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.     

Assessing European primary school performance through a conditional nonparametric model

This paper uses a fully nonparametric framework to assess the efficiency of primary schools using data about schools in 16 European countries participating in PIRLS 2011. This study represents an original enterprise since most of the empirical research in the field is restricted to evaluations at regional or national level and focused on secondary education. For our purpose, we adapt the metafrontier framework to compare and decompose the technical efficiency of primary schools operating in heterogeneous contexts, which in our case is represented by different educational systems or countries. Similarly, we use an extension of the conditional nonparametric robust approach to test the potential influence of a mixed set of environmental school factors and variables representing cultural values of each country. Our results indicate that the intergenerational transmission of non-cognitive skills such as responsibility or perseverance are significantly related to school efficiency, whereas most school factors do not seem to have a significant influence on school performance.     

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.     

Assessing the Effectiveness of Schools with Pupils of Different Ability Using Data Envelopment Analysis

Research suggests that many schools have a differential effectiveness with pupils of different ability. For example a school may be more effective in raising the performance of pupils of low rather than higher ability or vice versa. The identification of the existence of any differential effectiveness at a school is important as it can prompt a review of teaching practices, which will benefit ability ranges hitherto disadvantaged and thereby improve the overall effectiveness of the school. The most appropriate data for assessing differential effectiveness would be at pupil or, at least, at ability range level. Such data is not generally available. This paper develops a data envelopment analysis (DEA) based method that can identify the existence, and indicate the direction of, differential effectiveness at a school using data covering the full range of pupil abilities. The method can also identify role model schools for a school seeking to alter the bias in its differential effectiveness.     

The efficiency of public and publicly subsidized high schools in Spain: Evidence from PISA-2006

This paper compares the efficiency of Spanish public and publicly subsidized private high schools by data envelopment analysis (DEA), employing the results provided by a hierarchical linear model (HLM) applied to PISA-2006 (Programme for International Students Assessment) microdata. The study places special emphasis on the estimation of the determinants of school outcomes. The educational production function is estimated through an HLM that takes into account the nested nature of PISA data. Inefficiencies are then measured through DEA and decomposed into two types: managerial (related to individual performance), and programme (related to structural differences between management models), following the approach adopted by Silva Portela and Thanassoulis. Once differences in students’ backgrounds, school resources and individual management inefficiencies are removed, the results reveal that Spanish public high schools are more efficient than their publicly subsidized private equivalents.     

Assessing pupil and school performance by non-parametric and parametric techniques

This paper discusses the use of the non-parametric free disposal hull (FDH) andthe parametric multi-level model (MLM) as alternative methods for measuringpupil and school attainment where hierarchical structured data are available.Using robust FDH estimates, we show how to decompose the overall inefficiency ofa unit (a pupil) into a unit specific and a higher level (a school) component.By a sample of entry and exit attainments of 3017 girls in British ordinarysingle sex schools, we test the robustness of the non-parametric and parametricestimates. Finally, the paper uses the traditional MLM model in a best practiceframework so that pupil and school efficiencies can be computed.     

Nonparametric analysis of educational costs

Traditional economic analyses of the public sector that assume cost minimization are not consistent with political models of bureaucracy. If costs are not minimized then estimated cost functions will be biased. The purpose of this paper is to provide a flexible nonparametric technique based on Farrell-type efficiency measures to estimate public sector costs. Standard indices need to be modified to fit the special nature of public sector service provision which is characterized by an influence of exogenous variables on cost. A useful by-product is an index of environmental harshness faced by local governments. For illustrative purposes, this technique is applied to a sample of New York State school districts. It is found that nearly 64% of districts are cost inefficient, spending on average $1200 per pupil above the cost minimizing level. In addition, it is estimated that the average school district faces environmental cost of over $1700 per pupil.     

普通高中教育投入绩效评估实证研究——基于江门市47所高中调查的多层数据

基于江门市47所高中调查的多层数据,运用多层统计分析模型,进行普通高中教育投入绩效评估的实证研究,结果表明:中考成绩与学校绩效之间呈负相关态势;高考成绩最重要的决定因素是学生先前的知识储备和起始能力水平;教育经费投入对高考成绩有显著正影响;学校师资质量对提高学生学业成就有正影响;在47所学校中,有18所学校教育绩效较好,有27所学校教育绩效还有待进一步提高,相应的教育资源的配置需要进一步优化等,并提出相应的政策建议.     

Analysis of complementary methodologies for the estimation of school value added

This paper analyses the value added (VA) of a sample of Portuguese schools using two methodologies: data envelopment analysis (DEA) and the methodology used presently by the UK Department for Children, Schools and Families (DCSF). The VA estimates obtained by the two methods are substantially different. This reflects their different focus: DEA emphasizes on best-observed performance, whereas the DCSF method reveals average performance. The main advantage of the methodology used by the DCSF is its simplicity, although it confounds pupil effects with school effects in the estimation of school VA. In contrast, the DEA methodology can differentiate these effects, but the complexity may prevent its use in a systematic way. This paper shows that the two methods provide complementary information regarding the VA of schools, and their joint use can improve the understanding of the relative effectiveness of schools regarding the progress that pupils make between educational stages.     

Schools in Southampton: A Quantitative Approach to School Location,Closure and Staffing

Between 1965 and 1976 the number of children born in the UK decreased by about one third. The fall in the number of births was followed by a fall in the number of children on roll in compulsory education, which resulted in many schools being closed. This paper examines the dynamics of falling rolls in the city of Southampton. Multidimensional scaling techniques are used to explore the social characteristics of the schools proposed for closure. The paper examines also the consequences of the exercise of parental choice of school. It is shown that social dynamics and staffing rules based on constant pupil/teacher ratios remove resources from the schools that are most in need of them.     

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.     

Online study collaboration to improve teachers’ expertise in instructional design in mathematics

Online study collaboration is a recent professional development approach that goes beyond school and regional boundaries and even helps reach rural schools in China. In this study, we focused on a specific online study collaboration program to examine its potential benefits for improving participating teachers’ expertise in instructional design. Data were collected from the online study collaboration organizers and four main participating schools. The results reveal the program’s well-structured process and organization for planning and conducting the online study collaboration. Participating teachers benefited from their sharing and discussions with experts and other teachers. Their instructional designs show many important changes that are aligned with experts’ comments. Selected teachers’ expertise improvement includes their knowledge about the textbook and content, their perspectives about students’ learning and instruction, and their learning of different instructional approaches to engage students in classroom instruction. The use of online study collaboration for improving teachers’ expertise and the study’s limitations are then discussed.     

A multilevel finite mixture item response model to cluster examinees and schools

Within the educational context, a key goal is to assess students’ acquired skills and to cluster students according to their ability level. In this regard, a relevant element to be accounted for is the possible effect of the school students come from. For this aim, we provide a methodological tool which takes into account the multilevel structure of the data (i.e., students in schools) and allows us to cluster both students and schools into homogeneous classes of ability and effectiveness, and to assess the effect of certain students’ and school characteristics on the probability to belong to such classes. The proposed approach relies on an extended class of multidimensional latent class IRT models characterised by: (i) latent traits defined at student and school level, (ii) latent traits represented through random vectors with a discrete distribution, (iii) the inclusion of covariates at student and school level, and (iv) a two-parameter logistic parametrisation for the conditional probability of a correct response given the ability. The approach is applied for the analysis of data collected by two national tests administered in Italy to middle school students in June 2009: the INVALSI Language Test and the Mathematics Test.     

Private versus public high schools in Spain: disentangling managerial and programme efficiencies

The purpose of this paper is to compare the efficiency of a set of Spanish public and private high schools using data envelopment analysis (hereafter DEA). In view of the usual difficulties of obtaining reliable budget figures on private schools, we have used a restrictive efficiency notion which focuses on the relation between the academic results obtained by each school and the socio-economic background and academic profile of its pupils. In this study, special emphasis is placed upon decomposing the overall inefficiencies of each school into managerial (due to individual performance) and programme (due to structural differences between management models) components. Our results reveal that although, in general, private schools obtain better academic results than public schools in absolute terms, this is not the consequence of comparatively more effective management but rather of having pupils with a more favourable background for the educational process.     

Mathematics coaching and instructional reform: Individual and collective change

Mathematics coaching initiatives are being implemented in schools and districts across the country, guided by the notion that these initiatives will foster individual teacher’s learning and thereby support system-wide instructional improvement in mathematics. This paper explores the evolving roles that mathematics coaches played in a system-wide instructional improvement effort focused on elementary mathematics education in a medium-sized suburban school district. Using social network analysis and qualitative analysis of interviews, we argue that coaches facilitated teachers’ implementation of a new mathematics curriculum by acting as brokers, first as intermediaries between the district office and schools, then as catalysts for collective inquiry. Further, we show how coaches’ work was both enabled and constrained over time by various organizational dimensions at the school and district levels. Overall, our findings suggest that district and school leaders should think beyond the roles and responsibilities of individual coaches, and consider how to support coaches as participants in system-wide networks focused on continuous learning and instructional improvement.     

PANEL DISCUSSIONS

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.     

Some environmental and attitudinal characteristics as predictors of mathematical creativity

There are many things which can be made more useful and interesting through the application of creativity. Self-concept in mathematics and some school environmental factors such as resource adequacy, teachers’ support to the students, teachers’ classroom control, creative stimulation by the teachers, etc. were selected in the study. The sample of the study comprised 770 seventh grade students. Pearson correlation, multiple correlation, regression equation and multiple discriminant function analyses of variance were used to analyse the data. The result of the study showed that the relationship between mathematical creativity and each attitudinal and environmental characteristic was found to be positive and significant. Index of forecasting efficiency reveals that mathematical creativity may be best predicted by self-concept in mathematics. Environmental factors, resource adequacy and creative stimulation by the teachers’ are found to be the most important factors for predicting mathematical creativity, while social–intellectual involvement among students and educational administration of the schools are to be suppressive factors. The multiple correlation between mathematical creativity and attitudinal and school environmental characteristic suggests that the combined contribution of these variables plays a significant role in the development of mathematical creativity. Mahalanobis analysis indicates that self-concept in mathematics and total school environment were found to be contributing significantly to the development of mathematical creativity.     

Measuring equity of educational outcomes in the presence of inefficiency

Disparities in school expenditures have been a major concern in school finance. Equalization of spending presumably fulfills the ideal of equal educational opportunity. Differences in spending, however, result not only from differences in service provision, but also from variations in resource prices, exogenous cost environments and efficiency. As a result, equity measures that use expenditures per pupil as the object will capture these other variations and, therefore, may not be indicative of unequal educational outcomes. The purpose of this paper is to provide a systematic non-parametric framework for measuring outcome equity of school districts. Data Envelopment Analysis is used to adjust expenditures for differences in cost environments and to control for inefficiency in New York State school districts. The results suggest that nearly one-half of the measured inequity can be attributed to sources other than disparities in outcomes.