Students' gendered perceptions of mathematics in middle grades single‐sex and coeducational classrooms

With the introduction of single‐sex classroom settings in coeducational public schools, there is an ongoing debate as to whether single‐sex education may reduce or reinforce traditional stereotypes and gender roles. In this article we present findings from a study that investigated the extent to which mathematics is perceived as a gendered domain among adolescent students enrolled in single‐sex classes and coeducational classes. Further we analyzed the relationships between student characteristics, class‐type, and teacher variables on students' perceptions of gender in mathematics. Findings from this study challenge the traditional view of mathematics as a male domain. Female participants more frequently considered mathematics to be a female domain than the male participants. Male participants, on the other hand, typically did not stereotype the mathematics as a gendered domain. Results from this study do not indicate, for girls at least, that participation in single‐sex classes results in a greater propensity to stereotype mathematics as a gendered domain than would be the case in coeducational classes. This study contributes to the evolving discourse and understanding of adolescents' gendered attitudes and beliefs towards mathematics—especially in light of stereotyped assertions that have a bearing on efforts to promote the learning of mathematics and science.     

Influence of gender,single-sex and co-educational schooling on students’ enjoyment and achievement in mathematics

This research investigates the influence that gender, single-sex and co-educational schooling can have on students’ mathematics education in second-level Irish classrooms. Although gender differences in mathematics education have been the subject of research for many years, recent results from PISA (Programme for International Student Assessment) show that there are still marked differences between the achievement and attitude of male and female students in Irish mathematics classrooms. This paper examines the influence of gender in more detail and also investigates the impact of single-sex or co-educational schooling. This is a follow on study which further analyses data collected by the authors when they designed a pedagogical framework and used this to develop, implement and evaluate a teaching intervention in four second-level Irish schools. The aim of this pedagogical framework was to promote student interest in the topic of algebra through effective teaching of the domain. This paper further analyses the quantitative data collected and investigates whether there were differences in students’ enjoyment and achievement scores based on their gender and whether they attended single-sex or co-educational schools.     

Mathematical Dimensions of Students' Use of Proportional Reasoning In High School Physics

This study examines the mathematical processes used by students when solving physics tasks requiring proportional reasoning. The study investigates students' understanding and explanations of their mathematical processes. A qualitative and interpretive case study was conducted with 6 students from a coeducational urban high school for 5 months. Students were engaged with some high school physics tasks requiring proportional reasoning, during which a hermeneutic dialectic design was used to investigate their processes, understandings, and difficulties. Research techniques such as interviews, dialectical discourses, journal dialogue, and video and audio recordings were employed to generate, analyze, and interpret data. Results of the study indicate that the students employed mathematical proportional reasoning patterns and algorithms which they could not explain. Students also had difficulties translating physics tasks into mathematical statements, symbols, and relations. Students could not perform mathematical operations that were not directly obvious from the physics tasks, and some had difficulty with division. Students did not have adequate understanding of the mathematical processes involved in proportional reasoning.     

Equity in mathematics education: unions and intersections of feminist and social justice literature

Traditional models of gender equity incorporating deficit frameworks and creating norms based on male experiences have been challenged by models emphasizing the social construction of gender and positing that women may come to know things in different ways from men. This paper draws on the latter form of feminist theory while treating gender equity in mathematics as intimately interconnected with equity issues by social class and ethnicity. I integrate feminist and social justice literature in mathematics education and argue that to secure a transformative, sustainable impact on equity, we must treat mathematics as an integral component of a larger system producing educated citizens. I argue the need for a mathematics education with tri-fold support for mathematical literacy, critical literacy, and community literacy. Respectively, emphases are on mathematics, social critique, and community relations and actions. Currently, the integration of these three literacies is extremely limited in mathematics.     

Student Academic Self‐Concept and Perception of Classroom Environment in Single‐Sex and Coeducational Middle Grades Mathematics Classes

In this article, we present findings from a study that investigated the relationship between all‐girls classes, all‐boys classes, and coeducational classes on student mathematics self‐concept and student perception of classroom environment. Further, we compared responses of girls in all‐girls classes to girls in coeducational classes and responses of boys in all‐boys classes to boys in coeducational classes. Using the Mathematics Attitude Scale and the What Is Happening in This Class? questionnaire, we found no significant differences in student responses on any of the subscales or domains for any of the subgroups, except for Math as a Male Domain. Our findings indicate that student mathematics self‐concept and student perception of the classroom environment are similar regardless of whether students are in a single‐sex or a coeducational class.     

Paying the Price for Sugar and Spice: Shifting the Analytical Lens in Equity Research

The analytical stance taken by equity researchers in education, the methodologies employed, and the interpretations that are drawn from data all have an enormous impact on the knowledge that is produced about sources of inequality. In the 1970s and 1980s, a great deal of interest was given to the issue of women's and girls' underachievement in mathematics. This prompted numerous different research projects that investigated the extent and nature of the differences between girls' and boys' achievement and offered reasons why such disparities occurred. This work contributed to a discourse on gender and mathematics that flowed through the media channels and into schools, homes, and the workplace. In this article, I consider some of the scholarship on gender and mathematics, critically examining the findings that were produced and the influence they had. In the process, I propose a fundamental tension in research on equity, as scholars walk a fine and precarious line between lack of concern on the one hand and essentialism on the other. I argue in this article that negotiating that tension may be the most critical role for equity researchers as we move into the future.     

Paying the Price for "Sugar and Spice": Shifting the Analytical Lens in Equity Research

The analytical stance taken by equity researchers in education, the methodologies employed, and the interpretations that are drawn from data all have an enormous impact on the knowledge that is produced about sources of inequality. In the 1970s and 1980s, a great deal of interest was given to the issue of women's and girls' underachievement in mathematics. This prompted numerous different research projects that investigated the extent and nature of the differences between girls' and boys' achievement and offered reasons why such disparities occurred. This work contributed to a discourse on gender and mathematics that flowed through the media channels and into schools, homes, and the workplace. In this article, I consider some of the scholarship on gender and mathematics, critically examining the findings that were produced and the influence they had. In the process, I propose a fundamental tension in research on equity, as scholars walk a fine and precarious line between lack of concern on the one hand and essentialism on the other. I argue in this article that negotiating that tension may be the most critical role for equity researchers as we move into the future.     

Improving Science Teaching for All Students

An inservice program designed to enhance the knowledge and skills of elementary school teachers with respect to science content, effective teaching strategies, and gender equity was implemented as a semester-long course. During the course, teachers explored new science content in chemistry and physics and then collaboratively developed lesson plans from it based on hands-on, discovery-centered learning, enmeshed in strategies that could maximize female student interest and participation in science. Teachers tried out their lessons between course sessions in their own classrooms and then collaboratively reflected on their progress and problems in subsequent sessions. Program results were positive for both teachers and students. Teachers reported significant increases in both their level of knowledge of and their confidence in teaching chemistry and physics concepts, as well as in their knowledge of strategies for addressing gender inequities. Project students' attitudes, particularly those of the girls, improved for some dimensions, remained stable for others, and declined for one; the girls also increased their level of active participation in science activities. Overall, the project seems to have had a positive impact on science teaching content and pedagogy, and on student (especially girls') interest and active participation in science.     

Efficiency and equity tradeoffs in voting machine allocation problems

Efficiency and equity are the two crucial factors to be considered when allocating public resources such as voting machines. Existing allocation models are all single-objective, focusing on maximizing either efficiency or equity despite the fact that the actual decision-making process involves both issues simultaneously. We propose a bi-objective integer program to analyse the tradeoff between the two competing objectives. The new model quantifies the sacrifice in efficiency in order to achieve a certain improvement in equity and vice versa. Using data from the 2008 United States Presidential election in Franklin County, Ohio, we demonstrate that our model is capable of producing significantly more balanced allocation plans, in terms of efficiency and equity, than current practice or other competing methods.     

高管个人特征对股权激励模式选择的影响研究

上市公司股权激励模式的选择问题一直受社会各界关注。本文利用2006年到2017年期间实施股权激励的上市公司数据,研究了高管个人特征如何对股权激励模式的选择产生影响。结果表明,被激励高管的个人特征如高管年龄、任期、学历与社会资本显著影响公司股权激励模式的选择,年龄越大、任期越久、学历越高、社会资本越丰富的高管,公司更倾向选择限制性股票激励模式;男性高管越多的公司,越倾向选择股票期权激励模式,然而性别对其影响并不显著。本文在经过一系列的稳健性和内生性检验后,研究结论依然成立。本文研究结果丰富了股权激励相关理论,并为上市公司科学合理地选择股权激励模式提供参考。     

Bicriteria efficiency/equity hierarchical location models for public service application

As is often the case in healthcare provision, public services may offer facilities at a hierarchy of levels in different locations, ranging from basic to specialised levels of care. In addition to efficiency objectives, with public services there is the concern of equity of provision when locating new facilities. We present, as a tool-kit for decision makers, a range of discrete hierarchical location models with bicriteria efficiency/equity objectives. These models are for use in location of facilities within hierarchical systems where a fair but efficient hierarchical service is sought. The hierarchical models have as efficiency criteria both p-median and maximal-covering types. These components are combined in a novel manner with appropriate equity objectives to give decision makers a range of choices of scenarios. We illustrate use of the models in a healthcare setting.     

Policy analytics need more than a spreadsheet: a case study in funding formulae

This article presents two case studies, concerning the allocation of £Billions by a mechanism communicated via spreadsheet models. It argues that technical analytic skills as well as policy development skills are a vital component of governance. In the UK, Central Government uses funding formulae to distribute money to local service providers. One commonly stated goal of such formulae is equity of service provision. However, given the complexity of public services, together with variations in need, delivery style and the exercise of stakeholder judgement as to which needs should be met and how, such formulae frequently obscure the process by which equity has been taken into account. One policy ‘solution’ to managing such tensions is to seek ‘transparency’. With respect to funding formulae, this commonly involves publishing the underlying data and formulae in spreadsheets. This paper extends the argument that such ‘transparency’ requires an audience that understands the policy assumptions (and related conceptualisations), data sources, methodological approaches and interpretation of results. It demonstrates how the search for policy ‘transparency’ is also met by the technical quality assurance goals that the operational research community would recognise as best practice in the development both of software generally and spreadsheet models specifically. Illustrative examples of complex formulae acting to subvert equity are drawn from the English Fire and Rescue Service and Police Service allocation formulae. In the former, an increase in the amount of deprivation, as measured by one of six indicators, has the perverse effect of decreasing the financial allocation. In the latter, metropolitan areas such as London are found to gain most from the inclusion of variables measuring sparsity. The conclusion from these scenarios is that the steps needed to for technical quality assurance and policy transparency are mutually reinforcing goals, with policy analysts urged to make greater use of technical analytic skills in software development.     

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.     

Compensation differences between male and female CEOs for publicly traded firms: a nonparametric analysis

A recent article in the popular press suggested that gender is one determining factor of corporate executives' pay. The average compensation for the top 20 men was more than 10 times larger than for the top 20 women. We would expect, however, that direct compensation from salary and bonuses would be similar for both genders given the public nature of the data. There have been few academic articles on the topic of gender pay differences among top executives. One paper found marginally significant statistical evidence that women CEOs are paid more than their male counterparts. In this paper, we extend the literature by looking at compensation differences of male and female CEOs. Our sample includes over 40 female CEOs for publicly traded companies and matched pairs of comparable male CEOs. In addition, we use data envelopment analysis to derive a gap measure representing the difference between male and female compensation. The results suggest that there is a statistical difference between male and female potential compensation.     

Science and Mathematics Equity Issues at a Local School District Level

Many reports to the nation have revealed differences in the educational experiences of males and females. This is especially true in mathematics and science where females are not receiving the necessary educational background to develop the skills and understanding required to be citizens and employees in today's technological world. As a result, females are underrepresented in science, mathematics, and engineering professions. This study compares one school district's data with the data in national reports and then attempts to analyze what factors exist in the community and school district that reinforce and perpetuate inequitable situations for females. This study also provides a model for other school districts to conduct a self-study of gender equity education issues.     

Platonic solids symmetry in particle physics

Non-linearity of the Yang-Mills fields caused by the commutator in the Lagrangian calls attention to symmetries helping to reveal important features of the system, while obviating the need of actual solutions. To this end, a charge fixing procedure is carried out by means of counting photon oscillations between test particles moving along trajectories that form Platonic solids shaped patterns. With the infinite-range electromagnetic interaction as its origin, the procedure defines a class of interactions allowed for particle physics. Besides the familiar electromagnetic, weak and strong interactions, the scheme suggests an unusual force that cannot be detected with conventional means though possibly contributes to gravitation.     

Inquiry as an entry point to equity in the classroom

ABSTRACT

Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom.     

Socio-economic and cultural mediators of mathematics achievement and between-school equity in mathematics education at the global level

This paper aims at identifying and understanding how and to what extent socioeconomic and cultural factors mediate mathematics achievement and between-school equity in mathematics education among countries. First, under the assumption that equity and quality of education are independent constructs, the construct of equity-in-quality in mathematics education is developed. Second, the 18 countries that were identified in the previous work of the author Jurdak in (Toward equity in quality in mathematics education. Springer, New York, 2009) as being diverse in mathematics education will serve as study cases to illustrate, compare, and contrast the mediatory role of socio-economic and cultural factors in mathematics achievement and between-school equity in mathematics education. The results show that the differences in mathematics achievement and between-school equity in mathematics education at the country level are associated with, and can be accounted for in some cases, by socioeconomic and cultural factors.     

Left and right convergence of graphs with bounded degree

The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorphisms from fixed graphs into members of the sequence (left‐convergence), or counting homomorphisms into fixed graphs (right‐convergence). Under appropriate conditions, these two ways of defining convergence was proved to be equivalent in the dense case by Borgs, Chayes, Lovász, Sós and Vesztergombi. In this paper a similar equivalence is established in the bounded degree case, if the set of graphs in the definition of right‐convergence is appropriately restricted. In terms of statistical physics, the implication that left convergence implies right convergence means that for a left‐convergent sequence, partition functions of a large class of statistical physics models converge. The proof relies on techniques from statistical physics, like cluster expansion and Dobrushin Uniqueness. © 2012 Wiley Periodicals, Inc. Random Struct. 2012