603982
research-article2015
EDRXXX10.3102/0013189X15603982Educational ResearcherMonth XXXX
Feature Articles
The Role of Schooling in Perpetuating Educational
Inequality: An International Perspective
William H. Schmidt1, Nathan A. Burroughs1, Pablo Zoido2, and Richard T. Houang1
In this paper, student-level indicators of opportunity to learn (OTL) included in the 2012 Programme for International Student
Assessment are used to explore the joint relationship of OTL and socioeconomic status (SES) to student mathematics
literacy. Using multiple methods, we find consistent evidence that (a) OTL has a significant relationship to student
outcomes, (b) a positive relationship exists between SES and OTL, and (c) roughly a third of the SES relationship to literacy
is due to its association with OTL. These relationships hold across most countries and both within and between schools
within countries. Our findings suggest that in most countries, the organization and policies defining content exposure may
exacerbate educational inequalities.
Keywords: comparative education; curriculum; equity; mathematics education; mixed methods; social class
T
he relationship of socioeconomic status (SES) and student
achievement is a well-established phenomenon (Chudgar
& Luschei, 2009). A compendium of research focusing
on the United States suggests that more-affluent students receive
greater investments from parents (Kaushal, Magnuson, &
Waldfogel, 2011) and higher-quality teachers (Boyd, Grossman,
Lankford, Loeb, & Wyckoff, 2009) and that these advantages
can be identified as early as preschool (Fernald, Marchman, &
Weisleder, 2013).
The United States generally has higher SES inequality than
other countries, as exhibited by its relatively large GINI coefficients (using World Bank, CIA, or Organisation for Economic
Co-operation and Development [OECD] data), lower socioeconomic mobility (Corak, 2013; D’Addio, 2007), and higher
childhood poverty rates (UNICEF report). However, SES is not
the only important contributor to student achievement. For
example, economic inequality alone does not account for the
middling performance of U.S. students on international assessments (Lenkeit & Caro, 2014; Sousa & Armor, 2010). Research
suggests that schools also play a large role in educational outcomes, whether through the structural characteristics of educational systems or through specific policies related to schooling
(Chudgar & Luschei, 2009; Fuchs & Woessman, 2007;
Hanushek & Woessman, 2005; Schlicht, Stadelmann-Steffen, &
Freitag, 2010), especially those related to the enacted curriculum
and curricular standards (Schmidt et al., 2001).
Much of the attention on the role of schools in mitigating
educational inequalities has focused on factors indirectly
influencing student learning, with a strong emphasis on school
inputs: resources, teacher quality, school autonomy, standardization, privatization, and class size. However, a small but significant
body of work is directed toward the role of curriculum, and particularly of educational content exposure (Schmidt & McKnight,
2012). Ultimately based on the work of Carroll (1963), the concept of opportunity to learn (OTL) rests on the logical proposition that students’ ability to learn a subject is dependent on
whether and for how long they are exposed to it in school.1
Early international studies by the International Association for
the Evaluation of Education (IEA), such as SIMS (Second
International Mathematics Study), included measures of OTL,
but the most extensive collection of such data occurred in the
original 1995 Third International Mathematics and Science Study
(TIMSS; Schmidt et al., 2001; Schmidt, McKnight, Valverde,
Houang, & Wiley, 1997). Those earlier iterations of the IEA studies included a number of OTL indicators based mainly on teacher
responses. The small number of classrooms sampled in any one
school (rarely more than two) and the steadily shrinking battery of
questions over time has limited the usefulness of TIMSS OTL
data for exploring issues of inequality. Similarly, the Programme
for International Student Assessment (PISA) has traditionally
relied on principal/headmaster surveys to gather data on student
sorting. Despite these limitations, Schmidt et al. (2001; Schmidt,
Cogan, Houang, & McKnight, 2011), Fuchs and Woessman
1
Michigan State University, East Lansing, MI
Organisation for Economic Co-operation and Development, Paris, France
2
Educational Researcher, Vol. 44 No. 7, pp. 371­–386
DOI: 10.3102/0013189X15603982
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October 2015 371
(2007), and Dumay and Dupriez (2007) found that greater OTL
in mathematics was related to higher student achievement in
mathematics. Studies focused on the United States similarly demonstrate a relationship between OTL and mathematics learning
(Gamoran, Porter, Smithson, & White, 1997; Reeves, 2012;
Rowan, Correnti, & Miller, 2002). Further, research based on the
2006 PISA found a relationship between science content indicators (content coverage, instructional time, course work) and student outcomes (Sousa & Armor, 2010; Willms, 2010).
Although there is strong evidence that OTL influences student achievement, it remains an open question whether variations in instructional content coverage are related to educational
inequalities, in particular, achievement gaps among different
SES groups. Although Chudgar and Luschei (2009) questioned
whether schools mediate SES achievement inequality, other literature indicates that curricular differentiation leads to unequal
outcomes, for example, through tracking—that the separation
of students into different courses with different content exposure
tends to mirror background inequalities.
Work by Oakes (1985) details the nature of curricular differentiation in the United States, describing how low-income students
are explicitly and implicitly routed into classes with lower time on
task and weaker instructional quality. But tracking is not simply a
U.S. phenomenon; there is an international literature examining
the influence of curricular differentiation on educational inequality. Tracking and curricular differentiation have been operationalized in a number of different ways in comparative educational
research: age of first tracking/selection, number/type of programs,
between-school segregation, selection policy, and types of courses.
Nearly all studies have found that tracking exacerbates SES
inequality (e.g., Causa & Chapuis, 2009; Chmielewski, 2014;
Horn, 2009; Montt, 2011; Schlicht et al., 2010; Schmidt, 2009;
Schmidt & McKnight, 2012; Vandenberghe, 2006). Studies of
U.S. tracking also suggest that inequalities in OTL among U.S.
students contributes to educational inequality (Schmidt &
McKnight, 2012). Abedi and Herman (2010) and Wang (2010)
found that OTL also is related to achievement gaps for English
language learners and minority children, respectively.
Most of the measures employed in these studies aggregate students, from simple country-level dummy variables to measures
based on a few classrooms. Distinct from this general pattern is
Chmielewski (2014), who makes use of student-level survey
responses identifying different courses taken to distinguish
between course-by-course “à la carte” tracking and more systematic educational streaming (see also Abedi & Herman, 2010).
Notably, Chmielewski finds that both systems of curricular differentiation are characterized by large SES achievement gaps.
Chmielewski’s (2014) work is an advance in that it identifies
types of courses, rather than broad educational tracks, but it does
not account for the variation in content coverage among the same
types of classes. Cogan, Schmidt, and Wiley (2001) and Brown
et al. (2013) revealed that two classes with the same course title
and the same school could offer very different content. This difficulty is a specific example of a more general problem: that most
studies have relied on indicators of curricular differentiation too
imprecise to identify the effects of unequal classroom content.
One exception is Schmidt (2009), who addresses whether
content coverage mediates the effect of tracking. Using the 1995
TIMSS data (the only data set where the sampling information
was extensive enough to do these analyses), a series of statistical
models fitted to eighth-grade data indicated that “controlling for
prior student achievement and SES the estimated effect for the
algebra track compared to the regular mathematics track was
about two-thirds of a standard deviation” (Schmidt, 2009, p. 28).
To date, most studies of curricular differentiation have lacked
detailed data on the content of instruction that are (a) directly
relatable to the individual student, (b) capable of differentiating
within-school differences beyond those at the classroom level,
and (c) more specific than broad categories or course titles. To
the final point, identifying general tracks or course titles presumes that there are real differences in the content offered to
students without directly measuring it. Differentiation need not
be explicit to generate inequalities. Second, school- or classroomlevel measures of differentiation cannot adequately capture the
degree of curricular inequality within schools. TIMSS’ sampling
of two classrooms in the same school was a step in the right
direction, but such a limited sample could yield only partial
insights into within-school variation, depending on the extent of
the tracking within schools and how the two were sampled.
As argued in Schmidt and Burroughs (2013), properly
accounting for the joint effect of class composition and OTL
requires more specific student-level measures (see also Dumay &
Dupriez, 2007) or else risks model misspecification. Schmidt
et al. (2001) suggests that OTL is directly related to student
achievement, and district-level analyses by Schmidt, Burroughs,
and Houang (2012) based on the TIMSS finds a positive association between SES and exposure to mathematics content. These
findings imply a model in which SES has a direct effect on student outcomes but also an indirect effect through OTL (see
Figure 1). In other words, OTL may be an important mediator
for the effects of SES.2 Studies that exclude OTL from their analyses might as a result obtain biased estimates, as part of the relationship that appears to be due to unequal background conditions
may in reality be due to unequal curricular opportunities. Such a
finding would have major implications for researchers and policymakers alike, given that OTL is far more subject to educational
policies than are broader socioeconomic conditions.3
In this paper, we address the question of whether variations in
instructional content coverage (OTL) are related to achievement
differences in mathematics literacy among various SES groups.
To explore this question, we address it with three distinct but
related research questions.
1.
2.
3.
What is the joint relationship of SES and OTL to PISA
literacy at both the between- and within-school levels?
What is the relationship of both between- and withinschool inequalities in OTL to the corresponding
between- and within-school inequalities in SES and how
those inequalities relate to differences in achievement?
To what degree does content coverage (OTL) function as
a meditator of SES in its relationship to achievement?
We address these questions using three analytical strategies.
The first two reflect methods used in the existing literature:
treating SES as a predictor of achievement (Analytical Strategy
1) and modeling SES-related achievement gaps as an outcome
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Content
Coverage
Student
Learning
SES
Figure 1. The conceptual model
variable (Analytical Strategy 2). Our third approach employs a
structural model to examine OTL as a mediator of SES
(Analytical Strategy 3).
Data Sources
The lack of data with which to study student-level curricular
differentiation and its relationship to SES inequality in multiple
countries has been partly remedied by the most recent PISA
study. The 2012 iteration of PISA surveyed students about the
intensity of their exposure to selected mathematics topics. The
release of these data means that for the first time, we have access
to a representative sample comprising indicators of student
mathematics knowledge, socioeconomic background, and exposure to mathematics OTL across 33 OECD and 29 non-OECD
countries.4 Because the PISA study randomly samples all
15-year-olds within a sampled school, it also yields information
about the full range of opportunities to learn in a given educational setting, rather than only in one or two classes. The sample
of students questioned about OTL is smaller than the general
PISA sample (two thirds of students were given those questions)
yet nevertheless yields an adequate sample size for analyses that
is representative of the country as a whole.
In our analyses, we relied principally on three PISA variables
measured at the student level: student mathematics literacy,
OTL formal mathematics, and an index of economic, social, and
cultural status (ESCS).
The PISA survey used a stratified cluster sampling design,
with schools and students within school sampled randomly. A
sample of 15-year-olds (across multiple grades) was taken from
each selected school. Sampling that target population resulted in
a sample of students that ranged in age from 15 years and 3
months to 16 years and 2 months. The survey used a random
rotated block design. The test items were scaled for difficulty,
and a unitary scale was developed to estimate a student’s knowledge of mathematics literacy, with an OECD mean of 500 and a
standard deviation of 100. Individual student scores were estimated by five plausible values. As a result, the analyses reported
in this paper were repeated five times with the mean serving as
the estimate of the various parameters. The corresponding standard errors were calculated following Mislevy (1991) and OECD
(2014, p. 148).
The ESCS is determined through a principal component
analysis of three separate indices: parental occupation, parental
education (measured by years of schooling), and household possessions. Household possessions in turn is a combination of family wealth (determined by student survey responses to items in
the home), number of books in the home, and number of cultural possessions. Each index is standardized, and the overall
scale has an OECD mean of 0 and a standard deviation of 1.5
The OTL measure was developed by student responses to
two separate questions as follows:6
Two separate scales were constructed using the item asking for
the degree of the student’s familiarity with 7 of the 13
mathematics content areas (Question 2). The five response
categories reflecting the degree to which they had heard of the
topic were scaled 0 to 4 with 0 representing “never heard of it” 4
representing they “knew it well”. [As stated in another section of
the report, “having heard of a topic more often was assumed to
reflect a greater degree of opportunity to learn” (OECD, 2014,
p. 146).] The frequency codes for the three topics—exponential
functions, quadratic functions, and linear equations—were
averaged to define familiarity with algebra. Similarly, the average
of four topics defined a geometry scale, including vectors,
polygons, congruent figures, and cosines.
The third scale was derived from the item where students
indicated how often they had been confronted with problems
defined as formal mathematics (Question 4). The frequency
categories were coded as “frequently”, “sometimes”, and “rarely”
equalling 1 and “never” equal to 0, resulting in a dichotomous
variable. The algebra, geometry and formal mathematics tasks
were averaged to form the index “formal mathematics”, which
ranged in values from 0 to 3, similar to the other three indices.
(OECD, 2014, pp. 172–173)
In our study, we focused on formal math for two reasons:
because it more closely resembles the conception of OTL
employed in previous research and, second, recent studies suggest that formal mathematics OTL exhibits greater diversity
than the other PISA OTL measures and has a stronger relationship to student achievement (Schmidt, Cogan, & Zoido, 2014;
Schmidt, Zoido, & Cogan, 2013).
Several control variables employed in the analyses are also drawn
from the student-level PISA data, including student sex, age, grade,
and whether the test was administered in the student’s first language. Finally, responses from the PISA principal’s survey were
merged with the individual student data in order to include an
additional two indicators of curricular differentiation: grouping by
ability between classes (referred to as tracking) and grouping by
ability within classes (referred to as ability grouping). These are
relatively blunt indicators, since principals were asked only whether
such clustering occurs never, frequently, or always within the
school.
A working paper by Schmidt et al. (2013) provides preliminary evidence (a) that there was a wide variation in OTL, SES,
and mathematics literacy within and across all 62 countries and
(b) that in nearly every country, the SES and OTL variation was
greater within schools than between them. For OECD countries, on average, 64% of variation in performance, 76% of variation in SES, and 80% of variation in OTL was within school,
with considerable variation between countries.
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Analytical Strategy 1
Several methods for analyzing the relationship of curricular differentiation to inequality have been employed in the literature. One
common means is to use an indicator of SES as a predictor variable
in a regression equation and to assess whether its coefficient varies
with the inclusion of other measures (Ammermuller, 2005; Causa
& Chapuis, 2009; Marks, Creswell, & Ainley, 2006; Chmielewski,
2014; Schlicht et al., 2010). A related approach uses interaction
terms of SES and a curricular variable (such as tracking; Horn,
2009; Schutz, Ursprung, & Woessman, 2008). Another common
empirical strategy is to directly model the influence of curricular
variables with SES achievement gaps serving as an outcome variable. SES inequality is measured using the difference between a
high-SES and a low-SES group, defined by deciles (Reardon &
Chmielewski, 2012), terciles (Causa & Chapuis, 2009), or quartiles (Duru-Bellat & Suchaut, 2005). Another method uses the
explanatory power (e.g., adjusted r-square) of regressing SES on
student performance (Dupriez & Dumay, 2006).
We will employ modified versions of most of these approaches
to test the hypothesis that greater inequalities in OTL are associated with higher SES-related inequality. However, we chose not
to adapt the strategy of using total variation in achievement as
the dependent variable (Hanushek & Woessman, 2005; Mont,
2011), which to be useful in this context requires the partitioning of the total variation along SES-related lines. Put simply, the
total variance as a dependent variable is not an accurate measure
of SES or OTL inequality.
Our approach builds on the work of Schmidt et al. (2013),
which employed modeling at three levels (country, school, and
student) and two levels (student and school) for each participating PISA country. Schmidt et al. estimated the relationship of
(centered) school- and student-level SES and OTL variables
both separately and in combination. They found that studentand school-level OTL had a statistically significant relationship
to performance whether or not SES was included. Further, they
found accounting for OTL reduced the size of SES coefficients.
Replication of the Schmidt et al. analyses confirms their results.
Using a three-level model with individual SES and OTL centered on the school mean and school average SES and OTL centered on the country mean, we found that student-, school-, and
country-level indicators of SES and OTL had a statistically significant relationship to student mathematics performance on the
PISA. The inclusion of both variables into a single model
reduced the size of the student-level SES coefficient by 32%, but
the positive coefficient for the student-level OTL variable was
essentially the same being reduced by only 5%.
Similarly, two-level (school and individual) analyses within
each country indicated that these relationships were quite consistent across PISA participants. In the full model, SES continued to have a statistically significant relationship with student
mathematics outcomes in most countries (57 of 62), whereas
OTL was significant in all but one (Sweden). In comparison
with the SES-only model, the size of student- and school-level
SES coefficients was reduced for 62 countries, with an average of
about one third in the OECD.
The Schmidt et al. (2013) three-level model is open to considerable elaboration, however. The argument is not simply that
OTL influences student learning controlling for SES but that
the organization of schools and classrooms have a joint relationship to educational outcomes. The inclusion of OTL on the predictive side of the equation does not address the possibility of an
interrelationship between student background and learning
opportunities. Our revised model included interaction terms of
SES and OTL at the student and school levels. Supplementary
indicators of curricular differentiation at the school level on the
prevalence of tracking and ability grouping were added to the
model as controls, as were the age, grade, sex, and student’s
foreign-language status.
The results of these analyses are displayed in Table 1. As with
Schmidt et al. (2013), student- and school-level SES and OTL
had a statistically significant relationship with student mathematics literacy. Consistent with other literature, males and native
speakers generally did better on the mathematics assessment,
and tracking and ability grouping were both negatively associated with student performance. Older students and those in earlier grades generally did worse. The fact that the estimated
coefficient relating grade level to performance was large and
positive may reflect OTL not captured by the formal math variable, given the likely difference in content coverage across grades.
The hypothesis that SES and OTL have an interactive effect on
student mathematics literacy receives partial support at the student level, with a statistically significant relationship in the full
model. Notably, the interaction effects were stronger at the
school than at the individual level, a finding that is not dependent on the inclusion of within-school differentiation (tracking
and grouping). These results suggest that much of the SES-OTL
interaction may be between rather than within schools, a possibility we explore in the next section.
Analytical Strategy 2
Unequal learning opportunities are often treated as occurring
between schools. In the United States, there is considerable public attention on the problem of “failing schools”—schools that are
often high poverty, have a large proportion of minority students,
and are lower achieving. The relationship between lower SES and
weaker OTL in the United States has been demonstrated by
Schmidt and McKnight (2012) and is likely related to the pattern
of U.S. residential segregation by wealth. In many countries,
inequality between schools is a product of educational policy
rather than housing patterns. Many OECD nations have a longstanding tradition of segmenting students into vocational and
preparatory institutions, with a recent recognition that affluent
students are more likely to be routed into rigorous schools.
Schmidt et al. (2013)’s analysis highlighted the relationship
of between-school inequalities in OTL to between-school
inequalities in SES. Dividing schools into SES quartiles relative
to that country’s average school SES, they calculated the average
difference in OTL for schools in the top and bottom quartiles.
They found a statistically significant gap in OTL in all but two
educational systems, with an average gap of one half a point on
the PISA formal mathematics index. Further, the mean betweenschool OTL gap accounted for around half (R2 = .49) of the
corresponding average between-school variation in performance
across countries (see Figure 2).
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Table 1
Three-Level Models Predicting PISA Mathematics Literacy
Variable
Model 1
Model 2
Model 3
Model 4
Model 5
486.8*
14.6*
390*
392.6*
10*
41.7*
38.5*
83.7*
47*
54.3*
391.1*
10*
41.7*
38.1*
84.2*
47.3*
54.7*
0.36
8.5*
3498109
3498058
491*
8.5*
36.8*
33.7*
75.3*
41.7*
53.5*
0.65*
12.8*
–1.2*
–1.5*
17.2*
–8.3*
–7.1*
26.2*
3202029
Intercept
Student SES
Student OTL
School SES
School OTL
Country SES
Country OTL
SES × OTL
SKSES × SKOTL
Tracking
Grouping
Male
Language
Age
Grade
Avg –2LL
44*
64.9*
122*
44.6*
47.9*
3537863
3506238
Note. PISA = Programme for International Student Assessment; SES = socioeconomic status; OTL = opportunity to learn; SKSES = school mean SES centered on country
means; SKOTL = school mean OTL centered on country means.
*p < .05.
180
Czech Republic
160
Between-School Performance Gap
140
Israel
Turkey
Korea
Italy
New Zealand
Greece Portugal United Kingdom
Ireland Luxembourg
80
Canada
Estonia
60
Chile
United States
Poland
Denmark
Netherlands
Germany
Japan
120
100
France
Slovak Republic
Belgium
Hungary
Slovenia
Austria
Australia
Switzerland
Spain
Mexico
Iceland
Sweden
Finland
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Between-School OTL Gap
Figure 2. Relationship of size of opportunity-to-learn gap and performance gap, between school level
However, buttressing earlier research based on TIMSS
(Schmidt, McKnight, Cogan, Jakwerth, & Houang, 1999), the
PISA demonstrates that in virtually all 62 countries the majority
of socioeconomic and curricular variation exists within rather
than between schools. To further investigate this point, in each
country we divided students participating in the 2012 PISA into
four quartiles by the PISA SES index (ESCS). Rather than a
single, international standard of what constitutes a low-, middle-, or high-SES student, we allowed those categories to be
defined within each country—which also helps alleviate concerns that the meaning of SES might differ across countries as
well as incorporates both relative and absolute disadvantage.
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We divided schools into SES quartiles using average school
ESCS and quartiles defined within each country. We then identified the proportion of students who were in a school that matched
the school SES profile, that is, the percentage of lower-SES students in a country in a lower-SES school and of higher-SES students in higher-SES schools. The results of the analysis cast doubt
on the assumption that inequality is mainly a between-school
problem or that analysis of between-school inequalities accurately
reflects the overall inequality in a country’s educational system. If
students were randomly distributed across schools, we would
expect to find roughly 25% of high-SES students in high-SES
schools, 50% in middle-SES schools, and 25% in low-SES
schools. In that case, there would be no meaningful ranking of
schools within country on overall SES, as the schools would all be
essentially the same. As the percentage of a country’s low-SES
students in low-SES schools increases beyond 25%, the resulting
SES segregation would impact a greater number of low-SES students’ OTL since the previous analysis has shown large average
OTL gaps between the low-SES schools and the high-SES
schools. This suggests the hypothesis that the relationship of SES
and OTL would be related to the degree to which a country segregates the low-SES students. The data suggest significant SES
segregation but also considerable diversity across countries.
Among OECD countries, an average of 48% of low-SES students attended low-SES schools, and 53% of high-SES students
attended high-SES schools. These averages, although representing many countries, including the United States, mask massive
variation across countries, with some having higher SES segregation between schools (e.g., Luxembourg, Mexico, and Hungary)
and some much lower (e.g., the Nordic countries, such as
Sweden, Finland, and Iceland). At one extreme, over three quarters of Chile’s low-SES students (78%) and high-SES students
(89%) went to school with similarly situated 15-year-olds. At
the other end, Norway exhibited more commonality in student
background between schools, with 19% of low-SES students
and 33% of high-SES students attending poorer and richer
schools, respectively.
The socioeconomic heterogeneity of schools raises the prospect of within-school achievement gaps. Previous research has
estimated countrywide SES achievement gaps using the average
score difference between the top and bottom SES quartiles, and
Schmidt et al. (2013) has extended this analysis to average
between-school achievement differences. Because the PISA data
include student-level data, they permit the estimation of average
within-school SES achievement gaps by determining the difference between first and fourth SES quartile (defined separately
for each country, as above) for each school, and then averaging
across all schools within a country. Further, the student-level
OTL measures included in the PISA survey allow us to estimate
OTL gaps through an identical procedure of taking the average
difference in OTL between SES groups.
The mean OTL and performance gaps between top and bottom
SES quartiles are presented in Table 2, including between-school,
within-school, and overall country gaps. Substantial SES withinschool achievement gaps exist in most countries, with an average
44-point difference in PISA scores in OECD countries (approaching half a standard deviation), ranging from New Zealand’s 74
points to Slovenia’s mere 7 points. Within-school achievement gaps
are smaller than between-school gaps in every country but Sweden
and Finland but are still appreciable, with an average of 42% the size
of the mean between-school gap of 105 points.
The data also show similar inequalities in OTL, with a .27
average OECD difference in OTL within school and .46
between schools, with substantial variation across countries.
One unexpected finding was the particularly large within-school
OTL gaps in English-speaking countries, with the United States
(No. 2), New Zealand (No. 3), Australia (No. 4), United
Kingdom (No. 5), and Ireland (No. 7) all in the top 10 of the
PISA sample of countries (and four in the top five). These findings reinforce the point that the abolition of formal differentiation between or within schools may conceal the persistence of
unequal learning opportunities.
We next use the estimates of within-school inequality between
the top and bottom SES quartiles to analyze the relationship
between inequalities in OTL (the OTL gap) and inequalities in
student performance (PISA math scores). Earlier studies employing SES achievement gaps as an outcome variable (Duru-Bellat
& Suchaut, 2005; Reardon & Chmielewski, 2005; Causa &
Chapuis, 2009) relied on country-level aggregates, but in this
analysis, the school serves as the unit of analysis, with the difference between the mean top- and bottom-SES-quartile PISA
scores serving as the dependent variable. The main independent
variable is the difference between the mean top- and bottomSES OTL. Mean school SES and OTL, grade, age, language status, and gender are included as controls, as are the school-level
tracking and grouping measures. We examined this issue with
both OLS regressions done within each country separately and
by combining countries in a pooled within-country regression
analysis.
The findings of both types of analysis are quite comparable.
Countries with larger average differences in OTL between high- and
low-income students within the same school tend to have larger
average differences in performance. The results of the pooled withincountry analysis (see Table 3) suggest that a one-unit increase in a
school’s OTL gap is associated with a 31-point increase in the SES
achievement gap (about a third of a standard deviation).
Turning to the ordinary least squares regressions for each
country separately, the association between within-school OTL
and within-school performance inequalities is positive for every
OECD country (and 59 of the 62 in the PISA sample) and statistically significant for 23 of the 33 OECD countries and 20 of
the 28 non-OECD systems.7 Again, the strength of the relationship of the two gaps is particularly strong in English-speaking
countries: Ireland (No. 1), the United Kingdom (No. 2), New
Zealand (No. 3), and Australia (No. 4) are in the top five of
OECD countries, with the United States and Canada above
average but closer to the OECD mean. Other than these Englishspeaking countries, Belgium, Estonia, Ireland, Japan, Korea, and
Spain also exhibited a strong statistically significant relationship
between the two gaps. Countries in which the strength of the
relationship between inequalities in OTL and performance was
the least among the 33 OECD countries include Germany,
Greece, Iceland, Slovenia, and Luxembourg, where the estimated
relationship was small, positive, and not statistically significant.
(Note that these are within-school, not between-school,
inequalities.)
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Table 2
Mean Differences in OTL and Performance Between Top and Bottom SES Quartiles
Country
Country
Australia
Austria
Belgium
Canada
Chile
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Israel
Italy
Japan
Korea
Luxembourg
Mexico
Netherlands
New Zealand
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
OECD average
Between School
Within School
OTL Gap
Performance
Gap
OTL Gap
Performance
Gap
OTL Gap
Performance
Gap
0.59
0.7
0.68
0.4
0.55
0.42
0.46
0.2
0.35
0.54
0.54
0.34
0.48
0.32
0.48
0.49
0.41
0.36
0.45
0.63
0.39
0.52
0.67
0.32
0.44
0.53
0.36
0.63
0.23
0.54
0.34
0.54
0.54
0.47
92
94
117
77
99
101
88
65
72
121
93
90
117
65
84
115
76
79
79
106
62
84
119
96
111
126
93
92
83
88
85
94
92
93
0.58
0.85
0.71
0.31
0.49
0.57
0.37
0.11
0.18
0.67
0.74
0.31
0.53
0.19
0.4
0.32
0.55
0.47
0.57
0.46
0.38
0.81
0.58
0.18
0.36
0.69
0.48
0.44
0.2
0.59
0.39
0.46
0.36
0.46
99
112
146
67
89
154
72
60
39
156
141
101
145
57
96
131
115
125
120
102
67
151
114
82
101
150
142
72
55
95
127
102
84
105
0.43
0.28
0.39
0.34
0.22
0.15
0.34
0.14
0.33
0.24
0.18
0.22
0.07
0.31
0.4
0.36
0.15
0.12
0.23
0.41
0.15
0.2
0.45
0.28
0.3
0.17
0.13
0.48
0.19
0.3
0.16
0.42
0.47
0.27
56
34
38
57
24
25
66
46
70
46
28
46
21
49
56
61
13
13
32
35
18
15
74
69
70
50
7
67
67
50
15
57
60
44
Note. OTL = opportunity to learn; SES = socioeconomic status; OECD = Organisation for Economic Co-operation and Development.
It is important to note that the traditional methods by which
within-school differentiation is measured—tracking and grouping—
are no longer statistically significant once the OTL gap is controlled for. This finding reinforces the role student sorting plays
in exacerbating SES inequalities but also suggests that OTL
accounts for most of the tracking effect, a result supporting the
results of Schmidt (2009). There is certainly variation across
countries in the magnitude of the relationship, but the results
support the idea that the unequal learning opportunities available to lower-income students exacerbates unequal student outcomes whether one is referring to students in different schools or
within the same school.
Analytical Strategy 3
So far we have mainly extended the existing body of research,
making use of the characteristics of the PISA to test the influence
of OTL on student achievement and to elaborate on the literature
by incorporating within-school effects. Our principal focus in
this section is to explore the degree to which OTL functions as a
mediator of SES. In the previous sections, related analyses have
been somewhat oblique, using interaction terms on the predictive
side of the equation or moving SES to the dependent side of the
equation in the form of interquartile differences. In both cases,
there was support for the hypothesis that curricular differences
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Table 3
Two-Level Model Predicting School SES
Achievement Gaps
Effect
Intercept
OTLGAP
SKSES
SKOTL
Tracking
Grouping
SKGRADE
SKAGE
SKMALE
SKLANG
CNTOTL
CNTSES
Estimate
SE
p Value
610.31
31.05
2.56
8.62
0.16
–0.43
–3.58
–34.98
–3.6
–2.77
–8.95
14.2
96.6
1.24
2.08
2.09
1.18
0.76
2.47
5.74
2.65
2.89
6.25
3.04
<.0001
<.0001
.2175
<.0001
.8906
.5741
.1474
<.0001
.1754
.3391
.1525
<.0001
Note. SES = socioeconomic status; OTLGAP = difference in mean opportunity
to learn (OTL) between the top-quartile-SES students and bottom-quartile-SES
students; SKSES = school mean SES centered on the country mean SES; SKOTL =
school mean OTL centered on the country mean OTL; SKGRADE = school mean
grade level; SKAGE = school mean age; SKMALE = percentage of students who
are male; SKLANG = percentage of students whose primary language is other than
the language of the test; CNTOTL = country mean OTL; CNTSES = country mean
SES.
mediate socioeconomic inequalities’ relationship to student performance. In this section, we test this proposition more directly.
Given the nature of the proposed relationships in Figure 1,
the most straightforward method for exploring the interrelationship of SES, OTL, and student performance is through a structural (path analytic) model. Our approach is similar to that of
Reeves (2012), although the former relies on course titles rather
than student-level measures of content and is restricted to U.S.
data. For the purposes of this study, we used a simple, threevariable saturated model. To characterize the overall relationship
within a country, we pooled all students, ignoring schools, to
estimate the total variance-covariance matrix.
As discussed above, differing educational systems exhibit distinct approaches to clustering students and differentiating
instructional content, leading to structural differences that are
important in understanding the policy implications of these
analyses. To explore those issues, we also estimated the OTLSES-performance path analysis model for between-school differences and within-school differences. Assuming the multivariate
random-effects model as both schools and students within
schools were randomly selected, the total variance-covariance
matrix for a country is equal to the sum of the variance component matrices for the between and within-school as follows:
ΣT = Σ B + Σ w ,
where
ΣT is the total variance-covariance matrix for a country,
ΣB is the between-school variance component matrix representing the variation/covariation attributable to betweenschool differences, and
Σw is the total within-school variance component matrix representing the variation/covariation attributable to withinschool differences including both between-classroom and
between-students-within-classrooms differences.
We estimated ΣT with the overall sample covariance matrix
and, using maximum likelihood procedures, estimated the two
component matrices ΣB and Σw. The three matrices were then
used as the sufficient statistics for estimating the three structural
models for each country. Both least squares and maximum likelihood procedures were used in estimating the structural equations and were found to lead to the same general conclusions.
The overall country results are presented first, ignoring for the
moment the subdivision of the covariance matrix, ΣT , into its
between and within components.
The focus in this section of the paper is on the relationship of
SES to PISA performance as it is mediated by OTL. As a result,
the findings from those analyses for the 33 OECD countries
focus on the estimated total, direct, and indirect effects for SES.8
The estimated path coefficients among SES, OTL, and performance as hypothesized by the model (see Figure 1) were statistically significant at the .05 level across 32 of 33 OECD
countries. The magnitude of the direct relationship between
OTL and PISA performance controlling for SES was consistent
with Schmidt et al. (2013). The OECD average was 60, suggesting an effect size of three fifths of a standard deviation. Three
countries stand out for their somewhat extreme values. Korea
and Japan had estimated values of around 100 (a full standard
deviation), and Sweden’s estimated path coefficient was only 5
(5% of a standard deviation).
The total effect for SES includes not only its direct effect
(controlled for OTL) but also the indirect effect SES has on performance through its relationship to OTL and, correspondingly,
OTL’s direct effect (controlled for SES) on performance. In
reporting these analyses, we use the traditional path analytic way
of referring to the estimated relationships as defined by the path
coefficients as effects, recognizing the difficulties in establishing
causal inferences.9
The first question we asked was, Does the estimated size of
the total relationship of SES to performance depend on its
source (direct vs. indirect)? For the 33 OECD countries, the
short answer is no. To illustrate, there are two ways of characterizing the nature of the relationship of SES to performance and
hence to the degree of inequality: by the size of the total SES
effect and by the percentage of that effect that is indirect or
direct. Contrasting the countries in which the total SES effect
was the largest with those for which the largest percentage of the
total effect was indirect or direct shows the relatively weak relationship between the two (R2 = .09); few countries ranked similarly on the two measures (e.g., Austria and Estonia).
Figure 3 portrays the size of the estimated total effect of SES
on PISA performance for each country further subdivided by the
relative contribution that is indirect versus direct. There is a large
variation across the 33 countries, with an average total SES effect
size of 39, ranging from 19 in Mexico to 58 in France. The average proportion of that total effect that was attributable to the
indirect effect was one third but varied appreciably, ranging from
1% in Sweden to 58% in the Netherlands.
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France
Slovak Republic
Israel
New Zealand
Belgium
Hungary
Korea
Austria
Australia
Czech Republic
Japan
Germany
Poland
Slovenia
United Kingdom
Switzerland
Denmark
Ireland
Netherlands
Luxembourg
United States
Portugal
Greece
Chile
Sweden
Finland
Spain
Turkey
Italy
Iceland
Canada
Estonia
Mexico
SES Direct
SES Indirect
0
20
40
60
80
Figure 3. Estimated total, direct, and indirect effect for
socioeconomic status at the country level
With respect to inequality, the countries can be ordered by
the sizes of (a) the total SES effect and (b) the indirect effect. The
first orders the countries in terms of an overall measure of
inequality relating SES to PISA performance. The second orders
the same 33 countries by the size of the inequality resulting from
schooling, the major component being driven by the relationship of SES to OTL. The latter is the most malleable with respect
to educational policy.
The countries in which the total SES effect is most prominent include the Slovak Republic, France, Israel, and New
Zealand, but when we focus only on that part of the total effect
due to schooling, as defined by OTL, Australia, Korea, Japan,
and the Netherlands rank the highest. Most relevant to this
paper is that the size of the indirect effect of SES in many countries is a relatively large contributor to the total SES effect. This
suggests that the perceived role of schooling as the “great equalizer” may well be a myth and that the reality is better characterized as the “exacerbater.” Consider especially Australia, Korea,
and the Netherlands, where over one half of the total estimated
effect contributed by the relationship of SES to performance is
mediated by OTL.
Given that on average a third of the inequality in the OECD
countries was contributed indirectly as mediated by OTL, the
question arises as to whether it is possible for a country to have
both high average PISA performance and high equality (i.e.,
where SES does not determine the coverage of important mathematics content). We divided the 33 countries into four quadrants using the OECD means for PISA performance and the
New Zealand
Finland
Denmark
Poland
Sweden
Spain
Switzerland
Ireland
Australia
Israel
Iceland
United States
Slovak Republic
Portugal
United Kingdom
France
Canada
Greece
Belgium
Estonia
Luxembourg
Korea
Austria
Germany
Czech Republic
Chile
Netherlands
Italy
Turkey
Mexico
Hungary
Japan
Slovenia
SES Direct
SES Indirect
0
10
20
30
40
Figure 4. Estimated total effect size for socioeconomic status
(including direct and indirect effects) at the within-school level
indirect SES effect. The fact that all four quadrants (especially
the first quadrant) were populated with OECD countries indicates that high performance and greater equity are not mutually
exclusive. This implies that countries can be both relatively high
performing and equitable, as evidenced by Canada, Poland,
Finland, and Estonia.
Since the PISA data were randomly collected at the school
and student levels, we were able to estimate the three coefficients
of the structural model at both the school and within-school
levels. This is important since each country has its own particular educational structure and policies governing curricular differentiation. The degree to which these are related to SES also
varies. Of critical importance is the variation in how countries
cluster their students according to SES and curricular opportunities, with major differences in how differentiation occurs
between schools and within schools.
Turning first to within-school relationships, we show in
Figure 4 statistically significant relationships along all three paths
for nearly all countries, with an OECD average OTL effect of 45
and an SES total effect of 19 (13 direct, 6 indirect). SES was
positively related to OTL in all 62 educational systems in the
PISA sample.10 As with the overall results, the SES-OTL relationship accounts for roughly a third of the total SES effect on
performance, with sizable variation across countries, ranging
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Netherlands
Japan
Czech Republic
France
Korea
Slovenia
Israel
Belgium
Slovak Republic
Germany
New Zealand
Austria
Hungary
Australia
United Kingdom
Switzerland
SES Direct
Italy
SES Indirect
Turkey
Luxembourg
Ireland
Greece
Sweden
Poland
Denmark
Iceland
Canada
Finland
United States
Estonia
Portugal
Chile
Spain
and the smallest in Sweden and Estonia. Further, the relationships between SES and OTL were greatest in a group of European
countries: the Netherlands, Austria, Switzerland, and Germany.
As with the within-school analyses, SES was related to OTL
for between-school differences, increasing the effect of SES on
PISA performance. In the Netherlands and Korea, all of the very
large total SES effect was derived from the SES-OTL relationship, together with the largest effect sizes for OTL at the
between-school level. The size of the path coefficients relating
SES to OTL and the range in values were quite large. The large
values exhibited for the Netherlands, Austria, Switzerland, and
Germany are most probably related to the structure of schooling
at the secondary level in those countries. Although the tracking
between schools is not explicitly defined by SES, these data
would suggest that the sorting mechanisms are strongly associated with student background. In the Netherlands and Korea,
the resulting size of the indirect effect is very large. SES is also
strongly related to OTL in France and Belgium.
The preceding results from the between-school and withinschool analyses reveal considerable variation across countries in
within-school and between-school differentiation. For example,
although Korea has the largest OTL path coefficient at both the
between- and within-school levels, Turkey has a coefficient
whose magnitude ranks it 30th at the within-school level but 4th
at the between-school level. Other countries, such as Finland,
show a relatively much larger estimated effect for OTL at the
within-school level when compared to the other countries but a
much smaller one at the between-school level.
Discussion
Mexico
0
50
100
150
200
Figure 5. Estimated total effect size for socioeconomic status
(including direct and indirect effects) at the between-school level
from the indirect effect accounting for nearly three quarters
(Japan) to less than 10% (Iceland and Sweden). In 23 out of the
33 OECD countries, the inequalities contributed through
schooling represent 25% or more of the total SES effect on PISA
performance. It is interesting to note that ranking countries by
the size of the estimated indirect effect of SES reveals that in
English-speaking countries, including the United States, SES has
a relatively stronger relationship to within-school learning
opportunities, comprising five of the top seven educational
systems.
The results of the path analysis for differentiation between
schools again shows positive and statistically significant but
highly variable relationships among SES, OTL, and student performance (see Figure 5).11 Among OECD countries, SES has a
large positive average total SES effect (100), with indirect effects
constituting a large share of that relationship (average 43 points
in the OECD, statistically significant in 29 of 33 systems). OTL
is also strongly related to PISA performance (average coefficient
of 90, statistically significant in 29 countries). In all 62 PISA
educational systems, SES is significantly related to OTL (OECD
average .44). Between-school relationships varied appreciably
across countries, with the indirect effect related to OTL having
the strongest relationship in Korea, the Netherlands, and Japan
Contemporary debates in the United States and other countries
have placed a strong emphasis on contextual factors in education, in particular on the relative contribution of student poverty
to educational inequality and aggregate achievement (see, for
example, Carnoy & Rothstein, 2013). At least since the Coleman
Report, many researchers have questioned whether schools have
the capacity to overcome unequal background conditions. In
part due to the lack of appropriate data, the role of classroom
content has generally been absent from these discussions.
Scholars emphasizing the role of curricular differentiation have
found evidence that it contributes to educational inequality, yet
they have been forced to use relatively blunt measures, a fairly
small sample size, or were restricted to only one country (or
regions within one country). Compiling data from a range of
sources, Schmidt and McKnight (2012) argued for the existence
of pervasive inequalities in OTL and hypothesized that part of
the apparent role of SES was related to the systematically weaker
content offered to lower-income students—that rather than
ameliorating educational inequalities, schools were exacerbating
them. However, evidence for the link between SES and OTL,
and their joint relationship to student achievement, remained
tentative and largely restricted to the United States.
By exploiting new student-level indicators of OTL in the most
recent PISA, this study provides strong support for Schmidt and
McKnight’s (2012) hypothesis. A variety of modeling strategies
and statistical techniques, including path analysis, multilevel modeling, and adapting the approaches of previous work, all support
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three specific relationships: (a) OTL has a strong direct relationship
to student achievement, (b) high-SES students tend to receive
more rigorous OTL, and (c) a substantial share of the total relationship of SES to literacy occurs through its association with OTL.
Further, the international character of the PISA study indicates that
this is a cross-country phenomenon, one not restricted to the
United States: The most affluent students generally receive more
rigorous opportunities to learn important mathematics.
However, the results of this study also identify major differences between countries. Some educational systems exhibit a
lower propensity to worsen SES inequalities through unequal
OTL, in part by reducing the variability in OTL across students
and having much more socioeconomically integrated schools. In
addition, there are dramatic differences in how countries group
their students and structure their instructional opportunities,
although these distinctions do not always result in lower net
inequality. In some systems, such as France, Belgium, the Slovak
Republic, Germany, Austria, and the Netherlands, there are
larger between-school gaps in OTL. Other systems, like Spain
and Luxembourg, have greater within-school inequalities in content coverage. Future research should attend to these differences
and explore more deeply the role of between- and within-school
inequalities. There is an intriguing pattern in English-speaking
countries (the United Kingdom, Australia, New Zealand, and
the United States), with some of the highest levels of withinschool inequality in OTL and a stronger relationship to achievement gaps—a finding that deserves closer attention.
For the United States, the largest source of OTL inequality is
within (ranking second among OECD countries) and not between
schools (ranking among the 10 lowest OECD countries). The
relationship of OTL to achievement and of SES to OTL are
among the strongest of the 32 other wealthiest nations. These two
relationships lead to the United States having essentially half of the
within-school relationship of SES to mathematics literacy due to
the link between SES and OTL. The implication of these findings
is that any serious effort to reduce educational inequalities must
address unequal content coverage within schools.
The above results shed light on the long-standing debate in
the United States as to the cause of educational inequalities. Two
poles have emerged in the literature representing the cause as
primarily external or internal to schooling itself. Clearly the literature showing the role of social class and poverty to such
inequalities is supported by these results not only in the United
States but worldwide. What emerges, however, is a more complex story. We also learn that the magnitude of that observed
relationship reflects inequalities related not only to background
inequalities but also to schooling itself. Overall, 37% of the total
SES inequalities are related to OTL inequalities associated with
social class. This finding is remarkably similar to that of Reeves
(2012), who, using different data, found that 38% of the total
SES effect was due to indirect OTL-related effects.
It should be reiterated that the PISA data are cross-sectional,
preventing sweeping causal assertions based on the results.
Further work is needed on the longitudinal relationship of SESbased curricular differentiation. For example, the effects of OTL
inequalities may compound over time, by their relationship to
performance influencing OTL at the next grade level. Such a relationship could mitigate the direct influence of SES on student
performance. Also, the measures of OTL available in PISA were
very limited (in marked contrast to TIMSS) and need to be
greatly expanded in future studies in order to better estimate the
relationships reported here. Finally, there are other factors related
to inequalities in OTL, such as school funding, teacher quality,
and student motivation, that are likely related to the quality of
the opportunities, which could be included in future work.
Our findings also suggest that subsequent studies need to
incorporate OTL into models of educational inequality or risk
inflating the role of SES and unexplained variance because of
omitted-variable bias. Finally, because OTL is amenable to
changes in educational policy, it presents a vehicle for potential
reforms in real-world educational settings.
Notes
1
Our conception of opportunity to learn (OTL) is defined strictly
by exposure to formal mathematics content. Broader notions of OTL,
including teacher quality, resources, and peers, are also associated with
socioeconomic status (SES) and mathematics inequality (Levin, 2007).
Although certainly important, they are outside the scope of the present
work, which is focused on the role of instructional content as a mediator for socioeconomic inequality.
2
Our approach differs from that of Carnoy and Rothstein (2013).
We agree with them that SES is a significant contributor to student
achievement in early childhood and through structural inequalities
beyond curricular differentiation. Their focus is primarily on explaining cross-country comparisons, whereas our emphasis is on examining inequality within countries—which, after all, accounts for the vast
majority of variation in student performance.
3
Although McDonnell (1995) notes the challenges of using OTL
as a policy instrument.
4
Three other countries participated in the Programme for
International Student Assessment (PISA) but were excluded from our
analysis due to missing data: Norway, Cyprus, and Albania. Norway is
included in Table 2 because OTL is not considered.
5
Our analyses were also replicated using student responses to number of books in the home as the measure of SES, with essentially identical results.
6
Given the nature of the two PISA OTL scales of “degree of familiarity with math concepts” used to define formal mathematics, that index
could also reflect OTL from outside of formal schooling that would
make the concepts more familiar to the student. We believe although this
is a limitation of the index, the magnitude of such non-school-driven
OTL would be minimal given the nature of the mathematics concepts
included in the two scales. OTL related to typical arithmetic and algorithmic topics would be more susceptible to such influences (which is
typically what after-school classes, such as Kumon and Juku, focus on).
However, OTL-related topics, such as exponential and quadratic functions or cosines and vectors, are most likely to occur in regular mathematics classes. Second, as explained above, the construction of the index
of formal mathematics involved a third, dichotomously scored item that
directly asked students with what frequency they encountered algebratype problems in their classroom lessons and about the tests they took.
Indicating never for that item, when scaled with the other two, had the
effect of reducing the value of their OTL score.
7
Liechtenstein was excluded due to data restrictions.
8
Norway was excluded because it did not report OTL. Detailed
results for the Organisation for Economic Co-operation and Development
(OECD) countries are available in Table A1 of the appendix.
9
However, the fact that the three variables are all cumulative in
nature, especially OTL and achievement, adds some credence to the
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possible interpretation of these coefficients as causal. The OTL measure
is not defined with respect to a specific grade but rather is intended to
account for the cumulative OTL content coverage over the students’
schooling up through age 15. This is made possible due to the hierarchical nature of mathematics topics, especially those used to define the
OTL scale. The PISA literacy test is similarly cumulative with respect
to achievement. In one sense, both measures effectively have a “real zero
value” as students begin their schooling in mathematics. In that way,
the analyses relate the cumulative OTL with the students’ cumulative
knowledge. This is especially important in support of the parameterization of the model in which OTL is portrayed as exogenous.
10
Detailed results for the OECD countries are available in Table
A2 of the appendix.
11
Detailed results for the OECD countries are available in Table
A3 of the appendix.
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Authors
WILLIAM H. SCHMIDT, PhD, is a University Distinguished
Professor of statistics and education at Michigan State University;
bschmidt@msu.edu. His current writing and research concerns issues of
academic content in K–12 schooling, including the Common Core
State Standards for Mathematics, assessment theory, and the effects of
curriculum on academic achievement. He is also concerned with educational policy related to mathematics, science, and testing in general.
NATHAN A. BURROUGHS, PhD, is a senior research associate at
the Center for the Study of Curriculum at Michigan State University,
236B Erickson Hall, 620 Farm Lane, East Lansing, MI 48824;
burrou25@msu.edu. His research focuses on the relationship of institutions to inequality.
PABLO ZOIDO is an analyst at the Organisation for Economic
Co-operation and Development, Paris, France; Pablo.Zoido@OECD
.org. He works advising governments and education stakeholders on
how to use assessment and evaluation tools, such as the Programme for
International Student Assessment (PISA), to improve the quality,
equity, and efficiency of education systems.
RICHARD T. HOUANG, PhD, is the director of research for the
Center of Study of Curriculum at Michigan State University, Room
236, College of Education, 620 Farm Lane, East Lansing, MI 48824;
houang@msu.edu. His current research interest focuses on methodologies in quantifying mathematics and science curriculum and relationships between curriculum and student achievement.
Manuscript received January 14, 2015
Revisions received March 27, 2015, and July 31, 2015
Accepted August 4, 2015
October 2015 383
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Appendix
Table A1
Unstandardized Path Coefficients for SES and OTL Effects on PISA Performance, Pooled by Country
Country
SES Total
SES Direct
44*
44*
46*
30*
35*
43*
38*
29*
35*
58*
41*
35*
46*
30*
38*
54*
30*
42*
45*
37*
19*
37*
51*
41*
36*
57*
40*
33*
35*
39*
31*
40*
36*
39
21*
23*
26*
19*
25*
28*
28*
24*
24*
38*
24*
31*
32*
28*
25*
41*
20*
24*
20*
28*
15*
16*
31*
34*
27*
39*
32*
19*
35*
27*
25*
21*
23*
26*
Australia
Austria
Belgium
Canada
Chile
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Israel
Italy
Japan
Korea
Luxembourg
Mexico
Netherlands
New Zealand
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
OECD average
SES Indirect
23*
21*
20*
11*
10*
15*
10*
4*
11*
20*
18*
4*
14*
3*
13*
12*
11*
18*
25*
9*
5*
22*
21*
7*
8*
18*
8*
14*
1
12*
6*
19*
13*
13
OTL Direct
SES to OTL
% Indirect
78*
62*
68*
62*
52*
72*
45*
48*
62*
75*
73*
34*
71*
20*
60*
59*
64*
97*
105*
39*
40*
83*
72*
51*
59*
77*
52*
60*
5*
53*
53*
76*
65*
60
.29*
.33*
.29*
.18*
.20*
.21*
.22*
.09*
.18*
.26*
.24*
.13*
.20*
.14*
.22*
.21*
.17*
.19*
.24*
.23*
.12*
.26*
.28*
.13*
.14*
.23*
.16*
.23*
.10*
.23*
.12*
.25*
.20*
.2
52
47
43
37
29
36
26
16
32
34
43
13
30
9
35
23
35
43
56
24
25
58
40
16
23
31
20
42
1
32
20
47
37
32
Note. SES = socioeconomic status; OTL = opportunity to learn; PISA = Programme for International Student Assessment; OECD = Organisation for Economic Co-operation
and Development.
*p < .05.
384 EDUCATIONAL RESEARCHER
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Table A2
Unstandardized Path Coefficients for Within-School SES and OTL Effects on PISA Performance
Country
Australia
Austria
Belgium
Canada
Chile
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Israel
Italy
Japan
Korea
Luxembourg
Mexico
Netherlands
New Zealand
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
OECD average
SES Total
SES Direct
SES Indirect
OTL Direct
25*
16*
19*
22*
11*
11*
31*
19*
32*
22*
12*
19*
5*
24*
25*
24*
6*
4*
16*
18*
5*
10*
34*
30*
24*
24*
3*
26*
27*
25*
6*
23*
24*
19
11*
11*
9*
13*
8*
7*
23*
14*
21*
18*
8*
17*
3
22*
15*
16*
4*
1
7*
13*
4*
5*
19*
25*
18*
19*
3
14*
27*
20*
5*
10*
13*
13
14*
4*
9*
8*
3*
4*
8*
4*
12*
4*
4*
2*
2*
2*
10*
8*
2*
3*
9*
5*
2*
5*
14*
6*
6*
5*
1*
12*
0
6*
1*
13*
11*
6
68*
33*
54*
57*
36*
45*
44*
54*
65*
37*
41*
23*
34*
18*
57*
52*
30*
53*
73*
30*
28*
46*
69*
47*
50*
50*
17*
58*
3
44*
24*
71*
60*
45
SES to OTL
.20*
.13*
.18*
.15*
.08*
.10*
.18*
.08*
.18*
.11*
.10*
.10*
.06*
.12*
.18*
.16*
.06*
.06*
.12*
.15*
.06*
.11*
.21*
.12*
.11*
.09*
.05*
.20*
.09*
.13*
.05*
.19*
.19*
.12
% Indirect
54
27
51
38
26
39
25
23
35
19
34
11
45
9
41
35
28
74
55
26
29
53
42
18
24
19
22
45
1
23
20
58
47
33
Note. SES = socioeconomic status; OTL = opportunity to learn; PISA = Programme for International Student Assessment; OECD = Organisation for Economic Co-operation
and Development.
*p < .05.
October 2015 385
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Table A3
Unstandardized Path Coefficients for Between-School SES and OTL Effects on PISA Performance
Country
SES Total
SES Direct
SES Indirect
OTL Direct
SES to OTL
% Indirect
106*
110*
128*
70*
56*
152*
71*
65*
69*
147*
124*
78*
109*
71*
86*
137*
102*
165*
146*
86*
36*
172*
112*
74*
61*
125*
145*
56*
76*
104*
94*
106*
68*
100
43*
39*
92*
39*
21*
100*
57*
69*
62*
59*
50*
45*
63*
65*
60*
117*
47*
59*
–1
78*
20*
–1
84*
57*
33*
81*
104*
32*
74*
69*
48*
73*
42*
57
64*
72*
36*
32*
35*
51*
13*
–4
7*
88*
74*
32*
46*
5
25*
19*
55*
106*
148*
9
16*
173*
28*
17*
28*
44*
41*
24*
2
35*
46*
33*
25*
43
105*
89*
57*
91*
117*
84*
34*
–27
35*
137*
113*
139*
112*
21
75*
57*
112*
173*
228*
21
84*
174*
50*
100*
141*
85*
86*
72*
14
49*
161*
68*
100*
90
.61*
.81*
.64*
.35*
.30*
.61*
.40*
.14*
.21*
.64*
.65*
.23*
.41*
.26*
.34*
.34*
.49*
.61*
.65*
.41*
.20*
.99*
.55*
.17*
.20*
.52*
.48*
.33*
.17*
.72*
.28*
.49*
.26*
.44
60
65
28
45
62
34
19
–6
11
60
59
42
42
7
29
14
54
64
101
10
46
100
25
23
46
35
28
42
3
34
49
31
38
39
Australia
Austria
Belgium
Canada
Chile
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Israel
Italy
Japan
Korea
Luxembourg
Mexico
Netherlands
New Zealand
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden
Switzerland
Turkey
United Kingdom
United States
OECD average
Note. SES = socioeconomic status; OTL = opportunity to learn; PISA = Programme for International Student Assessment; OECD = Organisation for Economic Co-operation
and Development.
*p < .05.
386 EDUCATIONAL RESEARCHER
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