The role of innovations in secondary school performance – Evidence from a conditional efficiency model

This paper studies the influence of educational innovations on school performance. We apply a tailored, fully nonparametric conditional efficiency model to study secondary school efficiency in the Netherlands. The application uses official school data and a self-collected questionnaire on recent innovations in schools. In the nonparametric model, it is assumed that schools aim to maximize educational attainments of students under a budget constraint. The results suggest that innovations are positively related to efficiency. We find that profiling, pedagogic, process and education chain innovations are significantly related to school efficiency, whereas innovations in the professionalization of teachers are insignificantly related to school efficiency. Furthermore, the number of locations per school and the number of schools per governing body are negatively and significantly related to school efficiency. School type and region significantly influence school efficiency, whereas share of disadvantaged students, degree of urbanization and student/teacher ratio do not have significant influence.     

Efficiency and equity in private and public education: A nonparametric comparison

We present a nonparametric approach for (1) efficiency and (2) equity evaluation in education. Firstly, we use a nonparametric (Data Envelopment Analysis) model that is specially tailored to assess educational efficiency at the pupil level. The model accounts for the fact that typically minimal prior structure is available for the behavior (objectives and feasibility set) under evaluation. It allows for uncertainty in the data, while it corrects for exogenous ‘environmental’ characteristics that are specific to each pupil. Secondly, we propose two multidimensional stochastic dominance criteria as naturally complementary aggregation criteria for comparing the performance of different school types (private and public schools). While the first criterion only accounts for efficiency, the second criterion also takes equity into consideration. The model is applied for comparing private (but publicly funded) and public primary schools in Flanders. Our application finds that no school type robustly dominates another type when controlling for the school environment and taking equity into account. More generally, it demonstrates the usefulness of our nonparametric approach, which includes environmental and equity considerations, for obtaining ‘fair’ performance comparisons in the public sector context.     

Performance in primary schools

Data for this paper was collected from the OFSTED database on Hampshire primary schools. The schools in Southampton and Porstmouth were used in order to assess the factors that influence their productive efficiency. The data set included 19 variables on 176 schools and was analysed by means of Data Envelopment Analysis. Contextual variables, not included in the efficiency analysis, were used to explain the sources of inefficiency. It was found that religious orientation, parental influence and level of exclusions all impacted on the ability of a school to deliver the best possible results in standard assessment tests. This study is set within local and national priorities in education.     

Enhancing the inclusion of non-discretionary inputs in DEA

The aim of this paper is to provide an alternative approach for estimating efficiency when a set of decision-making units uses non-discretionary inputs in the productive process. To test the influence of these variables, our proposal uses a multi-stage approach based on Tobit regressions. In order to avoid potential bias, a bootstrap procedure is used to estimate these regressions. This methodology allows enhancing other models previously proposed to introduce non-controllable inputs in data envelopment analysis (DEA) overcoming, thus, some of their main shortcomings. We illustrate our framework with an empirical application on Spanish high schools where non-controllable factors play a major role to explain educational achievements.     

Assigning mathematics instruction time in secondary schools: what are the influential factors?

Similar to countries such as the Netherlands and the United Kingdom, secondary schools in Ireland can decide how to allocate instruction time between curriculum subjects. Although there are national guidelines available from the Department of Education and Skills (DES), the majority of schools make their own decisions about how much time they allocate to different subjects. This results in variations between the amounts of time allocated to teaching mathematics in different schools and between different year and class groups within the same school. Decisions regarding time allocation are generally taken by the school management. This means that the ethos of the school and the individual opinions of school management can determine the amount of mathematics that students experience throughout their second level education. The aim of this study is to evaluate the most influential factors that management considers when assigning instruction time in Irish secondary schools. For the purpose of this research, seven possible factors were identified and 400 deputy principals from a stratified sample of secondary schools around Ireland were asked to select their top three. Timetabling constraints, the availability of mathematics teachers and the perceived importance of the subject were found to be the most influential factors.     

Efficiency assessment of primary care providers: A conditional nonparametric approach

This paper uses a fully nonparametric approach to estimate efficiency measures for primary care units incorporating the effect of (exogenous) environmental factors. This methodology allows us to account for different types of variables (continuous and discrete) describing the main characteristics of patients served by those providers. In addition, we use an extension of this nonparametric approach to deal with the presence of undesirable outputs in data, represented by the rates of hospitalization for ambulatory care sensitive condition (ACSC). The empirical results show that all the exogenous variables considered have a significant and negative effect on efficiency estimates.     

A bootstrap approach to analyse productivity growth in European banking

This paper analyses productivity growth for European banks over the 1995–2001 period. In contrast to previous literature, our study covers the majority of current European Union (EU) countries—all except Greece and those joining the EU in 2004. We also use resampling methods so as to gain statistical precision, which turns out to be especially important due to the limitations of the database. In order to be consistent, we use additional nonparametric methods to disentangle why productivity differentials might exist. Results show that productivity growth has occurred in most countries, mainly due to improvements in production possibilities. The bootstrap analysis yields further evidence given that for many firms and countries productivity growth or decline is not statistically significant. The two-stage analysis provides some extra insights, suggesting that the relevance of environmental variables found in other studies focusing on efficiency could be lessened when focusing on productivity.     

Nonparametric measurement of productivity and efficiency in education

Nondiscretionary environmental inputs are critical in explaining relative efficiency differences and productivity changes in public sector applications. For example, the literature on education production shows that school districts perform better when student poverty is lower. In this paper, we extend the nonparametric approach to decompose the Malmquist Productivity Index suggested by Färe et al. (American Economic Rewiew 84:66–83, 1994) into efficiency, technological and environmental changes. The approach is applied to analyze educational production of Ohio school districts. Applying the extended approach in an analysis of the educational production of 604 school districts in Ohio, we find changes in environmental harshness are the primary drivers in productivity changes of underperforming school districts, while technical progress drives the performance of top performing school districts.     

Policy and the standards debate: mapping changes in assessment in mathematics

ABSTRACT

The influences on governments for policy changes in schools range across many agencies, including the political party in power. When policies change, the sources of these influences are not always clear. The project whose work is presented in this special issue examines what these changes look like in terms of the differences in assessment tasks of school pupils’ mathematics, over time. In this article we attempt to develop a graph, which we argue will have general applicability internationally, that can help to reveal the sources and nature of those influences. We construct the graph in interaction with an examination of the most recent changes in two countries. We argue that our analysis is a necessary complement to the project’s findings in that it enables us to identify the fields of recontextualisation, their relative strengths in terms of influence and hence conjecture their impact on the mathematics curriculum.     

An International Project for the Development of Data Handling Skills of Teachers and Pupils

In this paper we provide an overview of the international CensusAtSchool project, designed, written and implemented first in the UK from October 2000 - April 2001 for pupils aged 7 -16 in primary and secondary schools. It has been adapted for similar aged school children in South Africa and Australia and was implemented in those countries in July and October 2001, respectively. We present our motivation, aims and objectives for carrying out such a project and show some results of analysis from the returns we have received from all three countries. Key outputs from the project include: worksheets that are suitable for enhancing data handling skills of pupils; a training course that wraps information and communications technology with data handling skills that is suitable to enhance the professional development of teachers; a raised awareness amongst pupils and teachers of the need to properly collect, present and analyze primary data; a contribution to improving the statistical numeracy and thinking skills of both teachers and pupils.     

How to measure the impact of environmental factors in a nonparametric production model

The measurement of technical efficiency allows managers and policy makers to enhance existing differentials and potential improvements across a sample of analyzed units. The next step involves relating the obtained efficiency estimates to some external or environmental factors which may influence the production process, affect the performances and explain the efficiency differentials. Recently introduced conditional efficiency measures (,  and ), including conditional FDH, conditional DEA, conditional order-m and conditional order-α, have rapidly developed into a useful tool to explore the impact of exogenous factors on the performance of Decision Making Units in a nonparametric framework. This paper contributes in a twofold fashion. It first extends previous studies by showing that a careful analysis of both full and partial conditional measures allows the disentangling of the impact of environmental factors on the production process in its two components: impact on the attainable set and/or impact on the distribution of the efficiency scores. The authors investigate these interrelationships, both from an individual and a global perspective. Second, this paper examines the impact of environmental factors on the production process in a new two-stage type approach but using conditional measures to avoid the flaws of the traditional two-stage analysis. This novel approach also provides a measure of inefficiency whitened from the main effect of the environmental factors allowing a ranking of units according to their managerial efficiency, even when facing heterogeneous environmental conditions. The paper includes an illustration on simulated samples and a real data set from the banking industry.     

A comparison of public and private schools in Spain using robust nonparametric frontier methods

This paper uses an innovative approach to evaluate educational performance of Spanish students in PISA 2009. Our purpose is to decompose their overall inefficiency between different components with a special focus on studying the differences between public and state subsidized private schools. We use a technique inspired by the non-parametric free disposal hull and the application of robust order-\(m\) models, which allow us to mitigate the influence of outliers and the curse of dimensionality. Subsequently, we adopt a metafrontier framework to assess each student relative to the own group best practice frontier (students in the same school) and to different frontiers constructed from the best practices of different types of schools. The results show that state-subsidised private schools outperform public schools, although the differences between them are significantly reduced once we control for the type of students enrolled in both type of centres.     

Examining Elementary School Science Achievement Gaps Using an Organizational and Leadership Perspective

There is the tendency to explain away successful urban schools as indicative of the heroic efforts by a tireless individual, effectively blaming schools that underperform for a lack of grit and dedication. This study reports the development of a research instrument (School Science Infrastructure, or SSI) and then applying that tool to an investigation of equitable science performance by elementary schools. Our efforts to develop a science‐specific instrument to explore associations between school‐level variables and equitable science performance are informed by James Coleman's tripartite notion of social capital: the “wealth” of organizations is encompassed within their social norms, informational channels, and reciprocating relationships. Grounded in school effectiveness research and social capital theory, the instrument that we report on here is a valid and reliable tool to support meso‐level investigations of factors contributing to school variations in science achievement.     

Beliefs and beyond: hows and whys in the teaching of proof

In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding which factors may influence such a treatment. This study is part of a wider project on proof carried out for many years. In our theoretical framework, we combine references from research on proof with those from research on teachers in relation to their beliefs. The study was carried out through interviews with secondary school teachers aimed at learning how they describe their work with proof in the classroom, and to elicit beliefs and other factors that shape this work. Through the interviews we were able to detect reasons behind teachers’ choices in planning their work in the classroom. In the present paper, we concentrate on four cases that, among other factors, offer elements suitable to unravel the problem of inconsistencies using the construct of leading beliefs, i.e., beliefs (whose nature may vary from teacher to teacher) that seem to drive the way each teacher treats proof.     

Decomposing school and school-type efficiency

This paper puts forward a Data Envelopment Analysis (DEA) approach to decomposing a pupil’s under-attainment at school. Under-attainment is attributed to the pupil, the school and the type of funding regime under which the school operates. A pupil-level analysis is used firstly on a within school and secondly on a between school basis, grouping schools by type such as state-funded, independent and so on. Overall measures of each pupil’s efficiency are thus disentangled into pupil, school and school-type efficiencies. This approach provides schools with a set of efficiency measures, each one conveying different information.     

Single-Period Markowitz Portfolio Selection,Performance Gauging,and Duality: A Variation on the Luenberger Shortage Function

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.     

Nonparametric estimation of returns to scale in the public sector with an application to the provision of educational services

Nonparametric programming models have been developed to measure technical efficiency and scale economies. The programming models used for public sector applications, however, are based on standard private sector production theory. In the public sector environmental variables have a significant impact on the provision of public services. Without controlling for these environmental factors point estimates of efficiency and returns to scale will be biased. This paper extends nonparametric methods to allow measurement of returns to scale in the provision of public services. The method is applied to the provision of educational services in New York State school districts for illustrative purposes.     

Integrated STEM in practice: Learning from Montessori philosophies and practices

In theory, STEM (interdisciplinary science, technology, engineering and mathematics) is cross‐disciplinary and situated in real‐world problem‐solving contexts. In practice, STEM disciplines are often implemented separately using contrived contexts. This paper examines theoretical and empirical aspects of Montessori middle school science in the United States, and its alignment with the conceptual framework of integrated STEM. We selected Montessori adolescent environments because the Montessori philosophy involves interdisciplinary application contextualized in purposeful work and learning. Our research sought to investigate how Montessori middle schools have designed their science programs, and to situate these findings within the current landscape of STEM education and reform‐based science. Based on the results of our survey of 96 U.S. Montessori middle schools, we argue Montessori offers an integrated educational approach that meaningfully situates academic disciplines to mirror local and global challenges, well supported by theory and literature on STEM and situated learning theories. We assert that integrated STEM happens organically in many Montessori middle schools, and takes place through authentic work in communities of practice. Our research communicates the value of looking outside traditional school settings to examine alternative formal education spaces, like Montessori classrooms where integrated STEM happens organically.