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Predicting Students’ Mathematics Achievement Through Elementary and Middle School: The Contribution of State-Funded Prekindergarten Program Participation


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Background Prekindergarten programs are instrumental for smooth transition to the primary grades. Although the prevalence of these programs has expanded, limited studies document the long-term outcomes associated with children’s engagement in such programs and for specific content areas such as mathematics. Objective This study predicted the longitudinal mathematics achievement of 458 students as they progressed through elementary and middle school, accounting for their participation in Georgia’s prekindergarten (Pre-K) program at age 4. Method Archived academic achievement data in mathematics were extracted from one school district in the southeastern United States. A multilevel approach was employed to account for the nesting of students within schools. Liner and logistic regression analyses were used to examine the long-term relationship between prekindergarten participation and mathematics achievement. Results After controlling for the effects of race, sex, and poverty, results indicated that participation in Georgia’s Pre-K program positively predicted mathematics achievement through seventh grade. For fourth through seventh grades, the odds of a Georgia Pre-K participant meeting the state’s academic standards on the statewide standardized test were 1.67–2.10 times greater than the odds for a nonparticipant. Conclusion Although the reported effect sizes were small, children’s participation in the Georgia Pre-K program had a long-term influence on their mathematics achievement through elementary and middle school, providing evidence of sustained benefits of a state-funded prekindergarten program. Quality learning experiences during the early years might provide skills and knowledge that serve as building blocks for later mathematics achievement.
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Predicting Students’ Mathematics Achievement Through
Elementary andMiddle School: The Contribution
ofState‑Funded Prekindergarten Program Participation
JisuHan1 · StaceyNeuharth‑Pritchett2
Accepted: 5 December 2020
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021
Background Prekindergarten programs are instrumental for smooth transition to the pri-
mary grades. Although the prevalence of these programs has expanded, limited studies
document the long-term outcomes associated with children’s engagement in such programs
and for specific content areas such as mathematics.
Objective This study predicted the longitudinal mathematics achievement of 458 students
as they progressed through elementary and middle school, accounting for their participa-
tion in Georgia’s prekindergarten (Pre-K) program at age 4.
Method Archived academic achievement data in mathematics were extracted from one
school district in the southeastern United States. A multilevel approach was employed to
account for the nesting of students within schools. Liner and logistic regression analyses
were used to examine the long-term relationship between prekindergarten participation and
mathematics achievement.
Results After controlling for the effects of race, sex, and poverty, results indicated that
participation in Georgia’s Pre-K program positively predicted mathematics achievement
through seventh grade. For fourth through seventh grades, the odds of a Georgia Pre-K
participant meeting the state’s academic standards on the statewide standardized test were
1.67–2.10 times greater than the odds for a nonparticipant.
Conclusion Although the reported effect sizes were small, children’s participation in the
Georgia Pre-K program had a long-term influence on their mathematics achievement
through elementary and middle school, providing evidence of sustained benefits of a state-
funded prekindergarten program. Quality learning experiences during the early years
might provide skills and knowledge that serve as building blocks for later mathematics
* Jisu Han
Stacey Neuharth-Pritchett
1 Graduate School ofEducation, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu,
Yongin-si, Gyeonggi-do17104, SouthKorea
2 Department ofEducational Psychology, The University ofGeorgia, G4G Aderhold Hall, 110
Carlton Street, Athens, GA30602, USA
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Keywords Opportunity gap· Early childhood· Mathematics education
With growing evidence that early childhood programs promote positive outcomes for chil-
dren and that such experiences yield benefits for their participants and the greater soci-
ety (Bassok etal. 2018; Calman and Tarr-Whelan 2005; Heckman etal. 2010; Watts etal.
2018), it is important to examine the impact of state-sponsored prekindergarten (Pre-K)
programs on specific academic outcomes. Although there is robust literature on the out-
comes of smaller-scale model demonstration projects (Campbell et al. 2012; Reynolds
etal. 2018; Schweinhart 2014), far less is known about the longer-term contributions of
large-scale state-sponsored programs for 4-year-olds (Barnett and Frede 2017; Dodge etal.
2019). Examining the role of a large-scale program for young children such as the Georgia
Pre-Kindergarten Program could contribute to understanding state-sponsored intervention,
which differs from tightly controlled demonstration projects (Reynolds etal. 2018; Sch-
weinhart 2014) in program intensity, length of day for services, and sample characteristics.
Given that previous work examining the impact of a large-scale Pre-K program has
often focused on links to children’s school readiness or academic skills in early elementary
school (Barnett etal. 2013; Early etal. 2019; Hill et al. 2015; Lipsey etal. 2018), more
evidence is needed to know whether Pre-K benefits persist through later school years. Also,
as a growing body of research demonstrates that early mathematics learning is predictive
of later achievement in mathematics and other content areas (Bodovski and Farkas 2007;
Duncan etal. 2007; Watts etal. 2017), it is of particular importance to focus on students’
mathematics achievement in relation to their participation in state-funded Pre-K programs.
By comparing academic outcomes of two naturally occurring groups, this study evaluated
the long-term contribution of Georgia’s Pre-K program on students’ mathematics achieve-
ment in elementary and middle school years. This study also analyzed students’ perfor-
mance levels on a statewide test to determine whether program participation affected the
likelihood that a student meets the state’s academic standards in mathematics.
State Pre‑K Initiatives
Pre-K serves as a natural transition from at-home care or formal child care settings to
elementary school (McCabe and Sipple 2011; Phillips etal. 2017). Policymakers promote
early childhood education as a mechanism by which to prepare children for successful tran-
sition to elementary school (Brown and Gasko 2012; Gormley etal. 2017; Phillips et al.
2016). With more states considering expansion of Pre-K, the number of 4-year-old children
enrolled in state-sponsored Pre-K programs has increased significantly over the past two
decades. According to the 2018 state of preschool yearbook (Friedman-Krauss etal. 2019),
44 states and the District of Columbia provided Pre-K programs in the 2017–2018 school
year, serving nearly 1.3 million 4-year-olds. State-funded Pre-K, along with Head Start, is
a major provider of early education services for 4-year-olds.
Although variations exist among state Pre-K initiatives, most state-funded programs
provide 4-year-old children with group learning experiences to prepare them for and
smooth the transition to formal schooling. These programs are funded and directed by state
governments and are often located in public elementary schools; also, community-based
organizations such as Head Start and private child care centers may house Pre-K. The 2018
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preschool yearbook (Friedman-Krauss etal. 2019) reported that state funding for Pre-K
surpassed $8.15 billion nationally, with modest increases in enrollment since 2016–2017,
with only three states meeting policy standards related to quality on 10 markers. Despite
increases in enrollment, access to high-quality preschool programs remains unequal across
the nation.
Georgia’s Pre-K programs. Georgia’s Pre-K program is a lottery-funded preschool
program available to all 4-year-olds, regardless of family income (Moore 2009); thus,
the population that the program serves differs from that of other state-funded programs
focused on targeting low-income families. With the goal of promoting young children’s
school readiness, the program offers full-day services. Children receive 6.5h of instruction,
5days a week, for 180days during the academic year. The program provides a variety of
educational services across all areas of child development, including health, approaches to
learning, socioemotional competence, cognition, and language and literacy (Moore 2009).
Instruction in the classrooms in the current study was guided by the Georgia Pre-K Content
Standards (since revised to the Georgia Early Learning & Development Standards) and
state-approved curricula, including High/Scope. In the area of mathematics development,
the Georgia’s Pre-K Program Content Standards in place at the time of the Pre-K experi-
ence included developing an understanding of numbers, creating and duplicating simple
patterns, sorting and classifying objects, developing a sense of space and an understanding
of basic geometric shapes, and learning how to use a variety of nonstandard and stand-
ard means of measurement (Georgia Department of Early Care & Learning 2012–2013).
The minimum educational requirement for a lead teacher was a bachelor’s degree in early
childhood education or related field. The 282 Pre-K children in this study came from 27
classrooms housed in public schools during the 1999–2000 school year where more than
50% of the teachers held master’s or specialist degrees. As measured by the 5-point scale
of the High/Scope Program Quality Assessment (PQA), the overall observed quality of
these Pre-K classrooms was very high (M = 4.52, SD = 0.66). All schools in this study used
the same curriculum in their preschool classrooms and, except for self-contained preschool
special education, there were no other preschool experiences in the schools competing with
the Pre-K program. Although the sample from one school district may not be representa-
tive of all children attending Georgia’s Pre-K, it provides important data on a high-needs
school district with significant numbers of children living in poverty in the state.
Young Children’s Mathematics Development
Mathematics achievement is one of the strongest predictors of future academic success
(Duncan etal. 2007; National Mathematics Advisory Panel 2008). Duncan etal. (2007)
analyzed six longitudinal data sets to examine the relationship between academic skills
at school entry and academic performance in later grades. One of the noteworthy find-
ings was that early mathematics skills had the greatest predictive power of later learning
of all school entry skills. Mathematics competencies might form a cognitive foundation
for thinking and learning across subjects such as vocabulary, complex utterances, and
inferential reasoning (Clements and Sarama 2011; Sarama etal. 2012; Siegler and Lortie-
Forgues 2014; Welsh etal. 2010). There has been a shift in thought in the past century as
researchers and policymakers have recognized the importance of young children’s math-
ematics knowledge development. While young children have traditionally been viewed
as incapable of engaging in mathematical thinking, a substantial body of the literature in
developmental psychology highlights that the development of mathematical knowledge
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and thinking begins well before formal schooling (Hachey 2013). Ginsberg (2009) cited a
change in educators’ perceptions from a notion that the teaching of mathematics to young
children was developmentally inappropriate to considering the practice to be developmen-
tally appropriate.
In fact, researchers have noted that mathematics knowledge develops rapidly during
preschool years (National Research Council 2005, 2009; Zur and Gelman 2004). Children
with better mathematics performance upon entering kindergarten had greater gains dur-
ing the elementary school years (Bodovski and Farkas 2007). Mathematics learning during
Pre-K that takes place in a developmentally appropriate way might solidify fundamental
skills and knowledge that serve as building blocks for mathematics learning in kindergar-
ten and beyond (Ramani and Siegler 2008; Weiland etal. 2012). Pre-K might also serve
as an exceptionally important opportunity for mathematics development, given that some
preschool children have limited opportunities to learn mathematics at home (Clements and
Sarama 2011; del Rio etal. 2017; Tudge and Doucet 2004) and that opportunities for chil-
dren from low-income homes often differ from those for their middle-class peers (Casey
etal. 2018; Rittle-Johnson etal. 2017; Wang 2010).
Although specific mathematical concepts and knowledge (e.g., counting, basic opera-
tions, shapes and patterns, measurement, geometry) learned through classroom activities
are important (Choi and Dobbs-Oates 2014; Jordan etal. 2009), a growing body of research
suggests that other cognitive and motor skills might contribute to young children’s math-
ematics development, as well (Becker etal. 2014; Kim etal. 2018; Verdine etal. 2014). A
study by Verdine etal. (2014) demonstrated that, in a sample of preschoolers, executive
function and spatial skills predicted 70% of the variance in their mathematics performance.
In a study investigating interrelations among motor and cognitive processes and mathemat-
ics skills (Kim etal. 2018), researchers found that visuomotor integration and mathematics
skills had reciprocal relationships and that fine motor coordination was indirectly related
to mathematics skills in kindergarten and first grade. Attention was a significant predic-
tor of mathematics skills, even after controlling for visuomotor integration and fine motor
coordination. Becker etal. (2014) reported similar findings that both behavioral self-regu-
lation and visuomotor skills were significantly related to early mathematics achievement.
Given that Pre-K programs place an emphasis on a holistic and comprehensive approach
to understanding child development (Friedman-Krauss etal. 2019), these findings suggest
that there might be multiple pathways that link children’s Pre-K experience to mathematics
Early Childhood Education Studies andMathematics Achievement
Researchers have examined the influence of Pre-K intervention on children’s mathematics
achievement. Some studies have suggested that mere participation in Pre-K has positive
impacts on children’s mathematics knowledge at kindergarten or school entry. Skibbe etal.
(2013), employing a hierarchical linear modeling and propensity score matching approach,
found that children who attended Pre-K had higher scores on mathematics skills in kin-
dergarten than those who did not attend Pre-K, as measured by the Woodcock-Johnson.
Similarly, Weiland and Yoshikawa (2013) found that participation in Boston’s universal
Pre-K produced effect sizes of 0.58 for early numeracy (as measured by the Woodcock-
Johnson Applied Problems subscale) and 0.49 for numeracy and geometry (as measured
by the shortened Research-Based Elementary Mathematics Assessment) at the point of
school entry. In New Mexico, participation in Pre-K during the 2007–2008 school year
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was associated with gains in early mathematics skills at kindergarten entry (Hustedt etal.
However, there are mixed findings regarding whether early gains in Pre-K are sustained
in later grades. Hill etal. (2015) investigated longer-term effects of Oklahoma’s universal
Pre-K program and found that Pre-K gains persisted through third grade in mathematics
but not in reading. Effects were found for one cohort of children where Pre-K participation
produced Oklahoma Performance Index Scores 18 points higher than those who did not
attend Pre-K, with an effect size of 0.18. Using data on a sample of children from Georgia
on National Assessment of Education Progress scores, Fitzpatrick (2008) found that, for
children from economically challenged households in small towns and rural areas, univer-
sal Pre-K availability in Georgia increased mathematics test scores at fourth grade, as well
as the probability of students being on-grade for their age. Most recently, Early etal. (2019)
reported a similar finding that enrollment in Georgia’s universal Pre-K was associated with
higher third-grade test scores compared to those of non-Pre-K students. A fourth- and fifth-
grade follow-up study by Barnett etal. (2013) also found that children who attended New
Jersey’s universal Pre-K program in 2004–2005 demonstrated higher achievement scores
in mathematics and lower grade retention rates than those who did not attend the program.
Magnuson etal. (2007), using data from the Early Childhood Longitudinal Survey-Kin-
dergarten Class of 1998–1999, investigated longitudinal outcomes in reading and math-
ematics skills. In mathematics in the areas of numbers, geometry, and spatial relations,
children who participated in Pre-K scored higher at kindergarten entry (p < 0.01) than
those who did not attend Pre-K, corresponding to an effect size of 0.09. However, these
mathematics score differences were no longer significant by first grade. Similarly, a recent
study from Tennessee’s voluntary Pre-K program indicated that mathematics results by the
end of kindergarten faded out and treatment and control children were indistinguishable by
that time point (Lipsey etal. 2018).
According to a meta-analysis of impact evaluations of 13 state-funded Pre-K programs
from 1977 to 1998 (Gilliam and Zigler 2001), significant impacts of Pre-K programs were
mostly limited to kindergarten and first grade and were not sustained beyond early grades.
Two exceptions were found in Maryland and New York, where Pre-K produced effects in
mathematics development that were sustained well into the middle school or high school
years. When Glass’s delta was computed as a measure of effect size, the program in Mar-
yland reflected significant impacts in fifth (effect size = 0.46), eighth (effect size = 0.49),
ninth (effect size = 0.29), and tenth grades (effect size = 0.30). Statistically significant
impacts were found in New York for sixth grade (effect size = 0.12). Phillips etal. (2016)
also noted significant positive effects for mathematics achievement into middle school,
along with lower grade retention and lower absenteeism rates.
Although researchers have paid increasing attention to long-term gains of universal or
statewide Pre-K programs, existing findings are not univocal (Barnett 2011; Dodge etal.
2017), and the strongest evidence is largely based on findings from small-scale demon-
stration programs (Andrews etal. 2012; Yoshikawa etal. 2013). More work is needed to
understand the longer-term impacts of large-scale Pre-K programs beyond kindergarten
and the early elementary grades (Yoshikawa etal. 2013). In particular, limited research
has associated participation in a state-funded Pre-K program with middle school outcomes.
Few evaluation studies have examined the role of Pre-K experience in predicting stu-
dents’ likelihood of meeting standards on statewide tests. Although test scores and perfor-
mance levels on statewide tests provide similar information in nature, knowing whether
students reached a minimum proficiency level as determined by the state has practical
implications because this criterion influences various decisions made in classrooms and
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school systems. As a way of examining school achievement for children who attend Pre-
K, Early etal. (2019) recently considered whether students reach the proficiency level and
examined test scores. They found that participation in Georgia’s Pre-K was associated with
an 11–17% increase in the odds of being proficient on third-grade tests in English language
arts, mathematics, science, and social studies. Peisner-Feinberg and Schaaf (2010), in their
evaluation of the North Carolina More at Four Pre-K program, also examined students
achievement levels as measured by state standards. However, the four achievement levels
were not considered as groups but were treated as a four-level continuous variable, which
limited the ability to estimate predicted probabilities of belonging to each performance
group. The current study adds to the literature by focusing on students’ likelihood of meet-
ing state standards in relation to Pre-K participation.
Research suggests that higher-quality preschool programs are tied to better learning out-
comes during preschool and are more likely to produce persistent gains (Yoshikawa etal.
2013). Burchinal etal. (2010) found that the quality of instruction in publicly funded Pre-K
programs was more strongly related to children’s language, reading, and mathematics skills
in higher-quality classrooms characterized by deliberate engaging instructions (for mathe-
matics, effect size = 0.34) than in lower-quality classrooms (effect size = 0.02). Researchers
have also examined mathematics achievement at kindergarten entry in relation to preschool
center quality, finding small but significant outcomes in mathematics where a 1 standard
deviation increase in quality produced a 0.03 standard deviation increase in mathematics
scores (Keys etal. 2013). Ensuring that preschool children experience at least the mini-
mum level of quality child care and education may be necessary to improve school readi-
ness outcomes (Burchinal etal. 2010).
The Present Study
The purpose of this study was to predict mathematics achievement by 458 students on
statewide tests as they progressed through elementary and middle school, accounting for
their participation in Georgia’s Pre-K program at age 4. Both students’ achievement scores
and performance levels (i.e., 1 = Does Not Meet the Standard, 2 = Meets the Standard) were
examined as outcome variables. Individual student enrollment in Georgia’s Pre-K program
at age 4 was considered as the major variable that would predict their mathematics achieve-
ment in the elementary and middle school years. Race, sex, and family socioeconomic sta-
tus (SES), as indicated by the enrollment in free or reduced-price meals during their pre-
school year, were used as covariates in predicting students’ achievement. Observed quality
for the Pre-K classrooms was considered in the preliminary analysis phase to examine
whether variations in classroom quality would affect child outcomes in later years.
Based on the review of the literature, robust evidence for the immediate benefits of
Pre-K education have been documented, but inconsistent findings have been reported
regarding its longer-term effects on achievement outcomes in subsequent grades. Thus, we
hypothesized that participating in Georgia’s Pre-K would contribute to higher mathematics
achievement scores in later grades and sought to determine until when these benefits would
persist. The research questions and hypotheses were as follows:
Research question 1. What is the relationship between children’s participation in Geor-
gia’s Pre-K program at age 4 and their mathematics achievement
scores in first grade and third through seventh grades?
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Research hypothesis 1. Children who attended Georgia’s Pre-K program at age 4 will
perform better on mathematics achievement tests in later grades.
Research question 2. For third through seventh grades, what is the relationship
between children’s participation in Georgia’s Pre-K program at
age 4 and their likelihood of meeting the state standards in the
area of mathematics?
Research hypothesis 2. Children who attended Georgia’s Pre-K program at age 4 will be
more likely to meet the state standards in the area of mathematics.
Examining these research questions will provide unique incremental contributions to the
literature about evaluations of Pre-K programs in several important ways. First, although
an increasing number of studies have documented the long-term relationship between pre-
school education and children’s academic achievement in later grades, much of the evi-
dence comes from experimental evaluations of smaller-scale programs (Andrews et al.
2012), and findings are inconsistent across studies. This study compared two naturally
occurring groups in a local school district, children who enrolled in Pre-K and children
who did not have formal preschool experiences prior to kindergarten entry, which may
not fully represent all children attending Georgia’s Pre-K but reflects real-world data on a
large-scale Pre-K program existing in many communities across the state. Second, fewer
studies have examined middle-school outcomes for Pre-K attendees (Virginia University
Research Consortium on Early Childhood 2015), and less is known about specific con-
tent areas such as mathematics. Using standardized assessment data in mathematics, this
study increases knowledge about whether children’s engagement in a large-scale univer-
sal Pre-K program is associated with long-term achievement outcomes and whether the
benefit persists into middle school. Third, the present study adds knowledge to the field
by examining whether Pre-K participation predicts the likelihood of meeting academic
standards on statewide tests. Considering that important educational decisions are often
made based on students’ levels of performance on statewide assessments, educators might
be interested in predicting the likelihood that students will meet state-mandated academic
standards (Klingbeil etal. 2018). This ability might be of interest to educators and policy-
makers because information on student proficiency could be used to identify students in
need of additional support, which is tied to the allocation of funds and resources (Klingbeil
etal. 2018).
Research Design
This study used the natural groups design in which differences between two or more
naturally occurring groups are examined with regard to variables of interest. Instead of
using experimental manipulation, this study analyzed data extracted from archived school
records from one school district. All students who stayed in the district at the time of base-
line data collection and for whom there were data across time were included in the original
sample. For those students included in the study, the mathematics achievement outcomes
through elementary and middle school were compared between Pre-K attendees and non-
Pre-K attendees.
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All children who are 4years old and residents in Georgia are eligible to apply for Geor-
gia’s Pre-K program; program participants are chosen through a lottery system. At the time
of the study, not all schools in Georgia had the Pre-K program, but most children who
wanted access to Pre-K were able to be included in the program as the community had
other preschool options in Head Start, private child care centers, and university centers.
Although there were no direct measures of family-based experiences for children who did
not attend Pre-K, the children in the comparison group were coded in school records as
not having had any formal preschool experience. This control group was not a pure control
group, as placement in the group was based on the family’s voluntary lack of engagement
in enrolling the child in the Pre-K program; thus, there could be some potential selection
bias introduced by family engagement in seeking services. In addition, the families in the
control group could have provided enriching experiences at home. Unfortunately, school
records indicated only lack of a formal preschool experience and did not provide infor-
mation on parental behaviors in fostering readiness prior to school entry. It is also worth
noting the lack of access to detailed information regarding each student’s school history
through elementary and middle school years. Across the study years, 0.6–4.0% of the total
sample were missing, and these missing values for each grade level reflect students who
dropped out or changed schools or those who did not have assessment data for that particu-
lar grade level.
Data for this study were extracted from archived data from one school district in Georgia.
Researchers were provided with a de-identified dataset for the participating children in this
study by the partnering school district. This study was considered exempt by the Institu-
tional Review Board of a southeastern university. The original sample consisted of 467
students who had attended any of 13 public elementary schools in a local school district
in Georgia that housed Pre-K classrooms. Nine students were excluded to address analytic
issues arising from the problem of empty cells, resulting in a final sample of 458 students.
The final sample included 68% African American, 16% White, 13% Hispanic, and 3% mul-
tiracial students, with more females (53.1%) than males (46.9%).
Baseline variables of interest in this study were collected during the 1999–2000 and
2000–2001 school years, when the participants were 4 and 5years old. Of the total sample,
282 children (62%) had voluntarily attended Georgia’s Pre-K program at age 4, while 176
children (38%) had not. The 282 Pre-K attendees came from 27 classrooms. Data were also
collected on each child’s enrollment in the free or reduced-price lunch program. Because
family income is used to determine eligibility for free or reduced-price lunches, this infor-
mation is widely used as a proxy for poverty status (Bowen etal. 2000). Of the total sam-
ple, 385 children (84%) qualified for free or reduced-price meals, reflecting the fact that the
school district that provided the data was a high-needs district. Table1 provides descriptive
information for the overall sample and separately for the Pre-K children and non-Pre-K
children. The differences in race, sex, and poverty status between the Pre-K and non-Pre-K
groups were examined as part of exploratory data analyses.
The children’s mathematics achievement outcomes in the elementary and middle school
years were obtained from school records. SAT-9 data were used for first grade and the
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Criterion-Referenced Competency Tests (CRCT) scores and performance levels were
examined for third through seventh grades. Data were not available for second grade
because of a statewide data concern about the Stanford Achievement Test-Ninth Edition
(SAT-9) across Georgia from that academic year. About 30% of the students in the sample
had been retained at least once from kindergarten through ninth grade. When a student was
held back, that student’s test score from the year in which the student was successful in that
grade was used.
The mathematics achievement data examined in this study included students’ performance
on the SAT-9 (Harcourt Educational Measurement 2001) for first grade and their perfor-
mance on Georgia’s CRCT (Georgia Department of Education 2012) for third through sev-
enth grades.
SAT-9. The SAT-9 is a norm-referenced test designed to assess student achievement at
K-12 grade levels (Harcourt Educational Measurement 2001). The SAT-9 provides math-
ematics scores in the areas of Problem Solving, Procedures, and Total Math. The current
study examined first graders’ SAT-9 Total Math scores. The Kuder-Richardson Formula 20
(KR20) scores for the SAT-9 range from the mid-1980s to 1990s, and the test covers grade-
appropriate content aligned to national and state standards (Impara and Plake 1998).
Georgia’s CRCT. The total math score on the CRCT was used in the study as a major
student outcome measure. The CRCT is a state-mandated test designed to assess how well
students accomplish the learning goals outlined in the state-mandated curriculum. The test
was administered at the end of the school year in the content areas of reading, English lan-
guage arts, and mathematics in Grades 1 through 8. According to the Georgia Department
of Education (2012), the CRCT is a valid and reliable measure that satisfies professional
and technical standards for large-scale assessments. Studies comparing the constructs of
the CRCT with those of other commonly used instruments, such as the Iowa Test of Basic
Skills, provide evidence of external validity (Georgia Department of Education 2008).
Internal consistency reliability coefficients for the CRCT range from 0.87 to 0.93.
Table 1 Description of the
sample (N = 458) Total group
(N = 458)
Pre-K group
(N = 282)
(N = 176)
Characteristic n%n%n%
Male 215 46.9 122 43.3 93 52.8
Female 243 53.1 160 56.7 83 47.2
African American 312 68.1 224 79.4 88 50.0
Hispanic 60 13.1 27 9.6 33 18.8
Multiracial 14 3.1 7 2.5 7 4.0
White 72 15.7 24 8.5 48 27.3
Enrolled in free or
reduced-price Meals
385 84.1 251 89.0 134 76.1
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Two types of CRCT scores in the area of mathematics were examined in this study:
scale scores and performance levels (i.e., 1 = Does Not Meet the Standard, 2 = Meets the
Standard). The mathematics test, in particular, assesses knowledge and skills in domains
such as number and operations, measurement, geometry, algebra, and data analysis and
probability (Georgia Department of Education 2013). As the Georgia Department of Edu-
cation had adopted the Georgia Performance Standards (GPS) curriculum beginning in
2006, CRCT mathematics scores were rescaled (Georgia Department of Education 2012).
As this study analyzed longitudinal data, test scores on both scales were examined.
PQA. A credentialed High/Scope trainer used the High/Scope PQA to assess the qual-
ity of the Pre-K classrooms in this study. This tool measures program quality in the areas
of learning environment, daily routine, adult–child interaction, curriculum planning and
assessment, parent involvement and family services, staff qualifications and staff develop-
ment, and program management (High/Scope Educational Research Foundation 1998).
Evidence supports that the PQA is a reliable and valid tool to measure program quality. For
the previous edition of the PQA used at the time of the baseline study, the average percent-
ages of close to exact agreement among trained observers ranged from 79.4 to 96.7%, and
Cronbach’s alpha coefficient was 0.95. Previous studies reported that the PQA was sig-
nificantly correlated with other measures of program quality, with correlations ranged from
0.48 to 0.86 (High/Scope Educational Research Foundation 1998).
Analysis Strategies
Using the SPSS and R software packages, we conducted exploratory data analyses, mul-
tilevel regression analyses, and multilevel logistic regression analyses. Exploratory data
analyses involved obtaining descriptive statistics for the overall sample, the Pre-K chil-
dren, and the non-Pre-K children. Chi-square tests were performed to examine the differ-
ence between the two groups of children in terms of race, sex, and poverty status. In this
preliminary step, we explored the Pre-K classroom quality data, as well in relation to the
students’ mathematics achievement scores.
We employed a multilevel approach to consider the hierarchical structure of the data in
which students were nested in 13 elementary schools. Although whether the students had
attended Pre-K was not significantly related to the school that the students attended (
(12) = 6.81, p > 0.05), it is important to consider the fact that students in the same school
are more likely to function in the same way than students in different schools. The mul-
tilevel models consider the dependency in students’ test scores nested within the same
school. The nesting of the schools in this study was based on their elementary school
assignment. Using the BOBYQA algorithm implemented in R, a multilevel regression
analysis was conducted to examine the long-term relationship between children’s participa-
tion in Georgia’s Pre-K program during the early years of their lives and their mathematics
achievement scores in later grades (i.e., Research Hypothesis 1). The BOBYQA option was
chosen because it provides a reasonable balance between speed of convergence and stabil-
ity (Powell 2009). The multilevel logistic regression model was fitted to the data using
the Laplace approximation to examine whether Pre-K participation would significantly pre-
dict a student’s level of mathematics performance in relation to the state standards (i.e.,
Research Hypothesis 2). For both analyses, covariates of race, sex, and family SES status
were entered into the models. Based on the research literature suggesting that Pre-K might
have differential effects on students of varying SES (Fitzpatrick 2008; Peisner-Feinberg and
Schaaf 2010), we checked for the presence of an interaction between Pre-K participation
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and poverty. As the interaction was not statistically significant for all grade levels (p values
ranging from 0.37 to 0.88), the interaction term was dropped from the model.
It is worth mentioning why we did not analyze the data in terms of student growth over
time. Although a longitudinal analysis strategy might yield meaningful findings regard-
ing student growth trajectories, CRCT scores were comparable only within each grade and
content area and were not vertically aligned (Georgia Department of Education 2012). Fur-
ther, as the state’s curriculum had changed from the Quality Core Curriculum (QCC) to
the GPS in 2006, the students’ test scores examined in this study included two distinct
types of scale scores based on different curricula and content standards. For these reasons,
we chose to run a separate regression analysis for each grade level. Listwise deletion was
used for each analysis; of the total sample of 458 students, 0.6–4.0% were missing across
the elementary and middle school years. These missing values reflected students who did
not have assessment data for a particular year, as well as those who had dropped out or
changed schools. The sample size at each grade level is shown in Table2.
Exploratory Analysis Results
Tables 2 and 3 summarize descriptive statistics of the students’ scale scores and perfor-
mance levels on the CRCT in mathematics. Information is presented for the total sample,
the Pre-K group, and the non-Pre-K group. Table 2 reports the average scale scores of
students in the state of Georgia, as well. Although the mean mathematics scores of Pre-K
attendees and those of non-Pre-K students were not significantly different (p > 0.05), the
overall performance of the students in the study sample tended to be lower than the aver-
age performance of students in Georgia. This difference might be related to the fact that,
in 1999, 13% of Georgians lived below the poverty level (Bishaw and Iceland 2002) and
enrollment in free or reduced-price lunch programs was 84.1% in the study sample. The
sample in the current study was comprised of a higher proportion of children from under-
represented groups than the general population in Georgia in 1999. In all grade levels, a
Table 2 Descriptive statistics of the Students’ mathematics test scores (N = 458)
a SAT 9 = Stanford achievement test-ninth edition
b CRCT = Georgia’s criterion-referenced competency test
Grades NTotal group Pre-K group Non-Pre-K group State of Georgia
M (SD) M (SD) M (SD) M (SD)
SAT 9 a
Grade 1 446 35.20 (29.55) 35.62 (29.64) 34.51 (29.49) N/A
Grade 3 454 323.09 (26.85) 322.32 (25.97) 324.30 (28.21) 333 (27)
Grade 4 455 305.67 (29.49) 306.07 (29.18) 305.02 (30.05) 320 (31)
Grade 5 445 322.22 (30.13) 322.68 (28.91) 321.45 (32.11) 335 (30)
Grade 6 438 801.23 (31.13) 800.88 (31.12) 801.81 (31.23) 815 (32)
Grade 7 438 813.02 (32.67) 812.90 (32.69) 813.23 (32.72) 828 (33)
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1 3
significant portion of the students in the sample, ranging from 20 to 58%, did not meet
the mathematics academic standards determined by the state. Bivariate correlations were
analyzed among the students’ test scores across grade levels and are shown in Table4. The
correlations ranged from 0.71 to 0.86 (p < 0.01), showing substantial consistency of math-
ematics scores across the school years.
Further examining the demographic information presented in Table1, chi-square tests
were performed to determine whether there was a significant difference between the Pre-K
Table 3 Students’ performance
levels on the CRCT-mathematics:
proportion of students who meet
or did not meet state academic
Grades Level 1:
% Did not meet
Level 2:
% Met standards
Grade 3
Total group 19.8 80.2
Pre-K group 20.5 79.5
Non-Pre-K group 18.8 81.3
Grade 4
Total group 45.7 54.3
Pre-K group 44.5 55.6
Non-Pre-K group 47.7 52.3
Grade 5
Total group 23.1 76.9
Pre-K group 21.3 78.7
Non-Pre-K group 26.2 73.9
Grade 6
Total group 58.4 41.6
Pre-K group 59.1 40.9
Non-Pre-K group 57.3 42.7
Grade 7
Total group 38.4 61.7
Pre-K group 38.5 61.5
Non-Pre-K group 38.0 62.0
Table 4 Bivariate correlations among Students’ test scores across grade levels
a SAT 9 = Stanford achievement test-ninth edition
b CRCT = Georgia’s criterion-referenced competency test
1. SAT-9a Grade 1
b Grade 3 0.750***
3. CRCT Grade 4 0.738*** 0.844***
4. CRCT Grade 5 0.721*** 0.799*** 0.816***
5. CRCT Grade 6 0.711*** 0.780*** 0.823*** 0.803***
6. CRCT Grade 7 0.726*** 0.800*** 0.839*** 0.804*** 0.860***
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group and the non-Pre-K group in terms of race, sex, and poverty status. The difference in
the proportion of boys and girls between the two groups was only marginally significant
(1) = 3.99, p = 0.054). A significant difference between the Pre-K group and the non-
Pre-K group was found with regard to race
(3) = 45.80, p < 0.001) and poverty status
(1) = 13.40, p < 0.001). The Pre-K group consisted of 79.4% African American, 9.6%
Hispanic, 8.5% White, and 2.5% multiracial children, whereas the non-Pre-K group con-
sisted of 50% African American, 27.3% White, 18.8% Hispanic, and 4% multiracial chil-
dren. Eighty-nine percent of the Pre-K attendees qualified for free or reduced-price lunch,
whereas 76.1% of the non-Pre-K children were eligible for the lunch program. These group
differences suggest a potential for selection bias, which should be considered when inter-
preting the findings of this study. The demographic variables of race, sex, and poverty sta-
tus were included as covariates in the analyses to determine the unique contribution of
Pre-K participation to children’s academic achievement.
Approximately 30% of the students in the sample had been held back at least once from
kindergarten through ninth grade. Ninety-seven percent of the students who had been
retained had a low-income family background, suggesting a strong association between
poverty and retention (
(1) = 25.41, p < 0.001). However, the relationship between reten-
tion and Pre-K participation was not statistically significant (
(1) = 1.36, p = 0.25).
We explored the classroom quality data as part of the exploratory analyses. On the
5-point scale of the High/Scope PQA, the overall quality of the Pre-K classrooms ranged
from 3 to 5, with an average score of 4.52 (SD = 0.66). More than 63% of the Pre-K chil-
dren attended classrooms of excellent quality, followed by 27.4% in classrooms of good
quality and 9.3% in classrooms of moderate quality. No classrooms in this study were rated
as 1 or 2 on the 5-point scale.
Descriptive findings revealed no systematic pattern between classroom quality ratings
and students’ test scores. To further examine whether classroom quality is a factor that
significantly affects students’ mathematics achievement, we compared two linear regres-
sion models in the preliminary analysis phase. The full model included classroom quality,
in addition to race, sex, poverty status, and Pre-K participation, while the reduced model
excluded the classroom quality variable. For all grade levels, the results of the F-tests com-
paring the two models were not statistically significant at the alpha level of 0.05 (p-values
ranging from 0.08 to 0.65). The Scheffé multiple comparison procedure was performed,
but we found no significant difference in mathematics test scores across levels of class-
room quality. These results suggest that, in this study, classroom quality variations in Pre-K
programs did not significantly affect students’ mathematics achievement in later grades;
therefore, classroom quality was not included as a predictor in the regression models. One
important explanation for this null finding might be related to the fact that most of the
Pre-K classrooms in this study were of very high quality, with little variation (M = 4.52,
SD = 0.66) on the 5-point scale), and were staffed primarily with teachers with advanced
education degrees (e.g., master’s or specialist degrees).
Multilevel Regression Analyses: Predicting Students’ Mathematics Test Scores
The multilevel regression analyses were performed to test the first hypothesis, about the rela-
tionship between participation in Georgia’s Pre-K and mathematics tests scores in later grades.
Pre-K participation, as well as sociodemographic variables of race, sex, and poverty status,
were included in the model. Table5 presents unstandardized beta coefficients obtained from
the regression analyses, along with the main model equation. Across all grade levels, the final
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multilevel model accounted for 23.2–30.3% of the total variance in students’ mathematics test
scores. The method for calculating R2GLMM for mixed-effects models was used, and both mar-
ginal R2(variance explained by fixed factors) and conditional R2 (variance explained by the
entire model) values are shown in the table (Nakagawa etal. 2017; Nakagawa and Schielzeth
2013). Participating in the Georgia Pre-K program during the preschool year contributed posi-
tively to mathematics outcomes for all grades (p < 0.001 for fourth grade, p < 0.01 for first,
third, fifth, sixth, and seventh grades). We used effect size estimation procedures that can be
applied to mixed-effects models (Westfall etal. 2014). Effect sizes (measured as d) attribut-
able to the addition of the Pre-K variable ranged from 0.27 to 0.37, which indicated small
effects (Cohen 1988).
In terms of the effects of covariates, a similar pattern was found across all grade levels.
After controlling for all other variables in the model, the child’s sex was not a significant pre-
dictor of mathematics test scores; however, a significant achievement gap was found among
racial groups. Compared to White students, the predicted mathematics scores were signifi-
cantly lower for African American (p < 0.001) and Hispanic students (p < 0.01 for first and
third grades, p < 0.05 for fifth to the seventh grade). Poverty was a strong negative predictor of
mathematics outcomes for all grade levels (p < 0.001 for first, third, fourth, sixth, and seventh
grades, p < 0.01 for fifth grade).
Table 5 Summary of multilevel regression analysis that predicted Students’ test scores on criterion-refer-
enced competency test (CRCT)-mathematics
= Unstandardized regression coefficients. In this multilevel model, students were nested
within their elementary schools. For all grade levels, [Poverty * Pre-K] was tested and dropped
from the model because the interaction term was not statistically significant. Model equation:
=𝛾00 +𝛾10
Pr eKij
Pove rty ij
aSex was coded 0 = female, 1 = male. bReference group for race = White. cPoverty was coded 0 = Not eligi-
ble for free or reduced-price lunch, 1 = Eligible for free or reduced-price lunch. dPre-K was coded 0 = Did
not attend Georgia’s Pre-K program, 1 = Attended Georgia’s Pre-K program. eSAT 9 = Stanford Achieve-
ment Test-Ninth Edition. fCRCT = State of Georgia Criterion-Referenced Competency Test
*p < 0.05. **p < 0.01. ***p < 0.001
Dependent variable
Grade 1
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Predictor variable
Sexa−0.70 −0.91 −1.40 1.06 −0.66 −4.16
African Ameri-
−22.69*** −28.73*** −26.57*** −27.37*** −28.85*** −28.24***
Hispanic −16.29** −15.33** −9.73 −13.57* −12.73* −13.40*
Multi-racial −5.57 −6.98 −9.32 −9.65 −14.09 −3.34
Povertyc−18.84*** −14.51*** −19.67*** −15.40** −18.01*** −23.75***
Pre-Kd7.61** 6.14** 9.37*** 9.48** 7.86** 8.58**
R2GLMM(c) 0.277 0.303 0.284 0.232 0.245 0.275
R2GLMM(m) 0.212 0.277 0.254 0.213 0.231 0.257
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Multilevel Logistic Regression Analyses: Predicting Students’ Levels ofPerformance
Multilevel logistic regression analyses were performed to test the second hypothesis, about
the relationship between participation in Georgia’s Pre-K and levels of performance in
mathematics in later grades. In this logistic regression model with students’ performance
levels (1 = Does Not Meet the Standard, 2 = Meets the Standard) as the dichotomous out-
come, predictor variables were race, sex, poverty, and Pre-K participation. The R2GLMM
values indicated that the final model accounted for 13.6–33.2% of the total variance in stu-
dents’ mathematics test scores (Nakagawa and Schielzeth 2013; Nakagawa etal. 2017). As
displayed in Table6, when holding the other predictor variables constant, Pre-K participa-
tion was not a significant predictor for third grade; however, for grades four to seven, the
odds of a Pre-K participant meeting the state standards in mathematics were 1.67 to 2.10
times greater than the odds for a student who did not attend the Georgia Pre-K program
(p < 0.01 for fourth and fifth grade, p < 0.05 for sixth and seventh grades). Notably, the
odds ratios for Grades 4–7, which are measures of effect size in the context of logistic
regression, decreased slightly over time.
Controlling for the other variables in the model, poverty was negatively related to the
log of the odds of a student passing the minimum standards (odds ratios ranging from 0.06
to 0.38; p < 0.001 for seventh grade, p < 0.01 for fourth grade, p < 0.05 for third and sixth
grades); however, this relationship was not significant at Grade 5. African American stu-
dents were significantly less likely to meet the state standards in the area of mathematics
than White students (odds ratios ranging from 0.08 to 0.23; p < 0.001 for fourth and sixth
grades, p < 0.01 for fifth and seventh grades, p < 0.05 for third grade).
This study adds to the literature in its examination of a large-scale, state-sponsored pre-
school program. Previous studies have focused on the link between Pre-K education and
academic outcomes in the early elementary grades, but a limited number of studies have
examined whether the short-term benefits of Pre-K persist through middle school years.
This study followed Georgia Pre-K children through the seventh grade to measure the
long-term contribution of a state-funded universal Pre-K program on students’ mathemat-
ics achievement. Also, this study explored students’ academic outcomes in one additional
way by examining their performance levels on statewide tests. Although scale scores and
performance levels provide similar information, knowing whether Pre-K participation
increased the likelihood of meeting state standards in later grades may have practical pol-
icy implications.
When students’ scale scores were used as an outcome variable, regression results indi-
cated that, after controlling for the effects of race, sex, and family poverty status, participa-
tion in the Georgia Pre-K program significantly predicted students’ mathematics achieve-
ment scores in first grade and third through seventh grades. Although the effect sizes were
small, ranging from 0.27 to 0.37, it is a promising finding that Pre-K participation at age 4
remained a significant predictor of mathematics achievement until seventh grade. Although
the practical importance of these effect sizes should be understood in consideration of the
study context, these results are comparable to previous studies examining similar outcomes
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1 3
and reporting small to medium effect sizes (Gilliam and Zigler 2001; Hill etal. 2015; Mag-
nuson et al. 2007; Weiland and Yoshikawa 2013). It is worth noting that, in this study,
information was not available regarding the formative early learning experiences in their
own homes for children who did not attend the Georgia Pre-K program.
Multilevel logistic regression results indicated that receiving Pre-K education positively
influenced the likelihood that students would reach the state’s benchmarks in the area of
mathematics in fourth through seventh grades. For these grade levels, the odds of a Pre-K
participant being in a higher-performance group in mathematics were significantly greater
than those of a nonparticipant. Odds ratios were 2.10, 1.93, 1.68, and 1.67 for Grades 4
through 7, respectively. The odds ratios decreased slightly over time, indicating that the
benefit of Pre-K experience diminished to some extent as children progressed through
Table 6 Summary of multilevel logistic regression analysis that predicted the likelihood of meeting state
standards on CRCT-mathematics
= estimated logistic regression coefficients, followed by the standard errors.
OR = Odds ratio. In this multilevel model, students were nested within their elemen-
tary schools. For all grade levels, [Poverty * Pre-K] was tested and dropped from the
model because the interaction term was not statistically significant. Model equation:
=𝛾00 +𝛾10
Pr eKij
Pove rty ij
a Sex was coded 0 = female, 1 = male. bReference group for race = White. cPoverty was coded 0 = Not eligi-
ble for free or reduced-price lunch, 1 = Eligible for free or reduced-price lunch. dPre-K was coded 0 = Did
not attend Georgia’s Pre-K program, 1 = Attended Georgia’s Pre-K program. eSAT 9 = Stanford Achieve-
ment Test-Ninth Edition. fCRCT = State of Georgia Criterion-Referenced Competency Test.
*p < 0.05. **p < 0.01. ***p < 0.001
Grade 3 Grade 4 Grade 5
Predictor variable B SE OR B SE OR B SE OR
Sexa−0.29 0.26 0.75 −0.02 0.21 0.98 −0.02 0.24 0.98
African American −2.48* 1.06 0.08 −1.68*** 0.46 0.19 −1.90** 0.68 0.15
Hispanic −0.52 1.17 0.59 −0.34 0.52 0.71 −1.07 0.75 0.34
Multi-racial −1.02 1.48 0.36 −0.60 0.74 0.55 −0.99 1.01 0.37
Povertyc−2.12* 1.06 0.12 −1.60** 0.46 0.20 −0.96 0.61 0.38
Pre-Kd0.32 0.27 1.38 0.74** 0.24 2.10 0.66** 0.25 1.93
R2GLMM(c) 0.266 0.233 0.136
R2GLMM(m) 0.247 0.215 0.122
Grade 6 Grade 7
Predictor variable B SE OR B SE OR
Sexa−0.08 0.22 0.92 −0.20 0.22 0.82
African American −1.80*** 0.40 0.17 −1.48** 0.52 0.23
Hispanic −0.35 0.47 0.70 −0.08 0.59 0.92
Multi-racial −0.06 0.79 0.94 −0.11 0.96 0.90
Povertyc−1.00* 0.39 0.37 −2.90*** 0.77 0.06
Pre-Kd0.52* 0.25 1.68 0.51* 0.24 1.67
R2GLMM(c) 0.208 0.332
R2GLMM(m) 0.177 0.314
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Child & Youth Care Forum
1 3
upper grade levels. Despite the decreasing effect sizes, the long-term association between
Pre-K participation and the likelihood of students meeting academic standards in math-
ematics remained significant through the seventh grade.
The finding that the effect sizes for the Pre-K impact diminished over time is in line
with previous research reporting “fadeout” of effects. Often, initial positive effects of an
intervention are not fully sustained, and longer-term effects tend to be smaller than imme-
diate effects (Barnett 2011; Dodge et al. 2017). As Yoshikawa etal. (2013) highlighted
in their use of the term convergence, the phenomenon of fadeout is mainly indicated by
the pattern of decreasing differences between outcomes of program participants and those
of nonparticipants over time. For example, Lipsey etal. (2018) found that positive effects
of the Tennessee Pre-K program on achievement disappeared by the end of kindergarten
as the control group caught up with Pre-K participants. Not every program, even a high-
quality program, yields persistent impacts (Barnett 2011; Dodge etal. 2017). For interven-
tion programs to generate long-run effects, as Bailey etal. (2017) argued, an intervention
should address “skills that are malleable, fundamental, and would not have developed in
the absence of the intervention” (p. 2) at the right time during child development.
It is important to note that the multilevel logistic regression model did not indicate a
significant effect of Pre-K on the likelihood of meeting standards in third grade. Although
there was a significant third-grade result from the multilevel regression analysis exam-
ining students’ scale scores as an outcome variable, the effect size was smaller than for
other grade levels. This finding was unexpected in that one would expect to see a stronger
effect of Pre-K in this lower grade level. There may be several possible explanations for
this unexpected finding. Given that the Pre-K effect was consistently observed for subse-
quent grade levels, it is possible that the unexpected finding might be associated with the
test characteristics at this particular grade level. For example, the result could have been
influenced by diminished reliability or validity of the third-grade test or the criteria used to
determine performance levels. Although this speculation was not testable in this study, it is
worth considering that the CRCT assessment in mathematics was administered for the first
time in spring 2000 (Georgia Department of Education 2012) and that the third-grade test
was still in its early stages. Another possibility is that reading comprehension skills were
particularly intertwined with students’ performance on the assessment during that time
period, resulting in a different result for third grade. Indeed, research suggests that literacy
skills are significantly associated with performance in mathematics word problems during
the primary school years and even in adolescence (Kyttälä and Björn 2014). Also, the pat-
tern of observing null findings for the lower grade level and significant findings afterwards
might be explained by sleeper effects. Immediate gains from an early intervention might
disappear initially and reemerge some time afterward (Barnett 2011). From this viewpoint,
the benefits of Pre-K might have been embedded but not evident in third grade and might
have emerged in the subsequent grades.
Except for the insignificant finding for third grade, the analyses supported the long-
term relationship between participation in Georgia’s Pre-K and mathematics achievement
in the elementary and middle school years. Although limited research has examined the
long-term relationship between Georgia’s Pre-K program and children’s academic out-
comes in middle school, these findings are in line with those of other studies, demonstrat-
ing that the short-term benefits of the Georgia Pre-K program may persist into elemen-
tary school. A report of the findings from the Georgia Early Childhood Study (Henry etal.
2005) stated that children in Georgia Pre-K began preschool behind their peers across the
nation but made substantial gains from preschool through first grade and ended first grade
above the national norm on overall mathematics skills. Fitzpatrick (2008), in her analysis
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Child & Youth Care Forum
1 3
of individual-level data from the National Assessment of Educational Progress, found that
the universal Pre-K program in Georgia increased average mathematics scores of fourth
graders by 0.03 standard deviation. The estimated benefit of the program was greater for
disadvantaged students who were eligible for a school lunch program and living in small
towns and rural areas, where their mathematics scores increased by 0.06 to 0.09 standard
deviation. A recent study of the Georgia Pre-K program (Early etal. 2019) also demon-
strated stronger effects of Pre-K for children enrolled in free or reduced-price lunch pro-
grams. Inconsistent with these results, the current study did not find a significant interac-
tion between Pre-K participation and poverty status; that is, the effect of Pre-K on student
achievement outcomes did not significantly differ as a function of a student’s family SES
background. The nonsignificant interaction might have been due to the characteristics of
the sample, such as limited variability in SES backgrounds.
The findings regarding students’ levels of performance are particularly insightful in that
we examined student achievement data in terms of whether students reached a minimum
proficiency level as determined by the state. Although using this criterion exclusively for
making high-stakes decisions might be problematic (Polikoff etal. 2011), given that many
educational decisions in practice are made based on this information, it is helpful to under-
stand the factors that might contribute to students’ meeting statewide academic standards.
Mathematics is one of the content areas in which a large percentage of students have dif-
ficulty in reaching the minimum level of academic performance (de Mello etal. 2015). The
result in this study that Pre-K participation might increase the likelihood of students’ meet-
ing the standards until seventh grade is a promising finding that provides evidence on the
long-term impact of state Pre-K programs.
Preliminary analysis results indicated that the quality of Pre-K classrooms was not a
significant predictor of mathematics outcomes in elementary and middle schools in this
study. This is inconsistent with the findings of numerous previous studies, highlighting the
importance of classroom quality (Burchinal etal. 2010; Keys etal. 2013; Yoshikawa etal.
2013). The most likely reason for this discrepancy might be that minimal quality variations
among the Pre-K classrooms in this study made it difficult to detect the effect of quality on
student outcomes. These classrooms, as measured by the High/Scope PQA, were of good
to excellent quality, with minimal variations (M = 4.52, SD = 0.66 on a 5-point scale). No
classrooms received low-quality ratings. With a more variable level of quality, this study
might have yielded different findings.
Another lesson learned from this null finding is that observations of the overall qual-
ity of Pre-K environments, as measured in this study, might not fully capture content-spe-
cific characteristics of the classroom contributable to child outcomes. Researchers have
commented on the role of specific features in Pre-K classrooms that might be associated
with early mathematics achievement. For example, the Multi-State Study of Pre-K by the
National Center for Early Development and Learning (Early etal. 2005) found that children
were engaged in mathematics instruction during the school day far less than in any other
cognitive activity, including less than half the time spent in literacy activities. In addition
to time on task, Chien etal. (2010) delineated the contribution of instructional climate in
Pre-K classrooms and found that children who engaged in free play exhibited smaller gains
in mathematics outcomes than children who engaged in individual instruction in mathe-
matics. Teacher professional development and the use of center-based mathematics also
promoted Pre-K children’s fluency and flexibility with number concepts, their ability to
solve contextual problems, and their use of spatial strategies to solve problems (Brende-
fur etal. 2013). Future research that takes these classroom variables (e.g., the amount of
time spent on mathematics instruction, instructional climate, instructional strategies) into
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1 3
consideration might enhance understanding of a specific mechanism by which Pre-K edu-
cation is associated with mathematics achievement in later grades.
Although they were not of primary interest in this study, findings regarding the other
covariates suggested a substantial achievement gap by race and SES. There was a strong
relationship between students’ free or reduced-price lunch status during the preschool or
kindergarten year and their mathematics achievement, supporting existing evidence on
the adverse effect of low SES on students’ academic achievement. Similarly, for all grade
levels, there was a substantial difference in the performance of racial groups, even after
controlling for the effect of poverty. The mathematics scores of African American and
Hispanic children tended to be lower than those of the other racial groups, and the likeli-
hood of meeting the state standards was significantly lower for African American children.
These findings add to a growing body of literature that investigates the racial opportunity
gap (Potter and Morris 2016). Despite concentrated efforts to close the opportunity gap
among students of various backgrounds, these findings suggest that the gap remains one
of the foremost challenges to be addressed by educational researchers, practitioners, and
Limitations andConclusion
This study has several limitations. These limitations chiefly emerge from the fact that
the current study used data available from school records and was limited by the avail-
able information. First, the research design of this study did not include a pure control
group and baseline data. Although Georgia’s Pre-K program is a universal preschool pro-
gram, program participation was based on the family’s voluntary engagement in seek-
ing services, which is a potential source of selection bias. There might be systematic dif-
ferences between those who voluntarily enrolled in the program and those who did not.
Although we included important covariates such as poverty status and racial information
in the model, given the lack of baseline data, we were not able to adjust fully for the selec-
tion bias. Second, related to the first limitation, although we included main socioeconomic
variables as covariates, it would be informative to examine a more complex model with
additional covariates. For example, factors that could influence achievement outcomes
include individual students’ special education status, parental educational level, and other
classroom characteristics. Having additional information regarding non-Pre-K participants
(e.g., types and dosage of early childhood education services that they received during pre-
school years) would help to clarify the nature of the comparisons made in this study. Third,
enrollment in the free or reduced-price lunch program was used as a family SES variable.
Although this variable is widely used as an indicator of poverty status (Bowen etal. 2000),
this binary variable provides limited information compared to other quantitative variables,
such as a ratio of income to poverty. We performed a separate analysis for each grade level
instead of examining student growth over time. This analytic decision was made because
the statewide test scores used in this study were not vertically scaled or comparable across
grade levels.
Despite these limitations, this study provides additional evidence that children’s early
learning experiences in a state-funded universal Pre-K program can have an effect that
persists into the elementary and middle school years. This is one of the few studies that
looked at Georgia Pre-K participants through the middle school years and found persist-
ing academic gains in mathematics. Although the sample in this study may not be repre-
sentative of all children attending Georgia’s Pre-K program, it reflects the demographics
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Child & Youth Care Forum
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of a high-needs school district in the state. The study also provides findings particularly
relevant to educational policy by indicating that participation in Georgia Pre-K program
predicted whether students reached the state’s minimum level of proficiency in elementary
and middle school.
Funding This study was supported by a grant from Kyung Hee University (KHU-20182224).
Compliance with Ethical Standards
Conflict of Interest The authors declare that they have no conflict of interest.
Ethics Approval This research was considered exempt by the University of Georgia Institutional Review
Consent to Participate Researchers were provided with a de-identified dataset for the participating children
in this study by the partnering school district.
Access to Data Both authors take responsibility for the integrity of the data and the accuracy of the data
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The purpose of this study is to present a general perspective by examining the research works about primary school mathematics. In this direction, 637 articles in the Web of Science database and published in SSCI indexed journals between 1980 and 2021 were analyzed by bibliometric analysis, the general structure of the concepts in the studies was revealed, the emerging concept clusters were identified. Research findings include concepts related to primary school mathematics in general terms (1) “teaching anatomy”, which deals with teaching process of primary school mathematics, (2) “learning outcome”, which includes concepts related to the mathematical performance of students in primary school, (3) “affective comparison”, which covers the structure that includes the concepts related to affective characteristics as well as gender comparison and (4) “instructional practices”, which contains different strategies and teaching practices. This study provided maps indicating the richness and diversity of the concepts in primary school mathematics.
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The State of Preschool 2018 is the 16th edition of NIEER’s annual report tracking state-funded preschool access, resources, and quality. Since 2002, the preschool landscape has changed in many ways; and in others, it has remained the same – highlighting the need for a renewed commitment to progress.
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Propensity score matching was used to compare third-grade test scores in English language arts, mathematics, science, and social studies for children who had and had not participated in Georgia’s Pre-K 4 years earlier. After matching, each group included 46,262 children (mean age 8.36 years in third grade). In all subject areas, children who had participated in Georgia’s Pre-K scored significantly higher (Cohen’s D = .06 to .09), and pre-K participation was associated with an 11% to 17% increase in the odds of scoring proficient or above. Among children enrolled in free or reduced-price lunch, participation in Georgia’s Pre-K was associated with higher test scores and greater likelihood of scoring proficient or above; however, the opposite was true for children not enrolled in free or reduced-price lunch. Associations between pre-K participation and math scores were stronger for children whose home language was not English as compared to those whose home language was English.
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The current paper reports long-term treatment impact estimates for a randomized evaluation of an early childhood intervention designed to promote children's developmental outcomes and improve the quality of Head Start centers serving high-violence and high-crime areas in inner-city Chicago. Initial evaluations of end-of-preschool data reported that the program led to reductions in child behavioral problems and gains in measures of executive function and academic achievement. For this report, we analyzed adolescent follow-up data taken 10 to 11 years after program completion. We found evidence that the program had positive long-term effects on students’ executive function and grades, though effects were somewhat imprecise and dependent on the inclusion of baseline covariates. Results also indicated that treated children had heightened sensitivity to emotional stimuli, and we found no evidence of long-run effects on measures of behavioral problems. These findings raise the possibility that developing programs that improve on the Head Start model could carry long-run benefits for affected children.
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This report presents results of a randomized trial of a state prekindergarten program. Low-income children (N = 2990) applying to oversubscribed programs were randomly assigned to receive offers of admission or remain on a waiting list. Data from pre-k through 3rd grade were obtained from state education records; additional data were collected for a subset of children with parental consent (N = 1076). At the end of pre-k, pre-k participants in the consented subsample performed better than control children on a battery of achievement tests, with non-native English speakers and children scoring lowest at baseline showing the greatest gains. During the kindergarten year and thereafter, the control children caught up with the pre-k participants on those tests and generally surpassed them. Similar results appeared on the 3rd grade state achievement tests for the full randomized sample – pre-k participants did not perform as well as the control children. Teacher ratings of classroom behavior did not favor either group overall, though some negative treatment effects were seen in 1st and 2nd grade. There were differential positive pre-k effects for male and Black children on a few ratings and on attendance. Pre-k participants had lower retention rates in kindergarten that did not persist, and higher rates of school rule violations in later grades. Many pre-k participants received special education designations that remained through later years, creating higher rates than for control children. Issues raised by these findings and implications for pre-k policy are discussed.
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Importance Educational attainment is the leading social determinant of health, but few studies of prevention programs have examined whether the programs are associated with educational attainment outcomes after the mid-20s, especially for large-scale programs that provide a longer duration of services. Objective To examine the association between a preschool to third grade intervention and educational attainment at midlife and differences by program duration, sex, and parental educational level. Design, Setting, and Participants This matched-group, alternative intervention study assessed 1539 low-income minority children born in 1979 or 1980 who grew up in high-poverty neighborhoods in Chicago, Illinois. The comparison group included 550 children primarily from randomly selected schools participating in the usual early intervention. A total of 989 children who entered preschool in 1983 or 1984 and completed kindergarten in 1986 were included in the Chicago Longitudinal Study and were followed up for 27 to 30 years after the end of a multicomponent intervention. A total of 1398 participants (90.8%) in the original sample had educational attainment records at 35 years of age. The study was performed from January 1, 2002, through May 31, 2015. Interventions The Child-Parent Center Program provides school-based educational enrichment and comprehensive family services from preschool to third grade (ages 3-9 years). Main Outcomes and Measures Educational outcomes from administrative records and self-report included school dropout, 4-year high school graduation, years of education, postsecondary credential, and earned degrees from associate’s to master’s or higher. Results A total of 1539 participants (mean [SD] age, 35.1 [0.32] years; 1423 [92.9%] black and 108 [7.1%] Hispanic) were included in the study. After weighting on 2 propensity scores, preschool participants had higher rates of postsecondary degree completion, including associate’s degree or higher (15.7% vs 10.7%; difference, 5.0%; 95% CI, 1.0%-9.0%), master’s degree (4.2% vs 1.5%; difference, 2.7%; 95% CI, 1.3%-4.1%), and years of education (12.81 vs 12.32; difference, 0.49; 95% CI, 0.20-0.77). Duration of participation showed a consistent linear association with outcomes. Compared with fewer years, preschool to second or third grade participation led to higher rates of associate’s degree or higher (18.5% vs 12.5%; difference, 6.0%; 95% CI, 1.0%-11.0%), bachelor’s degree (14.3% vs 8.2%; difference, 6.1%; 95% CI, 1.3%-10.9%), and master’s degree or higher (5.9% vs 2.3%; difference, 3.6%; 95% CI, 1.4%-5.9%). The pattern of benefits was robust and favored male participants for high school graduation, female participants for college attainment, and those from lower-educated households. Conclusions and Relevance This study indicates that an established early and continuing intervention is associated with higher midlife postsecondary attainment. Replication and extension of findings to other locations and populations should further strengthen confidence in the health benefits of large-scale preventive interventions.
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The coefficient of determination R² quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R² for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R² that we called for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.
Small-scale studies have found that preschool education can produce sufficiently large effects on the educational achievement of economically disadvantaged children in the United States that it is theoretically possible for it to meaningfully reduce achievement gaps by income and race. However, studies of large-scale public programs tend to find smaller effects that do not persist. Plausible reasons for the disappointing results at scale are the limited quality and intensity of public preschool programs and failure to reach most disadvantaged children so that the schools they enter at age five must still target the needs of the many who do not attend pre-kindergarten. We present analyses for counterexamples that produce large persistent achievement gains in achievement and describe the resources and policies required to transform the quality of early education beginning at age three for the vast majority of children in 31 cities with high concentrations of poverty.
This study employs data from both kindergarten cohorts of the Early Childhood Longitudinal Study (n ~ 12,450 in 1998; n ~ 11,000 in 2010) to assess whether associations between preschool participation and children's academic and behavioral outcomes—both at school entry (Mage = 5.6 years in both cohorts) and through third grade—have changed over time. Findings are strikingly similar across these two, nationally representative, U.S. cohorts: preschool is positively associated with academic outcomes and negatively associated with behavioral outcomes both at school entry and as children progress through school. Heterogeneity is documented with respect to child and preschool characteristics. However, there is no evidence that associations between preschool and medium‐term child outcomes differ by elementary school characteristics.
Several states have changed their statewide achievement tests over the past 5 years. These changes may pose difficulties for educators tasked with identifying students in need of additional support. This study evaluated the stability of decision-making accuracy estimates across changes to the statewide achievement test. We analyzed extant data from a large suburban district in Wisconsin in 2014–2015 (N = 2,774) and 2015–2016 (N = 2,882). We estimated the decision-making accuracy of recommendations from the Measures of Academic Progress for predicting risk on a Common Core State Standards aligned test (2014–2015) and a new test based on updated academic standards (2015–2016) in reading and math. Findings suggest that sensitivity and specificity estimates were relatively stable in math. Changes in the criterion measure were associated with decreased sensitivity when predicting performance in reading. These results provide initial support for educators to continue existing screening practices until test vendors or state educational agencies establish cut-scores for predicting risk on the newer test. Using a lower cut-score to establish risk (increasing sensitivity while decreasing specificity) may be prudent in reading. Limitations and directions for future research are discussed.