Mathematics curriculum standards have become a major component of most educational systems. They define what a student should learn at each grade. The political question that accompanies the standards and all of its related components is, who makes what decisions. In this study, a senior-level mathematics administrator from each of 19 countries was asked to indicate who made what decision, if any, for each of 14 components related to the development of the national standards. The focus of the study was on teachers both collectively and individually. Three other stakeholders (national administration, regional administration, and schools) were included as well. The data (related to the OECD 2030 project) indicated a very large variation across countries and across the 14 areas on curriculum construction such as goals for teaching in terms of teacher involvement. Not only did the data indicate whether teachers were involved in the process but more importantly indicated the degree of authority they had in the process which varied appreciably across countries. Given related data from TIMSS 1995, this study also showed large variation from what was true of the teachers’ role in curriculum decision making some 25 years ago. Unfortunately, the previous data does not include an indication of the degree of authority the teacher had in the process, only whether or not the teacher was involved. The comparison across the two studies indicated a major increase in the involvement of teachers in the curriculum decision making process.

Measuring opportunities to learn (OTL) is crucial for evaluating education quality and equity, but obtaining accurate and comprehensive OTL data at a large scale remains challenging. We attempt to address this issue by investigating measurement concerns in data collection and sampling. With the primary goal of estimating group-level OTLs for large populations of classrooms and the secondary goal of estimating classroom-level OTLs, we propose forming a teacher panel and using an online log-type survey to collect content and time data on sampled days throughout the school year. We compared various sampling schemes in a simulation study with real daily log data from 66 fourth-grade math teachers. The findings from this study indicate that sampling 1 day per week or 1 day every other week provided accurate group-level estimates, while sampling 1 day per week yielded satisfactory classroom-level estimates. The proposed approach aids in effectively monitoring large-scale classroom OTL.

The recent PISA mathematics results delivered disappointing news for the United States of America (USA). These results underscored the education system’s continuing inequalities. An important question concerns to what extent and to which part of the educational system do these sources of inequality occur? In this paper we use PISA 2012 data merged with district- and school-level variables derived from five additional national databases to explore the way socio-economic status (SES) and race are related to inequalities in student performance as well as to inequalities in other components of schooling at both the system and student-levels, such as the academic ‘zeitgeist’ of the school, the nature of the mathematics curriculum and characteristics of both the teacher and the student. The results demonstrated how race and SES had significant relationships not only to student performance but to other aspects of schooling as well. Those relationships occurred at both the system- and within-school levels but differed in their implications. The policy implications of the research could help determine where the greatest effort could be made to provide all children of all racial and social classes equal opportunities to learn.

Opportunities to learn related to the use of quantitative reasoning to solve higher-order real-world applications that reflect the messy nature of the world are scarce and vary across countries. Those experiences are essential to the development of quantitative literacy. This literacy, like that related to language, is critical for all children. To examine this issue, 19 countries were involved in a study that analyzed the degree of emphasis placed on quantitative literacy in their curriculum standards. Most countries have such policies but vary appreciably regarding their degree of emphasis. Furthermore, the countries’ 8th grade textbooks were analyzed to determine the degree to which those books provided opportunities to develop quantitative literacy. The results identified a major policy-practice gap.

The Program for International Student Assessment (PISA) 2012 utilized data from 63 countries and economies to generate research questions that centered on the contribution of mathematics self-efficacy, opportunity to learn (OTL), and how their interplay affected students’ mathematical performance. This study reveals that in a majority of the surveyed countries/economies, students’ OTL can enhance the positive relationship between mathematics self-efficacy and mathematical performance. Path analysis further demonstrates that in 61 out of the 63 countries/economies, students’ OTL positively affect their mathematics self-efficacy, which subsequently enhances mathematical performance. It was observed that students with more OTL typically exhibit higher math performance, but this effect is explained by the mediating influence of having more mathematics self-efficacy.

Countries across the world have seen a growing gap in mathematics performance between low-SES children and those from wealthier backgrounds. The issue of inequality not only relates to student performance, but also to schooling—as defined by the mathematics curriculum and its distribution of the related opportunities to learn. Whether relationships between student background, schooling (curriculum coverage), and performance varies between countries with different levels of development has become a question of particular interest to countries and their curriculum-related policies. Those same countries want to achieve both international recognition for excellence as well as equality. Relatedly, the policy question that has arisen is whether both excellence and equality can be achieved simultaneously. The answers to both questions are complex as the relationships between the three key concepts vary among the 63 PISA countries by substantial amounts. Additionally, the averages between the three types of countries vary as well. This all leads to the conclusion that the probability of achieving both excellence and equality varies by the wealth of the country.

Responding to natural disasters requires a large and rapid deployment of resources to relieve the immediate needs of the victims. This includes immediate access to food, shelter, and medical assistance. These services are supported by, and eventually fully transitioned to, local infrastructure, such as grocery stores. We test for differences in the percentage change in prices paid for grocery products between low-income and high-income communities in the months following three large Atlantic hurricanes. We identify impacted communities using major disaster declarations by the United States federal government, and marry this information to U.S. Census Bureau data on household income, and third-party data on grocery store sales. Using a triple difference regression specification, we isolate the percentage change in prices paid by low-income versus high-income communities in disaster affected versus unaffected areas, before and after the disasters. Across the events we study, a common outcome is that low-income communities in the disaster zones endure higher average percentage price increases within grocery categories compared to high-income communities. Such differences can sap the purchasing power of those communities that are least able to absorb it. We establish the presence of several mechanisms that contribute to these results. Compared to high-income communities, low-income communities can experience a larger percentage drop in price promotions, higher percent price increases at the unit level, substitution paths that more likely transit from low-priced to high-priced goods, and a larger increase in actual substitution from low-priced products to high-priced products. These mechanisms are consistent with stock-outs that disproportionately disadvantage low-income communities. We suggest several policy changes that may alleviate these effects. Our results highlight how companies and emergency response agencies can make use of readily available, cross-organizational data to facilitate more targeted and equitable operational interventions in the aftermath of a disaster.

In contextual studies, group compositions are often extracted from individual data in the sample, in order to estimate the group compositional effects [e.g., school socioeconomic status (SES) effect] controlling for interindividual differences in multilevel models. As the same variable is used at both group level and individual level, an appropriate decomposition of between and within effects is a key to providing a clearer picture of these organizational and individual processes. The current study developed a new approach with within-group finite population correction (fpc). Its performances were compared with the manifest and latent aggregation approaches in the decomposition of between and within effects. Under a moderate within-group sampling ratio, the between effect estimates from the new approach had a lesser degree of bias and higher observed coverage rates compared with those from the manifest and latent aggregation approaches. A real data application was also used to illustrate the three analysis approaches.

Continuing efforts have been made in the United States (US) to examine the role of schooling in alleviating the ethnic/racial inequalities in student performance. Using the US data from the 2012 Programme for International Student Assessment (PISA), this study examines the between-school and within-school racial/ethnic differences in opportunities to learn (OTL) and their relationship to the corresponding differences in student mathematics achievement. In all models and for all types of students, OTL showed a significantly positive relationship to student mathematics achievement, and its effect size was about four times as large as the socioeconomic status (SES) effect. The results suggest the importance of OTL in alleviating the racial/ethnic inequalities in mathematics performance.

Employing data from a stratified random survey of newly certified teachers in Texas, we compare the mathematical content preparation of traditional teacher program graduates with graduates of alternative programs. We find that graduates of traditional programs have statistically significantly higher content preparation even when taking precollege preparation into account. These findings were consistent across different types of alternative programs. Alternatively certified teachers reported higher college entrance exam scores in mathematics, but this was statistically significant only for Grades 4 to 8. After merging survey results with NCES (National Center for Education Statistics) data about the schools at which teachers were employed, we found similar demographic characteristics between the two types of teachers—alternatively certified teachers were not more likely to teach in disadvantaged schools. Finally, while the content preparation of teachers was consistent across types of schools, teachers in disadvantaged schools tended to have lower SAT and ACT scores for both alternatively and traditionally prepared teachers.

This study addresses measurement issues around a standards-based content analysis of mathematics textbooks' coverage of standards for use in large-scale monitoring of standards implementation as proposed in a 2013 report by the National Research Council. An earlier study produced an exhaustive content analysis of textbooks using the 2012 Common Core State Standards for Mathematics. This yielded an accurate and reliable portrait of a textbook's coverage of standards. However, such an in-depth analysis is not feasible for large-scale standards-implementation monitoring in which a large number of textbooks may need to be analyzed. To provide such a portrait with sufficient accuracy while also substantially reducing the associated resources needed to produce such a portrait, a simulation study was conducted with the exhaustively coded database to compare different sampling schemes. Results indicated that sampling 1 day from each week and coding the corresponding lessons led to sufficiently accurate representations of the overall content of the textbook. The results provide empirical evidence for large-scale standards-based content analyses of mathematics textbooks for monitoring standards implementation which could be adapted for other subject areas.

ABSTRACT There is an increasing interest of policies and projects to adapt boarding schools as a means to provide quality education for educationally disadvantaged students. However, little evidence is available for the effectiveness of boarding schools. The current study examined the boarding effect on primary and middle school student mathematics achievement using stratified analysis and propensity score matching approach. The boarding on campus showed a negative and insignificant effect on fourth-grade student mathematics achievement, but a significantly positive effect on eighth-grade student achievement. The mechanisms through which boarding on campus might affect boarders’ achievement were also explored.

After a brief discussion of the history of IEA’s Trends in International Mathematics and Science Study (TIMSS), and the implications this has had for comparative research into the influence of teachers on student outcomes, this chapter details the key variables that are employed in the remainder of the book. These include several student-level control variables (such as gender, socioeconomic status, and language spoken in the home), teacher-reported measures (experience, education, gender, and time spent on teaching mathematics), and newly developed instruments based on TIMSS responses related to teacher self-efficacy and instructional alignment. All of the analyses in this report make use of TIMSS data, merging several distinct instruments: student assessments, teacher background surveys, and national background surveys. The design of TIMSS has a number of important implications. Relationships between variables should be treated as associations rather than strictly causal, thus a multi-model analytical strategy is needed to test the robustness of statistical results and improve confidence in the reliability of analyses. Relationships were examined across time, across different aggregations of data, and using different statistical procedures, and are discussed in more detail in later chapters. Many features of TIMSS and the topics included in the survey have changed considerably over time and some key variables of interest were not included in earlier versions of the TIMSS, greatly restricting the available sample when analyzing country-level trends (whether as means or regression coefficients). The complex sampling design has important implications for statistical modeling and analysis, and for purposes of analysis, the models in subsequent chapters ignore school effects. Multilevel and classroom-mean models treat each classroom as existing independently, rather than being clustered within schools. Given the acknowledged impact of schools, and the importance of within-school, between-classroom heterogeneity, any conclusions drawn from the analysis should be treated with caution.

Researchers agree that teachers are one of the most important school-based resources in determining students' future academic success and lifetime outcomes, yet have simultaneously had difficulties in defining what teacher characteristics make for an effective teacher. This chapter reviews the large body of literature on measures of teacher effectiveness, underscoring the diversity of methods by which the general construct of "teacher quality" has been explored, including experience, professional knowledge, and opportunity to learn. Each of these concepts comprises a number of different dimensions and methods of operationalizing. Single-country research (and particularly research from the United States) is distinguished from genuinely comparative work. Despite a voluminous research literature on the question of teacher quality, evidence for the impact of teacher characteristics (experience and professional knowledge) on student outcomes remains quite limited. There is a smaller, but more robust set of findings for the effect of teacher support on opportunity to learn. Five measures may be associated with higher student achievement: teacher experience (measured by years of teaching), teacher professional knowledge (measured by education and self-reported preparation to teach mathematics), and teacher provision of opportunity to learn (measured by time on mathematics and content coverage). These factors provide the basis for a comparative cross-country model.

To understand whether there are identifiable trends in teacher quality and instructional metrics over time, it is important to first recognize that measures of teacher effectiveness may vary by education system. Descriptive results for the teacher quality measures related to mathematics drawn from twenty years of the IEA's Trends in International Mathematics and Science Study (TIMSS) data provide a general picture of the variation in such measures; additional consideration is given to student-level variables. Combining information from multiple cycles of TIMSS, with a specific emphasis on teacher variables, greater focus is given to the post-2003 TIMSS data, largely because these later cycles contain additional teacher-related measures (such as preparedness to teach mathematics topics). Changes in education system means may be due to changes in underlying teacher characteristics. The data suggests that, among the pool of countries that participated in all the TIMSS between 2003 and 2015, there have been increases in the international averages for the number of years of experience that teachers possess, their level of educational qualification to teach mathematics, and classroom time spent on mathematics instruction. However, instructional alignment with national standards has remained surprisingly modest (at around 55-60%) and the international average for instructional alignment declined for grade eight over twenty years of TIMSS. The results suggest that, in many countries, teachers (especially grade four teachers) retain a substantial degree of discretion in what to teach. Variability in teacher behaviors related to opportunity to learn suggests it is highly advisable to consider this factor in studies of teacher effectiveness.

The central aim of this report was to investigate what international comparative assessments could reveal about the role of teachers in influencing student outcomes. A series of analyses attempted to identify potential trends in teacher quality and instructional metrics over time and their relationship with student achievement, but found no strong evidence for consistent predictable relationships between commonly-employed indicators of teacher effectiveness and student outcomes (both within and across educational systems). Further, although inequality in student outcomes remains pervasive across education systems, teacher quality is less subject to inequality, and, indeed, many countries have seen a rise in formal preparation to teach mathematics over the twenty years of IEA's Trends in International Mathematics and Science Study (TIMSS). While improving conventional measures of teacher quality may not have a significant impact on educational inequality, there is some evidence that increasing the average amount of time spent on teaching mathematics may reduce inequalities in student achievement. Researchers and policymakers should be extremely cautious about applying the associations identified in one education systems to a very different educational context. The results indicate that teachers with similar experience, credentials, and instructional strategies may regardless produce quite different results, indicating that parents, policymakers, community institutions, and cultural context likely play a powerful role in determining student outcomes.

Inequalities in teacher quality may be examined using several different lenses. To better investigate the relationships between student equity and teacher quality and instructional metrics, educational inequality in student performance across countries and time was explored as (1) variation in student mathematics scores, and (2) differences in socioeconomic status using descriptive, regression, and fixed-effects techniques. Measures of teacher quality (as measured by experience, education, preparedness, time spent on teaching mathematics, and instructional alignment) appeared to have only a limited effect on aggregate or within-classroom variation in student outcomes. The results also suggest that teacher quality may be more equitable at grade four than at grade eight, as measured by differences between higher and lower socioeconomic status classrooms.

Opportunity to learn (measured by time spent on teaching mathematics and mathematics content coverage) potentially acts as a mediator of instructional quality and teacher characteristics. Previous research used a multilevel structural equation model (SEM) to explore the relationship of teacher instructional quality (identified using a latent variable) to student mean outcomes at grade four. Here, this model is extended by incorporating two instructional quality variables related to opportunity to learn: teacher alignment with national curriculum expectations, and time spent on mathematics. This model was applied to grade four and grade eight data from the 2011 cycle of IEA’s Trends in International Mathematics and Science Study (TIMSS). Replicating the analysis at grade eight determined whether the mathematics performance of lower secondary students showed similar relationships with instructional quality as those observed for grade four students. Teacher instructional alignment and time on mathematics was found to have a weak mediating effect on student outcomes.