Immigrant parents’ perspectives on their children’s mathematics education

This paper draws on two research studies with similar theoretical backgrounds, in two different settings, Barcelona (Spain) and Tucson (USA). From a sociocultural perspective, the analysis of mathematics education in multilingual and multiethnic classrooms requires us to consider contexts, such as the family context, that have an influence on these classrooms and its participants. We focus on immigrant parents' perspectives on their children's mathematics education and we primarily discuss two topics (1) their experiences with the teaching of mathematics, and (2) the role of language (native language and second language). The two topics are explored with reference to the immigrant student's or their parents' former educational systems (the “before”) and their current educational systems (the “now”). Parents and schools understand educational systems, classroom cultures and students' attainment differently, as influenced by their sociocultural histories and contexts.     

Measuring technical and environmental efficiency in a state-contingent technology

Most developed countries support farming activities through policies that are tailored to meet their specific social, economic and environmental objectives. Economic and environmental efficiency have recently become relevant targets of most of these policies, whose sound implementation can be enhanced by monitoring farm performance from a multidimensional perspective. This paper proposes farm-level technical and environmental efficiency measures that recognize the stochastic conditions in which production takes place. A state-contingent framework is used to model production uncertainty. An implementable representation of the technology is developed using data envelopment analysis. The application focuses on a sample of Catalan arable crop farms. Results suggest that technical efficiency is slightly lower in bad than in good growing conditions. Nitrogen pollution can decrease substantially more under good than bad growing conditions.     

A Comparison of TIMSS Items Using Cognitive Domains

The results of international assessments such as the Trends in International Mathematics and Science Study (TIMSS) are often reported as rankings of nations. Focusing solely on national rank can result in invalid inferences about the relative quality of educational systems that can, in turn, lead to negative consequences for teachers and students. This study seeks an alternative data analysis method that allows for improved inferences about international performance on the TIMSS. In this study, four classroom teachers categorized a sample of TIMSS items by the cognitive domains of knowing and applying using the definitions provided by the TIMSS 2011 Assessment Frameworks. Items of different cognitive domains were analyzed separately. This disaggregation allowed for more valid inferences to be made about student performance. Results showed almost no significant difference between the performance of U.S. students and the students of five other nations. Additionally, no differences were observed in U.S. students' performance on knowing items and applying items, although students from some sample nations performed significantly better on knowing items. These results suggest that policy makers, educators, and citizens should be cautious when interpreting the results of TIMSS rank tables.     

Convexity,quality and efficiency in education

While Data Envelopment Analysis (DEA) has many attractions as a technique for analysing the efficiency of educational organisations, such as schools and universities, care must be taken in its use whenever its assumption of convexity of the prevailing technology and associated production possibility set may not hold. In particular, if the convexity assumption does not hold, DEA may overstate the scope for improvements in technical efficiency through proportional increases in all educational outputs and understate the importance of improvements in allocative efficiency from changing the educational output mix. The paper therefore examines conditions under which the convexity assumption is not guaranteed, particularly when the performance evaluation includes measures related to the assessed quality of the educational outputs. Under such conditions, there is a need to deploy other educational efficiency assessment tools, including an alternative non-parametric output-orientated technique and a more explicit valuation function for educational outputs, in order to estimate the shape of the efficiency frontier and both technical and allocative efficiency.     

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.     

Estimating the technical efficiency of health care systems: A cross-country comparison using the directional distance function

Economic activity produces not only desirable outputs but also undesirable outputs. Undesirable outputs are usually omitted from efficiency assessments (i.e., applications of Data Envelopment Analysis) which fail to express the true production process. The directional distance function model has been used for handling asymmetrically both desirable and undesirable outputs in the assessment process. In the present paper, we apply a generalized directional distance function to measure the efficiency of the health systems of 171 countries. We incorporate both desirable and undesirable outputs into the efficiency assessment without transforming the latter type of outputs into inputs or into their inverse form, as is done in most of the extant studies that deal with the measurement of health efficiency. The methodology that we apply introduces a modified definition of the efficiency score which yields results consistent with those obtained from radial DEA models. In addition, our results are independent of the length of the direction vector.     

Comparative efficiency analysis of Portuguese bank branches

The advent of Internet banking and phone banking is changing the role of bank branches from a predominantly transaction-based one to a sales-oriented role. This paper reports on an assessment of the branches of a Portuguese bank in terms of their performance in their new roles in three different areas: Their efficiency in fostering the use of new transaction channels, their efficiency in increasing sales and their customer base, and their efficiency in generating profits. Service quality is also a major issue in service organisations like bank branches, and therefore we analyse the way this dimension of performance has been accounted for in the literature and take it into account in our empirical application. We have used data envelopment analysis (DEA) for the different performance assessments, but we depart from traditional DEA models in some cases. Performance comparisons on each dimension allowed us to identify benchmark bank branches and also problematic bank branches. In addition, we found positive links between operational and profit efficiency and also between transactional and operational efficiency. Service quality is positively related with operational and profit efficiency.     

Measuring the joint impact of governance form and economic regulation on airport efficiency

This paper examines the joint impact that governance structure and economic regulation has on airport efficiency. The previous literature has focused on one or the other of these factors but not both. The empirical investigation uses a semi-parametric Bayesian distance stochastic frontier model, as well as a Data Envelopment Analysis (DEA) model. Based on a panel of airports in several countries we find that the form of economic regulation is relatively more important than the type of governance in affecting efficiency. The article provides measures of changes in expected efficiency when either or both the governance form and price regulation changes.     

Are You Convinced? Middle‐Grade Students' Evaluations of Mathematical Arguments

Students learn norms of proving by observing teachers generating proofs, engaging in proving, and generalizing features of proofs deemed convincing by an authority, such as a textbook. Students at all grade levels have difficulties generating valid proof; however, little research exists on students' understandings about what makes a mathematical argument convincing prior to more formal instruction in methods of proof. This study investigated middle‐school students' (ages 12–14) evaluations of arguments for a statement in number theory. Students evaluated both an empirical and a general argument in an interview setting. The results show that students tend to prefer empirical arguments because examples enhance an argument's power to show that the statement is true. However, interview responses also reveal that a significant number of students find arguments to be most convincing when examples are supported with an explanation that “tells why” the statement is true. The analysis also examined the alignment of students' reasons for choosing arguments as more convincing along with the strategies they employ to make arguments more convincing. Overall, the findings show middle‐school students' conceptions about what makes arguments convincing are more sophisticated than their performance in generating arguments suggests.     

Measurement of multiperiod aggregative efficiency

This article proposes a new method for measuring an aggregative efficiency of multiple period production systems. Every organization or firm generates a time series of data that represent its performances in the resource utilization and output production over multiple periods, and often desires an aggregated measure of efficiency for several periods of interest. Data envelopment analysis (DEA) has become an accepted and well-known approach to evaluating efficiency performance in a wide range of cases. However, most of the DEA studies have dealt primarily with ways to gauge the efficiency of production in only a single period so this efficiency reflects the insufficient or partial performance of multiple period productions. The new method is developed through extensions of the concept of Debreu–Farrell technical efficiency and is applied to evaluating the efficiency of cable TV service units with 3-year data.     

Joint use of DEA and constrained canonical correlation analysis for efficiency valuations involving categorical variables

The research on efficiency valuations has used two distinct approaches. One is the nonparametric approach known as data envelopment analysis (DEA), the other is the parametric approach based on regression analysis or its extension such as constrained canonical correlation analysis (CCCA). Interestingly, a recent study has employed a hybrid approach that cross-fertilizes DEA and CCCA to compensate for the drawbacks of the two methods and capture their positive aspects. This approach first applies DEA to select efficient units and then utilizes CCCA to identify a smooth efficient frontier with the selected efficient units only. We extend it to incorporate a categorical variable that reflects an environmental effect on efficiency performance. The need for considering a categorical variable arises in practice for an equitable efficiency valuation, as illustrated by managerial performance evaluation of the branches of a fast-food company, where the location of branches such as commercial or noncommercial area significantly affects their performance. We demonstrate various possible ways to handle such a categorical variable in the framework of a hybrid approach and characterize each of the methods. Based on this study, we suggest one method that simultaneously utilizes an extension of DEA, referred to as DEA with categorical variable, and CCCA employing a dummy variable, as in multiple regressions with dummy variables. Through an application to the branches of a fast-food company, we show the efficacy of the suggested method in terms of penalizing the advantageous location effect and compensating for the disadvantageous location effect. We also provide some discussions on the limitations underlying the hybrid approach in order to guide a proper use of this approach to the other potential applications.     

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.     

Digital game‐based learning for K–12 mathematics education: A meta‐analysis

Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta‐analysis study (a) investigates the current trend of digital game‐based learning (DGBL) by reviewing the research studies on the use of DGBL for mathematics learning, (b) examines the overall effect size of DGBL on K‐12 students' achievement in mathematics learning, and (c) discusses future directions for DGBL research in the context of mathematics learning. In total, 296 studies were collected for the review, but of those studies, only 33 research studies were identified as empirical studies and systematically analyzed to investigate the current research trends. In addition, due to insufficient statistical data, only 17 out of the 33 studies were analyzed to calculate the overall effect size of digital games on mathematics education. This study will contribute to the research community by analyzing recent trends in significant DGBL research, especially for those who are interested in using DGBL for mathematics education.     

A Modeling Perspective on the Teaching and Learning of Mathematical Problem Solving

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving.     

Improving the computational efficiency of metric-based spares algorithms

We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy.     

Perceived parental influence and students' dispositions to study mathematically-demanding courses in Higher Education

We explore the influence of family on adolescent students' mathematical habitus by investigating the association between students' perceptions of parental influence and their dispositions towards mathematics. A construct measuring ‘perceived parental influence’ was validated using Rasch methodology on data from 563 Cypriot students on ‘core’ and ‘advanced’ mathematics pre-university courses, and was then used to predict students' dispositions towards future study of mathematically-demanding courses at university. In most of the regression models, perceived parental influence was not associated significantly with students' dispositions towards mathematics, when other variables were included in the models. However, further statistical analysis showed that perceived parental influence is mediated by (i) the mathematics course students are studying and (ii) their mathematical inclination. We suggest that family influences on students' dispositions are significantly accounted for by students' prior choice of mathematics course and the family's inculcation of their mathematical inclination; these are important factors influencing university choices.     

Exploring Mathematics in Imaginative Places: Rethinking What Counts as Meaningful Contexts for Learning Mathematics

This paper explores what happens when students engage with mathematical tasks that make no attempt to be connected with students' everyday life experiences. The investigation draws on the work of educators who call for a broader view of what might count as real and relevant contexts for studying mathematics. It investigates students' experiences with two imaginative tasks and reports on the students' intellectual and emotional engagement. This engagement is examined and described in terms of the character and quality of the class and group discussions generated. Findings suggest that students can indeed engage productively with mathematics when it is explored in imaginative settings and that such contexts can help students support and sustain their engagement with the mathematics in the task.     

A Euclidean distance-based measure of efficiency in data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). Several efficiency measures have been proposed in the DEA literature, see, for instances, radial efficiency measure of Charnes et al. (CCR)(A. Charnes. W.W. Cooper, and E. Rhodes, 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–444), Russell graph measure (J.T. Russell, and R. Sirvant. 1999. An enhanced DEA Russell graph efficiency measure. Eur. J. Oper. Res. 115, pp. 596–607) and slack-based measure of Tone (K. Tone, 2001. A slack-based measure of efficiency in DEA. Eur. J. Oper. Res. 130, p. 498–509). In this article, we will propose an Euclidean distance-based measure of efficiency. Then, in order to discriminate the performance of efficient DMUs, an alternative super-efficiency DEA model is proposed. The applicability of the models developed is illustrated in the context of the analysis of gas companies performance.     

The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models

The infeasibility problem in traditional super efficiency models has been well established. A generalization of traditional input- or output-oriented super efficiency models, the directional distance function also suffers from infeasibility and related problems. The hyperbolic-oriented efficiency measure provides an alternative to the input-oriented, output-oriented, and directional efficiency measures in super efficiency models and it has the distinct advantage of eliminating the infeasibility problem for positive input/output data. We also show that using a hyperbolic orientation in a super efficiency model allows us to find feasible solutions for certain cases when the requirement for all data to be positive is relaxed. Further we demonstrate the hyperbolic orientated super efficiency method in an outlier detection application. Together, these results establish the use of the hyperbolic orientation in super efficiency analysis as a realistic alternative in practice.     

Understanding and representing the arithmetic averaging algorithm: an analysis and comparison of US and Chinese students' responses

Analysing the responses of 311 sixth-grade Chinese students and 232 sixth-grade US students to two problems involving arithmetic average, this study explored students' understanding and representation of the averaging algorithm from a cross-national perspective. Results of the study show that Chinese students were more successful than US students in obtaining correct numerical answers to each of the problems, but US and Chinese students had similar cognitive difficulties in solving the second task. The difficulties were not due to their lack of procedural knowledge of the averaging algorithm, rather due to their lack of conceptual understanding of the algorithm. There were significant differences between the US and Chinese students in their solution representations of the two average problems. Chinese students were more likely to use algebraic representations than US students; while US students were more likely to use pictorial or verbal representations. US and Chinese students' use of representations are related to their mathematical problem-solving performance. Students who used more advanced representations were better problem solvers. The findings of the study suggest that Chinese students' superior performance on the averaging problems is partly due to their use of advanced representations (e.g. algebraic).