001), parental involvement (Brown, 1996; Ford, Follmer,
& Litz, 1998), and in-school counseling programs (Bleuer &
Walz, 1993; Lapan, Gysbers, & Sun 1997; Shoffner & Vacc,
1999), schools can cultivate an overall atmosphere conducive to
student learning. Collectively, research seems to suggest that
policies which make good use of in-school time have greater
potential for improving achievement for all learners, thereby
closing 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 environment so that teachers are better able to teach and
students are better able to learn. Barton, Coley, and Wenglinsky
(1998) found that student disorder interrupted not only school
safety, but decreased student achievement as well. To ensure
institutional order, some principals have elected to implement
tough discipline responses such as “zero tolerance
policies,” reporting that strict consequences are absolutely
necessary for maintaining school safety (Holloway, 2001/2002).
Similarly, Echlelbarger and colleagues (1999) found that when
misconduct is not confronted, misbehaving students are likely to
infer that such behavior will be tolerated. The researchers
concluded that zero tolerance policies may send a clearer message
to students about the consequences associated with actions that do
not comply with school policy, thereby setting standards for
expected behavior.
Conversely, Van Acker (2002) argues that although discipline
policies are intended to curtail undesirable behavior, such
efforts may sometimes reinforce the very action they are intended
to suppress. Instead, shifting discipline from reducing negative
incidents to promoting positive functioning is recommended. Others
also have advocated for disciplinary practices that provide
guidance for desired behaviors as opposed to merely enforcing
punitive 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, & Mertens, 2002). Such benefits have
been found in research using National Education Longitudinal Study
(NELS) data where parental aspirations (Fan, 2001; Fan & Chen,
2001; Thomas, 1998) and involvement (Brown, 2000, Ma &
Klinger, 2000) contributed significantly to students’
mathematics test scores.
Consistent with literature citing positive effects of parental
involvement on mathematics achievement, school policy supporting
parental 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 (Shaver & Walls, 1998). These
studies highlight the importance of school-supported programs that
include parental involvement in students’ educational
progress. School policy: In-school counseling programs.
Effective school counseling programs have the potential to
contribute to school improvement by enhancing school climate and
raising student achievement (Bleuer & Walz, 1993; Lapan et
al., 1997; Shoffner & Vacc, 1999). Although this connection
may seem intuitively obvious, empirical studies supporting this
link are limited. One study by Fouad (1995) tested this connection
by examining urban inner-city middle school students’ math
achievement following a 1-year intervention program. An
experimental/control method was employed to test the efficacy of
school counseling program interventions. In experimental
classrooms, 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 compared between the two groups. Students exposed to
career-linking activities significantly outperformed their
control-group peers on mathematics homework and tests (although
the achievement was not linear). Moreover, by comparison, 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 participate in school counseling intervention
programs. Similarly, Lopez (2001) found that for at-risk Latino
high school students, counseling interventions related to higher
math grades for students in college preparation courses, but not
for students in the remedial track.
School policy and math achievement growth. Providing
students with academic counseling and assistance in coursework
selection could have direct implications for both principals and
counselors when adopting school policy. In particular, research
shows that prior success in mathematics increases the likelihood
of future mathematics achievement. Schneider, Swanson, and
Riegle-Crumb (1997) investigated the relationship between school
policy requiring course sequencing and math performance. Examining
data from NELS: 88-94, the researchers found course sequencing in
10th grade to be the greatest predictor of mathematics
coursework in 12th grade. Moreover, high school
students who participated in advanced mathematics classes showed
greater gains in mathematics achievement than their peers who did
not take additional math courses beyond graduation requirements.
In contrast, however, Hoffer (1997) found school policy requiring
an additional math course did not significantly help or hurt
mathematics achievement scores.
Math Achievement and School Context Variables
The relationship between school context and mathematics
achievement is well documented (Demery, 2000; Ma & Klinger,
2000; Patton, 2001; Roscigno, 2000; Thomas, 1998). Defined as
environment characteristics generally not under the control of
school policy (e.g., percentage 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, school crime,
and SES. Although National Assessment of Educational Progress
(NAEP) data indicate general gains in mathematics and reading
performance, 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 African-American and
Caucasian students have widened (Hoff, 2000; Lubienski, 2002).
Despite controlling for socioeconomic status (SES; i.e., as
measured by participation in free or reduced school lunch
programs) White students still outperformed black students in
mathematics (Rugutt, 2001).
The relationship between criminal activity (e.g., gang
affliliation, drug abuse) and drop out rates is also evident
(Arfaniarromo, 2001; Belitz & Valdez, 1994). Looking at school
context variables, Roscigno (2000) found racial inequalities in
school enrollment, social class composition, and school crime to
negatively mediate mathematics achievement during late elementary
and beginning middle school years. Similarly, Battin-Pearson,
Newcomb, and 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-parent families have lower achievement scores in
comparison to schools comprised predominately of two parent
households. The researcher did note, however, that when strong
social relations with a parent are controlled for, the negative
achievement gap among students from single-parent and step
families is reduced significantly.
School context and math achievement growth. Most of the
work in math achievement has focused on variables related to math
achievement; however, some authors have extended the realm of
study to include math achievement growth (Muthén, 1997).
Muthén determined that there is non-linear math achievement
growth from grade 8 to grade 10; however, 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, particularly achievement gains between grades 8 and
10, were only found when parental involvement was not controlled
for. As a school context variable, 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 linking school
policies and practices to mathematics achievement. Yet, it is not
clear if these same factors account for mathematics achievement
growth. As students transition from middle to high school, there
is the potential for the achievement gap to widen significantly
due to unequal math achievement growth. Consequently, the goal of
this study is to build a model for predicting math achievement
growth based on the prior literature on effective school policies
and practices and to test this model using random coefficients
growth modeling.
Methods
In order to assess school context, Raudenbush and Willms’
(1995) definition for Type B school effects will serve as the
guiding framework – the difference between a student’s
performance in one school and the performance that would have been
expected had that student attended another school with identical
context, but with a practice of average effectiveness. In other
words, Type B school effects control for school contextual
variables (e.g., percent free and reduced lunch), while examining
the effects of school policy and practice variables (e.g., school
disciplinary policies). As Raudenbush and Willms (1995) point out,
Type B effects are most important for evaluation studies of school
effectiveness. Keeping within this framework, the influence of
school policies and practices on math achievement growth were
examined 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 were
investigated.
Data Source
Data from the National Educational Longitudinal Survey of 1988
(NELS:88) was used in this study. The NELS:88 survey was designed
to assess educational transitions from middle school through early
adulthood, by assessing educational achievement and student,
parent, teacher, and school variables that may be related to
educational achievement. This nationally representative survey has
been conducted for the twelve-year period from 1988 to 2000,
tracking students initially in 8th grade through high
school and college and into the workforce. During the years 1988
to 1992, students 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 participated in
all three of these survey years (n = 16,489) were selected.
These students were from 1,011 different schools,
Math Achievement
Math achievement was assessed by the IRT-scaled mathematics
achievement score. The math test used in the NELS:88 assessed
basic math computational skills, as well as more advanced skills
of problem solving and comprehension. This score was vertically
scaled to enable measurement of change in achievement during the
survey period.
Variables Related to Math Achievement
All of the control and explanatory variables used in this study
came from the school administrator questionnaire. This
questionnaire was administered to the building principal,
headmaster, or another knowledgeable administrator and was
designed to collect information about the overall academic climate
of the school. Variables were selected from the administrator
questionnaire data that would relate to the study purpose; to
investigate variables related to mathematics achievement growth to
determine how school context and policy interplay to influence
mathematics achievement during key transition periods.
The school contextual effects explored in this study are listed
in Table 1. These variables were selected based on their expected
relationship to math achievement growth and their lack of
multicollinearity (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
indicators in the exploratory phase, as previous reports have
indicated that although composite school climate variables were
not related to achievement, individual variables were related to
achievement (Peng, 1995). In contrast to Peng’s findings,
the individual school climate variables used in this study had two
distinct correlation patterns with the growth parameters; one for
the attendance school climate variables and the other for the
illegal activities school climate variables. Hence, for purposes
of this analysis, two school climate composite variables were
created for both base year and first follow-up. The first
consisted of the three attendance-related items: tardiness,
absenteeism, and class cutting and the second consisted of seven
(base year) to eight (first follow-up) serious and/or illegal
activities (i.e., physical conflict, robbery or theft, vandalism,
alcohol use, use of weapons, gang activity, physical abuse of
teachers, and verbal abuse of teachers).
Table 1
Potential School-Level Predictors of
Math Achievement Growth
| Contextual Variables |
Policy and Practice Variables |
| Base Year |
|
| Percentage Hispanic |
Teacher base salary |
| Percentage African-American |
Number of teachers with graduate degree |
| Percentage single-parent |
Standardized tests to assign students to assign
8th graders to high school courses |
| Student emphasis on learning |
Counselors influence assigning high school
courses |
| Teacher morale |
Teachers influence assigning high school
courses |
| School absenteeism school climate composite |
Parents influence assigning high school
courses |
| 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 ratio |
| First Follow-up |
|
| Percent of 10th graders who dropped-out |
Middle school and high school administrators
meet |
| 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 |
| |
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 examined are
listed in Table 1. The criteria that were used to select these
variables were a lack of multicollinearity among variables
(r < .7) and a theoretical expectation that they would
correlate with math achievement growth, and relate to the
contextual variables – achievement relationships.
Data Analysis Procedures
Traditional approaches for analyzing longitudinal survey data
utilize repeated measures ANOVA or MANOVA techniques. These
methods have severe constraints on the form of the data. Perhaps
the two biggest problems in longitudinal research are that all
subjects must have 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,
random coefficients growth modeling technique, which does not
require full data or equal spacing of data and allows for random
variation in growth curve coefficients (Raudenbush & Bryk,
2002; Muthén & Curran, 1997). Using this method, 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 parameters. We took advantage of these growth
modeling techniques to enable us to more accurately model the
transition from middle school to high school in terms of
mathematics achievement.
Multilevel Growth Models
In this study, growth was not assumed to be linearly related to
time; that is growth was allowed to accelerate or decelerate as
time increased (quadratic growth). When students’ cognitive
changes coincide with transitions across developmental stages or
transitions in learning environments, achievement growth patterns
would be expected to change and this change would not be detected
with methods employed to assess linear growth. Because transition
in growth was of particular interest in this study, multilevel,
polynomial growth models were used to measure the acceleration or
deceleration in math achievement growth rate that occurred across
this learning 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 growth 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 related to average
achievement, linear growth, and acceleration/deceleration.
Missing data were imputed for the school-level variables using
mean imputation procedures in order to have complete data for
analyses using the algorithm HLM3 (Raudenbush, Bryk, Cheong, &
Congdon, 2000). Although, missing data can be tolerated at lower
levels of analysis in HLM3, complete data is needed at the highest
level of analysis, in this case the school 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 hierarchical
linear models (HLM). However, missing data were still present on
the math achievement measures for individual students. The time
series variable, grade, was centered at grade eight for
interpretability. Therefore, average achievement and the
instantaneous growth rate at grade eight were estimated.
Additionally, the acceleration or deceleration in growth was
estimated from grades 8 to grade 12.
The data analysis proceeded in three phases. In Phase I,
unconditional growth models were examined to determine if math
achievement 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 Table 1) to
determine where strong and weak relationships with math
achievement growth existed. These results, along with
theoretical-based decision-making, were used to determine
potential predictors of math achievement growth. In Phase III,
conditional models of growth were formulated using the variables
determined in Phase II. The relationships of these variables to
linear and quadratic growth were tested with multilevel polynomial
growth models.
Results
Phase I
Unconditional models of both linear and quadratic growth 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 (Raudenbush 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 data than the linear model. Further,
the coefficients (denoted by gfor 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 correlations
between the residuals for linear growth were negatively correlated
with both average achievement and quadratic growth, whereas
average achievement and quadratic growth were positively related.
This indicated that schools with higher average achievement had
flatter linear growth rates but steeper acceleration from grades 8
to 12 than schools with lower average achievement. Empirical Bayes
(EB) residuals for average achievement, linear growth, and
quadratic growth were outputted for further analysis.
Table 2
Intercorrelations Among Random
School-level Slopes and Intercept
| Parameter |
Linear Slope
(b10) |
Quadratic Slope
(b20) |
| |
Schools (n =
1011) |
| Intercept
(b00) |
-.662 |
.449 |
| Linear Slope
(b10) |
|
-.933 |
Phase II
School-level contextual and policy and practice variables were
correlated with the empirical Bayes residuals from the
school-level model to identify potential correlates of math
achievement and growth (Raudenbush & Bryk, 2002, p. 268). The
empirical Bayes residuals for the average achievement 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 potential 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 for Phase III (see Table 3).
Table 3
Predictors of Math Achievement
Growth from School-level Policy, Practice, and Contextual
Variables
| Variable |
Coefficient |
SE |
| Mean Achievement at Grade 8 |
46.352*** |
0.285 |
| Base year attendance school composite |
-1.234* |
0.619 |
| Base year illegal activity School composite |
-0.768 |
1.241 |
| Base year disciplinary policy |
-0.490 |
0.303 |
| Base year academic counseling offered |
0.705 |
0.953 |
| Base year behavioral counseling offered |
1.059 |
0.964 |
| Base year vocational counseling offered |
-1.127 |
0.593 |
| Base year percent Hispanic |
-0.062*** |
0.016 |
| Base year percent Black |
-0.070** |
0.019 |
| Base year percent single parent households |
0.004 |
0.017 |
| Mean growth rate at Grade 8 |
2.478*** |
0.309 |
| Base year attendance school composite |
-0.621 |
0.679 |
| Base year illegal activity School composite |
3.081** |
1.147 |
| Base year disciplinary policy |
0.009 |
0.346 |
| Base year academic counseling offered |
-1.680 |
1.095 |
| Base year behavioral counseling offered |
0.843 |
1.098 |
| Base year vocational counseling offered |
-0.687 |
0.687 |
| Base year percent Hispanic |
0.016 |
0.022 |
| Base year percent Black |
0.027 |
0.026 |
| Base year percent single parent households |
-0.036 |
0.019 |
| Mean change in growth rate |
0.593*** |
0.073 |
| Base year attendance school composite |
0.183 |
0.165 |
| Base year illegal activity School composite |
-0.724** |
0.254 |
| Base year disciplinary policy |
0.034 |
0.084 |
| Base year academic counseling offered |
0.563* |
0.268 |
| Base year behavioral counseling offered |
-0.221 |
0.284 |
| Base year vocational counseling offered |
0.132 |
0.165 |
| Base year percent Hispanic |
0.001 |
0.006 |
| Base year percent Black |
-0.002 |
0.007 |
| Base year percent single parent households |
0.010* |
0.005 |
| First follow-up school promotes parent
involvement |
0.094*** |
0.023 |
| First follow-up disciplinary policy |
-0.105** |
0.030 |
| First follow-up attendance school climate
composite |
0.044 |
0.076 |
| First follow-up illegal activity School climate
composite |
-0.017 |
0.037 |
| First follow-up percent drop-out in 10th
grade |
0.0005 |
0.002 |
| First follow-up percent on free and reduced
lunch |
-0.005** |
0.002 |
*p < .05; **p < .01, ***p <
.001
Phase III
The variables retained from Phase II were used to model math
achievement, math achievement growth, and
acceleration/deceleration in growth in a three-level hierarchical
model. The contextual variables used as predictors of level-one
average achievement at grade 8, growth rate at grade 8, and the
acceleration from grades 8 to 12 included: the school climate
absenteeism composite, the school climate illegal activities
composite, percent African-American, percent Hispanic, and percent
single parent. Additionally, the first follow-up absenteeism
composite, the school climate illegal activities composite, the
percent of 10th graders who dropped out, and the
percent on free and reduced lunch were used as predictors of
quadratic growth from grades 8 to 12.
The selected base year policy and practice variables that were
entered as predictors of level-one average achievement and linear
growth at grade 8, and quadratic growth from grades 8 to 12
included base year disciplinary policy, academic counseling,
vocational counseling, and behavioral counseling. Additionally,
first follow-up disciplinary policy and whether the school
promotes parent involvement were added as predictors of quadratic
growth from grades 8 to 12.
As presented in Table 3, there were several statistically
significant predictors of both average school achievement and
growth. Of particular interest in this investigation were the
predictors of growth. None of the base year policy and practice
variables were significant predictors of linear growth at grade 8,
although base year participation in illegal activities 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 composite, g202
= -.1054, p < .01; the base year illegal activity school
climate composite, 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
follow-up, g2015 = -.0051, p <
.01. The school policy and practice variables that contributed to
acceleration in growth, controlling for the contextual effects,
included whether academic counseling was offered in the base year,
g208 = .5927, p < .05; whether
the school promoted parent involvement at the first follow-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 variables accounted for
a significant amount of the unexplained variance in math
achievement and growth beyond that explained by the school context
variables, (increment in chi-square) =
56.72, df = 14, p < .001.
Discussion
The average school achievement growth trajectory accelerated
during the transition from middle to high school and the variance
in acceleration was related to contextual variables and school
policies and practices. This is particularly relevant for schools
considering strategies for improving mathematics achievement
growth by countervailing negative influences of SES and other
contextual variables.
School crime (i.e., physical conflicts, robbery, vandalism,
alcohol use, possession of weapons, physical and verbal abuse of
teachers) was positively related to math achievement growth at
grade 8 but negatively related to acceleration patterns in
mathematics achievement. Although, these results may seem
counter-intuitive, they are consistent with the negative
correlation between linear and quadratic growth. That is, schools
with lower math achievement had steeper math growth at grade 8,
but less acceleration in growth over time, and these schools also
had more school 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 students progress across the
transition from middle to high school. This is consistent with
previous research reporting the severe consequence of lowered
academic performance in schools with high levels of crime
(Roscigno, 2000). However, these results contrast with
Peng’s (1995) findings of no relationship between school
climate variables and measures of achievement. It is important to
note that Peng defined school climate very broadly, including both
contextual and policy variables. In this study, however, we
constructed school climate composites that were comprised of more
homogenous items thereby measuring more well-defined
constructs.
The percentage of single parent households with children
attending the school in the base year was positively related to
acceleration. Although contrary to previous research and as noted
by Pong (1997), it is 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 qualifying 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 less acceleration in math achievement from grades 8 to
12 than schools with families from higher SES strata. This finding
is consistent with prior research 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, inequity gaps
are increased due to the higher acceleration rate for students
from higher SES strata. Therefore, our findings suggest that
policies directed toward closing the mathematics achievement gap
between high and low SES groups would be more effective if
implemented prior to the transition from middle school to high
school.
School policy and practice variables were also related to
acceleration in math achievement, controlling for school context.
Schools with policies emphasizing parental involvement were found
to have greater acceleration in mathematics achievement than
schools without such an emphasis. This finding supports earlier
research documenting the importance of a stable home environment
and parental involvement in their children’s academic
success (Brown, 2000, Ma & Klinger, 2000; Pong, 1997).
Moreover, school policies that emphasize parental involvement
could offset the negative effects of SES on mathematics
achievement as noted by Shaver and Walls (1998). It is critical
that school policy makers, particularly in schools with large
numbers of students from low SES backgrounds, plan courses of
action that draw upon 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.
Moreover, a holistic view of school policy can aid in buffering
the negative influences of poverty that threaten the academic
success of students at risk.
This study also confirmed the importance of academic 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 counselors and students
collaborate on course selection and career planning. This is
consistent with previous work in which school counseling programs
were associated with a better school climate and higher
achievement levels (Bleuer & Walz, 1993; Lapan et al., 1997;
Shoffner & Vacc, 1999). This finding is particularly important
for economically poorer schools where low mathematics test scores
are more common. Schools with policies supporting fully developed
counseling intervention programs showed greater achievement
regardless of socioeconomic level. This suggests that schools that
support academic counseling may be able to offset the negative
effects 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 related to
acceleration in math achievement. This was likely not strictly due
to the effects of disciplinary policies, but rather the school
atmosphere that requires more disciplinary policies. Although
school climate related to attendance 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
attitudes among students that could result in school procedures to
maintain control.
Analysis of growth trajectories in this study indicates 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 produce dramatic effects in math
achievement growth for high achieving students, because these
variables increase the acceleration in academic growth that
occurred during the transition from middle school to high
school.
This study also demonstrates the effectiveness of polynomial
growth models to study variables related to transitional periods
in which growth rate changes. These transitional periods may be
due to developmental 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 occurred as a
result of the school transition. By using multilevel modeling, the
growth trajectories were allowed to vary across schools. The
variance in growth could then be modeled by school-level
variables, a strength of multilevel modeling. By controlling for
contextual effects and investigating the effects of policy and
practice variables through the use of Type B effects (Raudenbush
& Willms, 1995), we determined the effects of school policies
and practices in schools with similar contexts during these
transitional periods. This has particular importance in the study
of growth periods that have significant acceleration, because the
rate of growth is actually increasing. Therefore, any school
policy or practice initiated at this time, which affects
acceleration can have dramatic 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 opportunity to reframe questions about educational success
to study the variables related 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
acceleration across schools. Targeting achievement growth, rather
than average achievement may significantly improve current
understanding of cognitive changes during key transition
periods.
Note
Both authors contributed equally to the research and writing of
this article.
References
Arfaniarromo, A. (2001). Toward a psychosocial
and sociocultural understanding of achievement motivation among
Latino gang members in U.S. schools. Journal of
Instructional Psychology, 28(3), 123-136.
Barton, P., Coley, R., & Wenglinsky, H.
(1998). Order in the classroom: Violence, discipline, and school
achievement. Princeton, NJ: Educational Testing 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 excellence: Counselor strategies for contributing to the
national education goals. (ERIC Document Reproduction 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.
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 learning [and] Equity:
What can we do to enhance school climate? (ERIC Document
Reproduction Service No. ED457315.
Demery, J. (2000). The relationship between
teachers’ perceptions of school climate, racial composition,
socioeconomic status, and student achievement 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). School-family partnerships: Parents, children, and
teachers benefit! Teaching Children Mathematics, 4,
310-312.
Fouad, N. A. (1995). Career linking: An
intervention to promote math and science career awareness.
Journal of Counseling and Development, 73(5), 527-534.
Freiberg, H. J., Connell, M. L., & Lorentz,
J. (2001). 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).
Gender and racial differences in mathematical performance. The
Journal of Social Psychology, 139(6), 677-689.
Hoff, D. J. (2000). Gap widens between black and
white students on NAEP. Education Week, 20(1), 6-7.
Hoffer, T. B. (1997). High school graduation
requirements: Effects on dropping out and student achievement.
Teachers College Record, 98(4), 584-607.
Holloway, J. H. (2001/2002). The dilemma of zero
tolerance. Educational Leadership, 59(4), 84-85.
Jimerson, S., Egeland, B., & Teo, A. (1999).
A longitudinal 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 students: A statewide
evaluation study. Journal of Counseling and Development,
75, 292-302.
Littman, C. B. (2001). The effects of
child-centered and school-centered parent involvement on
children’s achievement: Implications for family interactions
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
“mathematical power for all?” A decade of national
data on instruction and achievement. (ERIC Document Reproduction
Service No. ED463166).
Ma, X., & Klinger, D. A. (2000). Hierarchical
linear 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 performance.
Middle School Journal, 34(2), 56-61.
Muller, C. (1998). Gender differences in parental
involvement and adolescents’ mathematics achievement.
Sociology of Education, 71(4), 336-356.
Muthén, B.O. (1997). Latent variable
modeling of longitudinal and multilevel data. In A. E. Rafferty
(Ed.), Sociological methodology (pp. 453-480). Washington,
DC: Blackwell.
Muthén, B.O., & Curran, P.J. (1997).
General longitudinal modeling of individual differences in
experimental designs: A latent variable framework for analysis and
power estimation. Psychological Methods, 2, 371-402.
Patton, D. K. (2001). Demographic and
education-related factors that influence student behavior.
Dissertation Abstracts International, 61(12-A), 4632.
Peng, S. (1995). Empirical evaluation of
social psychological, and educational 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
context 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 analysis
methods (2nd ed.). Newbury Park, CA: Sage.
Raudenbush, S.W., Bryk, A.S., Cheong, Y.F., &
Congdon, R. (2000). HLM 5. Chicago: Scientific Software
International.
Raudenbush, S. W., & Willms, J. D. (1995).
The estimation of school effects. Journal of Educational and
Behavioral Statistics, 20, 307-335.
Roscigno, V. (2000). Family/school inequality and
African-American/Hispanic Achievement. Social Problems,
47(2), 266-290.
Rugutt, J. K. (2001). A study of student academic
change 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 Title I parent involvement on student reading and mathematics
achievement. Journal of Research and Development in Education,
31(2), 90-97.
Shingles, B., Lopez-Reyna, N. (2002). Cultural
sensitivity in the implementation of discipline policies 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 Document Reproduction Service No.
ED466862).
About the Authors
Janet K. Holtis an Associate Professor in the Department
of Educational Technology, Research and Assessment at Northern
Illinois University. She teaches statistics and research methods
and her research interests include statistical modeling methods
for measuring growth during critical transitions and factors
related to success in math and science. Email: jholt@niu.edu
Cynthia Campbell is an Assistant Professor in the
Department of Educational Technology, Research and Assessment at
Northern Illinois University. Her research interests include
assessment in educational and counseling settings and standardized
testing. Email: ccampbell@niu.edu
|
