Post on 17-Jun-2018
KINDERGARTEN MATHEMATICS MISALIGNMENT
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The Misalignment of Kindergarten Mathematics Content
Mimi Engel
Vanderbilt University
Amy Claessens
University of Chicago
Tyler Watts
George Farkas
University of California at Irvine
March 13, 2015
Acknowledgments: The data used in this paper come from The National Center
for Education Statistics (NCES) and are available through a restricted-use license
agreement. The authors are grateful to the Spencer Foundation and to the National
Institute of Child Health and Human Development– supported Irvine Network on
Interventions in Development (HD065704 P01) for research support. The authors
thank Pamela Davis-Kean, Greg Duncan, and Robert Siegler for helpful feedback.
All errors are our own.
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Abstract
Analyzing data from two nationally representative kindergarten cohorts, we
examine the mathematics content in kindergarten classrooms. We replicate prior
research and find that kindergarten teachers emphasize basic content that students
already know. Although teachers reported increased coverage of advanced content
between the 1998-99 and 2010-11 school years, they continued to place more
emphasis on basic content. We find that time on advanced content is positively
associated with student learning, while time on basic content has a negative
association with learning. We also explore the extent to which content covered in
kindergarten aligns with the Common Core State Standards in Mathematics. We
argue that increased exposure to more advanced mathematics content could
benefit the vast majority of kindergartners.
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Despite evidence of and advocacy regarding the importance of
mathematics education for young children, mathematics is under-emphasized in
kindergarten, particularly when compared with reading (Engel, Claessens, &
Finch, 2013). Teachers of young children report being uncomfortable and unsure
teaching mathematics (Ginsberg et al., 2008). This discomfort is concerning,
particularly when considered in light of findings that suggest that young children
are able to understand and learn a wide range of mathematics in early childhood
(Clements & Sarama, 2011).
Children’s skills in mathematics at kindergarten entry, as well as their
learning in mathematics during kindergarten, are more important predictors than
reading skills or socioemotional behaviors of their subsequent success in both
reading and mathematics (Claessens & Engel, 2013; Claessens, Duncan, & Engel,
2009; Watts, Duncan, Siegler, & Davis-Kean, 2014). Key advocacy groups have
also noted the importance of mathematics instruction for young children. The
National Council for Teachers of Mathematics (NCTM), the National Association
for the Education of Young Children (NAEYC), and the National Mathematics
Advisory Panel (NMAP) have all argued that children under the age of six are
ready to learn, and will benefit greatly from exposure to, a range of mathematics
content (NAEYC & NCTM, 2002; NCTM, 2007, NMAP, 2008).
Research using data from the late 1990s found that the majority of the
mathematics content to which most kindergarteners were exposed covered topics
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they had already mastered (Engel et al., 2013). Although most kindergartners
entered school proficient in basic counting and knowledge of basic shapes,
kindergarten teachers reported emphasizing this content far more than topics that
students had yet to master, such as addition and subtraction. Further, exposure to
advanced content was associated with larger cross-kindergarten test score gains in
mathematics, whereas exposure to basic content was associated with smaller gains
for almost all students (Claessens, Engel, & Curran, 2014; Engel et al., 2013).
Despite this evidence, there is little agreement about what mathematics
kindergarteners should be taught.
There have been shifts in both public discourse and public policy toward
an increased academicization of kindergarten (Russell, 2011). Yet, research
suggests that this increased focus on academic content has been primarily
centered on reading instruction. Bassok and Rorem (2013) found that
kindergarten teachers reported dramatic increases in time spent on reading
between 1998 and 2006. Further, they reported a rise in teachers’ expectations
with regard to children’s school readiness skills across content areas during this
period. These changes to kindergarten have been controversial, however, with
some advocates arguing that an increased academic focus interferes with the
important role of play and socialization in kindergarten (Miller & Almon, 2009).
Recent policy changes have continued to highlight academics in
kindergarten. In 2010, the Common Core State Standards for Mathematics
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(CCSSM) were introduced. They have been fully or partially adopted by 43 states.
The CCSSM were designed to guide teachers’ mathematics instruction by
emphasizing both processes and proficiencies (Common Core Standards
Initiative, 2010) with the goal of deepening students’ knowledge of mathematics
(Schmidt & Burroughs, 2013). For kindergarten teachers, the CCSSM contains
detailed standards outlining the mathematics content that should be taught during
the kindergarten year. Although the CCSSM will likely influence kindergarten
mathematics, the nature and implications of this change for learning in
mathematics remain unclear.
The Current Study
We replicate and extend prior research on kindergarten mathematics
content. Recent evidence indicates that replication – crucial for building
knowledge in the social sciences – is extremely rare in educational research
(Makel & Plucker, 2014). Engel and colleagues (2013) found kindergarten
mathematics content to be poorly aligned with student knowledge and skills in
mathematics at school entry. Although evidence suggests that kindergarten has
become more academic (Bassok & Rorem, 2013; Russell, 2011), we know little
about whether and how the mathematics content taught in kindergarten has
changed.
We leverage newly released data to conduct cross-cohort comparisons
exploring changes in kindergarten mathematics content coverage over time. We
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use data from two nationally representative cohorts of kindergarteners and their
teachers to replicate and extend prior research (Engel, et al., 2013). We explore
the association between teacher-reported content coverage and student learning,
addressing the following questions:
1) Has the mathematics content that kindergarten teachers report
teaching changed between 1998-99 and 2010-11?
2) Has the relationship between mathematics content exposure in
kindergarten and student learning changed across this period?
We also explore the extent to which mathematics content coverage in
kindergarten aligns with the CCSSM for kindergarten.1 We ask the following
questions with regard to this topic:
3) How does the mathematics instructional content that
kindergarten teachers reported covering align with the CCSSM
for kindergarten?
4) What is the relationship between measures of CCSSM content
coverage in kindergarten and student learning?
Methods
Data
We use data from two longitudinal, nationally representative studies of
kindergarteners conducted by the National Center for Educational Statistics
(NCES); the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99
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(ECLS-K) and the Early Childhood Longitudinal Study, Kindergarten Class of
2010-11 (ECLS-K:2011). As shown in Table 1, the analysis samples for the
ECLS-K (n=17,810) and the ECLS-K:2011 (n=15,090) differ in a number of
ways. In 1998-99, 61 percent of kindergarteners attended a full day program,
whereas 87 percent did so in 2010-11. Further, one quarter of kindergarteners
identified as Hispanic in 2010-11, a 32 percent increase from 19 percent in 1998-
1999. Both data sets include over 3000 kindergarten teachers who had taught
kindergarten for an average of nine years. All sample sizes we report are rounded
to the nearest ten, in compliance with NCES restricted data use agreements.
[Insert Table 1 here]
For the ECLS-K:2011, restricted base-year data can be requested from the
National Center for Educational Statistics. These data allow for cross-cohort
comparisons across the ECLS-K and the ECLS-K:2011 in terms of children’s
classroom experiences. Direct child cognitive assessment scores that have been
released for the newer cohort are, at this time, not directly comparable to scores
from the original ECLS-K. Information about the ECLS-K comes from its user’s
manual (Tourangeau, Nord, Le, Sorongon, & Najarian, 2009), and information
about the sample and measures for the ECLS-K:2011 is drawn from its base-year
user’s manual (Tourangeau et al., forthcoming).
The ECLS-K and the ECLS-K:2011 are large, longitudinal, nationally
representative studies of children who were in kindergarten in either 1998-99 or
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2010-11, respectively. Both data sets contain extensive information about sample
children and their families, classrooms, teachers, and schools. For the analyses
that follow, we draw our independent variables of interest from the teacher
surveys administered in the spring of 1999 and 2011, respectively. Our dependent
variables are student achievement test scores in mathematics from the spring of
kindergarten. Controls are drawn from parent, student, teacher, and school-level
data. To address the issue of missing data, we use multiple imputation, imputing
independent and dependent variables for both data sets. Please see online
appendix for details on our multiple imputation procedures.
Measures
Student Achievement. In both cohorts, student achievement in
mathematics and reading was assessed at kindergarten entry and again in the
spring of kindergarten. The mathematics assessments were designed to measure
conceptual and procedural knowledge and problem solving ability. The
assessments were developed using Item Response Theory (IRT) to allow
researchers to use the measures to examine growth in student achievement
longitudinally (Tourangeau et al., 2009). We control for fall test scores and spring
mathematics test scores are our dependent variable of interest. We use the IRT
scale scores provided in each dataset, which we standardize to a mean of zero and
a standard deviation of one within each cohort.
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For the original ECLS-K, NCES used the hierarchical structure of the
assessments to create proficiency probability scores measuring student mastery of
various levels in mathematics and reading. Individual scores on these “proficiency
levels” are included as variables in the data files for the original ECLS-K. The
most basic proficiency level in mathematics measured student knowledge of
“Basic Counting and Shapes”, and the most advanced proficiency level (for
kindergarteners) measured “Basic Addition and Subtraction.” Proficiency
probability scores and proficiency levels have not been released for the ECLS-
K:2011. Thus, it is not possible to compare proficiency levels across the two
cohorts.
Both the mathematics and reading assessments created for the ECLS-K
were developed from national and state standards, and they were also designed to
align with the National Assessment of Educational Progress (NAEP). Although
the NAEP is not administered until fourth grade, the principles and content within
the NAEP were extrapolated to the kindergarten level. Further, mathematics
assessment designers also consulted the National Council for Teachers of
Mathematics (NCTM), and empirical work has shown that the CCSSM are
moderately aligned to the NCTM’s standards for mathematical practice (Porter et
al., 2011).
Content Measures
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Alignment measures. Replicating the measures used by Engel et al.,
2013, we create alignment measures in both cohorts using teacher reports.
Teacher surveys in both cohorts included items asking teachers about their
instruction with regard to mathematics content and activities. Teachers responded
on a six point Likert scale ranging from “never” to “every day”. We converted
these scales to a measure of number of days per month ranging from zero to 20.
We aligned these items to the proficiency levels created by NCES staff using
results from the fall of kindergarten mathematics test for the ECLS-K. We include
only items that matched the mathematics content described in the proficiency
levels. This procedure generated four categories of classroom-mathematics
content that were, again, aligned with the four proficiency levels in mathematics
in which kindergarteners in the original ECLS-K were scored. These correspond
to the measures used in Engel et al., 2013.
We calculate these as the average number of days per month of the items
contained within each category: Basic Counting and Shapes; Patterns and
Measurement; Place Value and Currency; and Addition and Subtraction. Alpha
values for the eight measures (four for each data set) range from .58 - .88.
Appendix Table 1 shows the individual items (with their means and standard
deviations) used to create each of the four scales. The online appendix provides
more detail on measure creation. Correlations between the four measures within
the two respective data sets are provided in Appendix Table 2.
KINDERGARTEN MATHEMATICS MISALIGNMENT
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CCSSM Content Measures. We also analyzed the teacher-reported
mathematics content items to align them with the CCSSM kindergarten domains.
We developed measures from the 1998-1999 and 2010-2011 cohorts to explore
the extent to which teacher-reported mathematics content coverage in
kindergarten aligns with the CCSSM domains and how content aligned with the
CCSSM domains relates to student learning in mathematics during kindergarten.
Appendix Table 3 presents the teacher-reported items that we coded into
these domains. For our CCSSM Content Measures aligned with the CCSSM
kindergarten domains, alpha values range from .49 - .88. The number of items per
measure ranges from five for our measure of Counting and Cardinality to two
items each for our measures of Operations and Algebraic Thinking, Numbers and
Operations in Base Ten, and Geometry. Our measure of the CCSSM kindergarten
domain of Measurement and Data includes three items.
In order to facilitate comparisons between the Alignment Measures and
our CCSSM Content Measures, in Appendix Table 3 we also detail when an item
is categorized under a particular CCSSM domain as well as an Alignment
Measure. For example, “Count out loud” is categorized under the CCSSM
Content Measure aligned with the domain of Counting and Cardinality and is also
included in the Alignment Measure of Basic Counting and Shapes.
Coincidentally, each of our five measures representing the CCSSM Content Areas
includes two items from one of the four Alignment Measures. We note that our
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CCSSM Content Measures of Counting and Cardinality and Geometry each
include two (mutually exclusive) items from the Alignment Measure of Basic
Counting and Shapes.
Control Variables. We control for fall of kindergarten mathematics and
reading test scores. Additional control variables included in all of our models are
student gender, race/ethnicity, age at kindergarten entry, preschool attendance,
mother's education, family income, whether the student lived with a biological
parent, number of siblings in the household, number of books in the home, and
whether English was the primarily language spoken in the home. We also control
for teacher-reported overall time on mathematics and whether the classroom was
full day kindergarten. Teacher characteristics we control for include teacher
gender, ethnicity, age, whether the teacher had obtained a master's degree, years
of teaching experience, whether the teacher had taken a pedagogical development
class in mathematics, reading, and/or early education, respectively, and
certification level. Finally, we included administrator-reported measures of school
region, urbanicity, and the percentage of the student body eligible for free or
reduced-price lunch. Appendix Table 4 reports descriptive statistics for control
variables.
Analysis Plan
We investigate the association between measures of teacher-reported
mathematics content emphasis and student achievement in mathematics. We
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estimate separate OLS regression models for each cohort in which we predict
student mathematics achievement as a product of mathematics instructional
content, and student, teacher, family and school characteristics. For the
Alignment Measures our model is specified as follows:
𝑀𝑎𝑡ℎ𝐴𝑐ℎ𝑖𝑠𝑘 = 𝑎1 + 𝛽1𝐶𝑜𝑛𝑡𝑒𝑛𝑡𝑖𝑘 + 𝛽2𝐴𝑐ℎ𝑖𝑓𝑘 + 𝛽3𝐶ℎ𝑖𝑙𝑑𝑖 + 𝛽4𝐹𝑎𝑚𝑖𝑙𝑦𝑖𝑓𝑘
+ 𝛽5𝑇𝑒𝑎𝑐ℎ𝑒𝑟𝑖𝑘 + 𝛽6𝑆𝑐ℎ𝑜𝑜𝑙𝑖𝑘 + 𝑒𝑖
where 𝑀𝑎𝑡ℎ𝐴𝑐ℎ𝑖𝑠𝑘 represents the mathematics achievement of child i measured
at the spring of kindergarten (sk). 𝐶𝑜𝑛𝑡𝑒𝑛𝑡𝑖𝑘 represents the days per month spent
on the set of each of the respective Alignment Content Measures (Basic Counting
and Shapes, Patterns and Measurement, Place Value and Currency, and Addition
and Subtraction) for child i during kindergarten (k). 𝐴𝑐ℎ𝑖𝑓𝑘 represents the
mathematics and reading achievement for child i measured in the fall of
kindergarten (fk). 𝐶ℎ𝑖𝑙𝑑𝑖 is a vector of background characteristics (e.g.,
race/ethnicity, gender). 𝐹𝑎𝑚𝑖𝑙𝑦𝑖𝑓𝑘 represents a vector of family background
characteristics (e.g., parental income). 𝑇𝑒𝑎𝑐ℎ𝑒𝑟𝑖𝑘 is a vector of teacher
characteristics (e.g., certification level, race/ethnicity) measured during
kindergarten. 𝑆𝑐ℎ𝑜𝑜𝑙𝑖𝑘 represents a vector of administrator-reported school
characteristics (e.g., proportion of students eligible for free or reduced-price
lunch) measured during the kindergarten year, and 𝑒𝑖 represents the error term.
Using the sample weights, we adjust all standard errors for
nonindependence due to sample-designed clustering in classrooms and schools.
KINDERGARTEN MATHEMATICS MISALIGNMENT
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We also tested models in which standard errors were adjusted at only the
classroom level. The resulting standard errors were nearly identical. We
standardize all measures of instructional content within cohort. Thus, coefficients
estimated for our various measures of instructional content (𝛽1) estimate the effect
of a standard deviation increase in reported coverage of specific mathematics
content on end-of-kindergarten mathematics achievement. Please see online
appendix for detailed information regarding the multiple imputation procedures
and sample weights that we use.
We estimate these models separately for the 1998 and 2010 cohorts,
respectively, and compare coefficients calculated for the Alignment Measures for
each cohort. We then run the same models replacing the Alignment Measures with
our CCSSM Content Area measures (𝐶𝑜𝑛𝑡𝑒𝑛𝑡𝑖𝑘) for each cohort.
It is important to note that our data are observational, which precludes us
from estimating the causal impact of our measures of instructional content in
mathematics on end-of-kindergarten mathematics achievement. However, the
inclusion of an extensive set of control variables should substantially reduce bias
due to possible omitted variables.
Results
Table 2 shows the percentage of students who had mastered particular
content areas at kindergarten entry in 1998. These mastery rates were calculated
by NCES staff for the original ECLS-K, but are not available for the ECLS-
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K:2011. The vast majority of children – 92 percent – had mastered mathematics
content related to Basic Counting and Shapes at the start of kindergarten. In
contrast, almost no students – 3 percent – had mastered Basic Addition and
Subtraction.
[Insert Table 2 here]
Table 2 also presents Cronbach’s alpha values and descriptive statistics for
the four content Alignment Measures and the five CCSSM Content Area Measures
by cohort. Average days per month reported on two of the four Alignment
Measures – those that measure more advanced mathematics content – increased,
with magnitudes that are both statistically significant and substantively large.
Reported coverage of Place Value and Currency went from approximately 8.5
days per month in 1999 to over 10.5 days per month, on average (p < .001), in
2011. Similarly, reported time on Basic Addition and Subtraction went from 7.5
days per month to nearly 9.5 days per month (p < .001). In contrast, average time
on Basic Counting and Shapes increased by only .4 days per month, and time on
Patterns and Measurement also increased slightly (by .029 days per month).
Comparing time spent on items aligned with the CCSSM content in 1998-
1999 with time spent on the same content in 2010-2011, as was the case with the
misalignment measures (with which these measures overlap considerably),
teachers reported spending more days per month on most of the CCSSM Content
measures in 2010-2011 than in 1998-1999.
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Figure 1 highlights the poor fit between the content teachers cover and
what students know at kindergarten entry. We contrast the number of reported
days per month on each content measure with the percentage of students who had
mastered the most basic and the most advanced content areas at kindergarten
entry in 1998. In both cohorts, teachers reported the greatest emphasis –
approximately 13 days per month – on Basic Counting & Shapes; content that
over 90 percent of students had already mastered. They reported less emphasis on
content, such as Addition & Subtraction, that few students had mastered.
[Insert Figure 1 here]
We estimated separate ordinary least squares (OLS) regressions for both
cohorts in which we model student mathematics achievement in the spring of
kindergarten as a function of our measures of mathematics content, controlling for
relevant student, teacher, family and school characteristics including student
mathematics achievement at kindergarten entry. We adjust all standard errors for
nonindependence due to sample-designed clustering in classrooms and schools.
We also standardize all measures of instructional content within cohort. Thus,
coefficients estimated for our measures of instructional content estimate the effect
of a standard deviation increase in reported coverage of specific mathematics
content on end-of-kindergarten mathematics achievement.
Table 3 shows results from regressions using the Alignment Measures we
replicate from (Engel, et al., 2013) described above as well as our CCSSM
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Content Area Measures. Each pair of columns (e.g., columns 1 and 2) shows
results from regressions that are identically specified, with coefficients in odd-
numbered columns generated from the original ECLS-K and even numbered
columns showing results for the ECLS-K:2011.
[Insert Table 3 here]
Columns 1 and 2 present results that include all four of the Alignment
Measures in a single model. Results displayed in Table 3 for the original ECLS-
K are consistent with results reported by (Engel, et al., 2013). Moreover, the
coefficients estimated using the more recent ECLS-K:2011 are similar to
estimates for the original ECLS-K cohort, indicating that the association between
instructional content and student achievement in kindergarten did not change over
this time period.
Coefficients are small in magnitude, ranging from an absolute value of
.015 (p < .05) for Patterns and Measurement for the ELCS-K to .046 (p < .001)
for Addition and Subtraction for the ECLS-K:2011. Results indicate that, on
average, students benefit from additional exposure to content that they had not
mastered at kindergarten entry including Place Value and Currency and Addition
and Subtraction. Further, we find that in both 1998-99 and 2010-11, students
gained less when teachers reported spending more days per month on Basic
Counting and Shapes or Patterns and Measurement; content that the majority of
students had already mastered at the start of kindergarten.
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Columns 3 and 4 present results from models using the CCSSM Content
Area Measures to predict end of kindergarten mathematics achievement. We find
the largest positive effects for time spent on the CCSSM Content Areas that are
similar to our Alignment Measures that cover more advanced content (content that
most students had not yet mastered at kindergarten entry): Operations and
Algebraic Thinking (ECLS-K: β = .036, p < .001; ECLS-K:2011: β = .044, p <
.001) and Numbers in Base Ten (ECLS-K: β = .020, p < .001; ECLS-K:2011: β =
.028, p < .001). The measure we created to align with the CCSSM domain of
Measurement and Data is statistically insignificant, with coefficient estimates
near zero for both cohorts.
In addition to the results described above, we conducted a series of
alternative model specifications and robustness checks. We used listwise deletion
as well as missing data indicators as alternative means for dealing with missing
data. We also tested specifications using more extensive, but not directly
comparable, sets of control variables for each cohort. Finally, we explored
whether results differed for subgroups by student race/ethnicity, socioeconomic
status, and school entry mathematics achievement. Results were similar across all
model specifications and for all subgroups. Please see online appendix for
additional details.
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Discussion
Our investigation of the mathematics content covered in kindergarten
classrooms in 2010-11 showed a pattern of results that was largely similar to what
Engel and colleagues (2013) found using data from the 1998-99 school year. We
show that kindergarten teachers continue to report spending more days per month
teaching content that students already know – particularly time on Basic Counting
and Shapes. Teachers reported covering this content an average of 13 days per
month in both 1998-1999 and 2010-2011. Moreover, coverage of this basic
content was negatively associated with student achievement gains for both cohorts
of kindergarteners. Thus, the misalignment between content coverage and student
knowledge has continued, with no evidence of a reduction in coverage of basic
content.
Our efforts at replication are important in light of recent calls across fields
and disciplines for an increased focus on replication in social science research
(e.g., Lieberman, 2010; Nosek, Spies, & Motyl, 2012). Although replication is
crucial to the advancement of knowledge in social science, publication of explicit
replication studies is exceedingly rare in fields including economics,
developmental psychology, and education (Duncan, Engel, Claessens, & Dowsett,
2014; Makel & Plucker, 2014). Our study explicitly replicates prior research on
kindergarten mathematics teaching and learning (Engel et al., 2013), finding a
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consistent pattern of results and extending that work to explore results with newly
released data and additional measures of mathematics content.
We find that time on more advanced topics increased between the 1998-
1999 and 2010-2011 school years. This increase could be due to the
accountability policies ushered in with NCLB, as NCLB required states to set
academic standards in mathematics and reading for elementary school students. It
is unclear how NCLB might have affected kindergarten teachers, since
accountability testing is not mandated until the third grade year. Yet, empirical
work has shown that kindergarten teachers’ academic expectations rose during the
years following NCLB (Bassok & Rorem, 2013), and those expectations may
influence what content teachers cover.
The adoption of the CCSSM was met with optimism on the part of some
educational researchers, with a hope that the new standards would move teachers
toward emphasizing more rigorous content (e.g., Schmidt, 2004). However, our
findings suggest that merely aligning instruction with the topics or overarching
domains recommended by the CCSSM for kindergarten may not be enough to
help teachers shift toward systematically providing more instruction on advanced
content and less on basic content most students have mastered. Our analyses
suggest that the instructional domains prescribed by the CCSSM are split
relatively evenly across items measuring basic and advanced content (based on
what students know at kindergarten entry) in the ECLS-K, and the effect of time
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spent on these CCSSM domains on student achievement was predictably mixed.
This suggests that teachers could simultaneously provide instruction that is
aligned with the CCSSM content domains and continue to overemphasize the
basics, to the detriment of learning for the vast majority of their students.
Our CCSSM measures are limited in that we have few items per domain
and the ECLS-K teacher surveys were not designed to measure alignment with the
CCSSM. Another important limitation of our CCSSM measures is that they do
not capture the cognitive complexity with which teachers approached each topic.
The CCSSM has been touted as a more conceptually-oriented, cognitively
demanding approach to mathematics education than previous state standards
(Schmidt & Houang, 2012), and much of this added complexity comes from the
information that goes beyond the recommended topics. For example, under the
kindergarten Counting and Cardinality domain, the CCSSM recommends that
teachers help students “understand that the last number name said tells the number
of objects counted” (Common Core State Standards for Mathematics, 2010). It is
possible that this type of conceptual emphasis could support student achievement
gains beyond rote counting exercises. Unfortunately, our measures only indicate
whether teachers reported spending time on particular content. One of the
limitations of the data that we use is that we are unable to discern more
information regarding how that content was taught.
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Further, we are unable to draw causal inferences due to the observational
nature of the data we use. As such, we cannot rule out possible omitted-variables
that could be driving our estimates. Teachers who spend more time on advanced
content could be qualitatively different from teachers who emphasize basic topics
in a variety of unobserved ways. However, some experimental evidence suggests
that designing professional development sessions that prevent early-grade
teachers from spending too much time on content that students had already
mastered can produce higher student-achievement gains (Clements et al., 2013).
This evidence suggests that professional development may be a means for
supporting kindergarten teachers in shifting some of their mathematics
instructional time to more advanced, as opposed to very basic, content.
Conclusion
Our central findings are clear: teaching students mathematics content that
they have not already mastered is positively associated with mathematics
achievement gains during kindergarten. Previous research indicates that time on
more advanced content in kindergarten benefits students at all ability levels, both
those who attended preschool and those who did not (Claessens et al., 2014).
Based on the results of our study and related research, we argue that education
policy and practice would benefit from efforts to help kindergarten teachers shift
some of their time on mathematics instruction from basic content to increase time
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spent teaching mathematics that students have not already mastered at
kindergarten entry.
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Notes
1. We note that while we consider our questions related to the CCSSM to be
important and interesting, our ability to draw conclusions with regard to the
CCSSM for kindergarten are limited. In terms of instruments, both the
achievement tests and the teacher questionnaires used in the two ECLS
kindergarten studies were created prior to the development and implementation of
the CCSSM. Thus, these data are not designed explicitly to explore the
relationship between the CCSSM, content, and student learning. We consider
these questions to be an extension of our primary analyses.
KINDERGARTEN MATHEMATICS MISALIGNMENT
25
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Table 1. Descriptive statistics for children and teachers from the ECLS-K and the ECLS-K:2011.
ECLS-K:1998-99 ECLS-K:2010-11 Difference P-Value
Child Characteristics
Full Day Kindergarten 0.61 0.87 0.26 0.001
White 0.58 0.52 -0.06 0.001
African American 0.15 0.13 -0.02 0.010
Hispanic 0.19 0.25 0.06 0.001
Asian 0.03 0.04 0.01 0.001
Other 0.05 0.05 0 0.029
Female 0.49 0.49 0 0.828
Age (in months at fall assessment) 68.44 68.48 0.04 0.579
Observations 17810 15090
Teacher Characteristics
Female 0.98 0.98 0.00 0.826
White 0.86 0.83 -0.03 0.004
Hispanic 0.04 0.08 0.04 0.001
African American 0.07 0.06 -0.01 0.709
Years teaching kindergarten 8.24 8.74 0.50 0.033
Observations 3020 3060
Note. Means were generated with the sample weights designed for non-response for each type of survey used. See
supplementary materials for information regarding the weights used. All non-missing cases for each variable were
used to calculate each respective mean. Values in the "difference" column represent the change in average teacher
and student characteristics between1998-1999 and 2010-2011. P-values denote the level of statistical significance
for the average change for each characteristic. Statistical significance was calculated using dummy-variable
regressions in which the two cohorts were pooled into a single dataset. P-values lower than .001 were rounded to
.001.
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Table 2. Cronbach's alphas, means, and standard deviations for Mathematics Content Measures created from teacher
survey items.
ECLS-K:1998-1999 ECLS-K:2010-2011
Mean
difference P-Value
Alignment Measures
%
Mastered
1998
α Mean
(days/month) SD
α
Mean
(days/month) SD
Basic Counting & Shapes (4 items) 92 0.58 12.73 4.16
0.58 13.17 3.94 0.44 0.925
Patterns & Measurement (5 items) 55 0.78 7.55 4.47
0.78 7.84 4.43 0.29 0.071
Place Value & Currency (4 items) 21 0.60 8.47 5.18
0.59 10.76 5.30 2.29 0.001
Addition and Subtraction (2 items) 3 0.88 7.84 6.57
0.86 9.66 6.52 1.82 0.001
CCSSM Content Area Measures
Counting and Cardinality (5 items)
0.59 11.46 3.99
0.60 12.79 3.77 1.33 0.001
Operations and Algebraic Thinking (2 items) 0.88 7.84 6.57
0.86 9.66 6.52 1.82 0.001
Numbers and Operations in Base Ten (2 items) 0.59 9.71 6.96
0.56 12.60 6.76 2.89 0.001
Measurement and Data (3 items)
0.78 8.12 5.28
0.76 8.55 5.25 0.43 0.006
Geometry (2 items)
0.49 9.28 5.62
0.59 9.42 5.79 0.14 0.006
Note. Means were generated with the sample weights designed for non-response in each cohort for the spring kindergarten teacher survey. See
the appendix text for information regarding the weights used. Only observations in the analysis samples were considered (ECLS-K-1999:
teacher N= 3020; ECLS-K:2011: teacher N= 3060), and all non-missing cases on each variable were used to calculate each respective mean.
See the appendix for means for each item used to generate the content measures. Values in the "difference" column represent the change in the
amount of time teachers spent on each topic between 1998-1999 and 2010-2011. Positive values indicate that teachers reported spending more
time on a given topic in 2010-2011. P-values denote the level of statistical significance in each reported content measure average change,
which were estimated using dummy-variable regressions in which both cohorts were pooled as one dataset. P-values lower than .001 were
rounded to .001.
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Table 3. Coefficients and standard errors from ordinary least squares regressions
predicting spring of kindergarten mathematics achievement with Alignment and
Common Core Measures of mathematics content.
1998-99 2010-11 1998-99 2010-11
Independent Variables (1) (2) (3) (4)
Alignment Measures
Basic Counting and Shapes
-
0.031*** -0.023**
(0.006) (0.007)
Patterns and Measurement -0.015* -0.020**
(0.006) (0.007)
Place Value and Currency 0.035*** 0.042***
(0.006) (0.006)
Addition and Subtraction 0.037*** 0.046***
(0.006) (0.007)
CCSSM Content Area Measures
Counting and Cardinality
0.013* 0.019**
(0.006) (0.007)
Operations and Algebraic
Thinking
0.036*** 0.044***
(0.006) (0.007)
Numbers in Base Ten
0.020*** 0.028***
(0.005) (0.006)
Measurement and Data
-0.011 -0.005
(0.006) (0.007)
Geometry
-0.027*** -0.040***
(0.006) (0.007)
Covariates X X X X
Observations 17810 15090 17810 15090
Note. Coefficients and standard errors were generated from 10 MI datasets for each
cohort, and both datasets were weighted with the "svyset" commands in Stata 13.0
according to the "base year" weights designed for use with student, parent, and teacher-
level measures. Standard errors were adjusted to account for sample designed clustering.
Standard errors are in parentheses. All coefficients displayed were generated from fully-
controlled models. See Appendix Table 4 for a full list of covariates. * p < .05, ** p <
.01, *** p < .001
KINDERGARTEN MATHEMATICS MISALIGNMENT
32
Figure 1. Student mastery rates and teacher reported coverage of mathematics content in kindergarten.
12.73
7.84
13.17
9.66
0
4
8
12
16
20
Days/Month Basic Counting & Shapes Days/Month Addition & Subtraction
1998-1999 2010-2011
In 1998, 92% of students had mastered Basic Counting & Shapes at kindergarten entry, whereas only 3% had mastered basic Addition & Subtraction.
92%
3%
Day
s p
er M
on
th