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.     

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.     

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.     

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.     

Assigning pupils to tutor groups in a comprehensive school

Comprehensive schools in the UK have the annual task of assigning their intake of new pupils to tutor groups. This case study describes how the problem has been addressed at one such school, where several factors are taken into account in order to make the groups as similar as possible and, since pupils have an induction day in June when they assemble in their tutor groups and meet their new tutors, where the time scale is short. Manual allocation has been used in the past, needing many staff-hours to achieve a satisfactory result. Heuristics implemented on a spreadsheet have enabled substantial savings in staff time and given more evenly balanced tutor groups.     

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.     

Word problems and mathematical understanding

One issue in the ongoing discussion about mathematics education in primary schools is how to improve weaker pupils' mathematical understanding. Two different training programmes for the solution of word problems were developed, each was tested in three classes of second graders, in addition, there were three control classes. One of the programmes focussed on pupils' real-life action-related behaviour, while the other programme was based on abstract and symbolic activities. Results indicate that pupils on lower levels of academic achievement profit most from the programme with abstract and symbolic activities, whereas the progress of the pupils in the action-related programme actually was less effective than the progress of the teaching methods used by teachers in the control classes.     

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.     

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.     

A multicriteria approach for optimizing bus schedules and school starting times

In many rural counties pupils on their way to school are a large, if not the largest group of customers for public mass transit. Hence an effective optimization of public mass transit in these regions must include the traffic caused by pupils. Besides a change in the schedules of the buses and the starting times of the trips, the school starting time may become an integral part of the planning process. We discuss the legal framework for this optimization problem in German states and counties and present a multi-objective mixed-integer linear programming formulation for the simultaneous specification of school and trip starting times. For its solution, we develop a two-stage decomposition heuristic and apply it to practical data sets from three different rural German counties.     

The Mathematics in Society Project: a new conception of mathematics(1) †

The Mathematics in Society Project (MISP) began in 1980 as an international association of mathematics educators in three continents. The main purpose of MISP is the writing of innovative secondary school mathematics courses based on a new conception of mathematics itself. The starting point for MISP was the fact that mathematics in school is found to be difficult and unpleasant by the great majority of pupils, but mathematics in society is widely diffused and used implicitly by most people. MISP therefore sees mathematics as a ‘living body’ representing all its uses (implicit and explicit) in society, in contrast to the ‘skeleton’ concept of mathematics which has led to such failure in schools. The gradual development of this new conception is informally analysed in the style of Kuhn and Lakatos.

     

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.     

Solving a school bus scheduling problem with integer programming

In many rural areas in Germany pupils on the way to school are a large if not the largest group of customers in public transport. If all schools start more or less at the same time then the bus companies need a high number of vehicles to serve the customer peak in the morning rush hours. In this article, we present an integer programming model for the integrated coordination of the school starting times and the public bus services. We discuss preprocessing techniques, model reformulations, and cutting planes that can be incorporated into a branch-and-cut algorithm. Computational results show that in our test counties a much lower number of buses would be sufficient if the schools start at different times.     

Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.     

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.     

Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.     

Investigating the impact of an urban community school effort on middle school STEM-related student outcomes over time through propensity score matched methods

This study investigates the impact of an urban community school reform initiative that focuses on an immigrant and refugee population in middle school. A 6th–8th grade cohort of students in the community school are followed over time and compared to a propensity score matched group on overall GPA, mathematics, and science academic outcomes and traditional college preparedness indicators. Further, a deeper dive into the intersection of gender and race/ethnicity was examined on all outcomes. Findings revealed that students in the urban community school demonstrated significantly more preparedness to enroll in college and move into a STEM field if they desired compared to the matched students. All gender/racial groups in the community school performed significantly higher than those in the matched group. Further, all gender/racial groups of students in the urban community school defied standard academic achievement drops common over time in middle school, and instead increase overall, math, and science grades from 6th to 8th grade.     

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.     

Evaluating Mathematics Achievement of Middle School Students in a Looping Environment

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school students' mathematical academic achievement. Student scores on the Mississippi Curriculum Test (MCT) were compared between sixth and eighth grade years for 69 students who looped during the seventh and eighth grades with a group of 137 students who did not loop. Looping students achieved statistically significantly greater growth on the MCT than their nonlooping counterparts between sixth and eighth grades. Further, the data were disaggregated by gender, ethnicity, and socioeconomic status. Findings indicate that looping may academically reengage students during the middle school years. Advantages and disadvantages of looping at the middle grades are discussed.     

School Timetabling Using Heuristic Search

This paper concerns a computer system which produces the bulk of the timetable for a large comprehensive school in England. The complexities of the school's lesson structure are discussed and the various constraints and objectives described. The timetable thus produced was successfully implemented for the academic year starting in September 1994 and was considered by the school to represent a marked improvement on previous timetables as well as being achieved much more swiftly. The solution method involves four phases of heuristic search with little or no manual intervention necessary. In contrast with other timetabling systems, the system completes all the difficult parts of the process to a high-quality standard, with only the final straightforward stages being left to the timetabler. Details of the solution method are outlined and dyiscussed in further detail in an appendix, especially the more innovative parts which involve a form of tabu search with influential diversification guided by the values of the subcosts as well as the overall cost. The system could be generalised so as to be applied to other schools.