School redistricting: embedding GIS tools with integer programming

The paper deals with a school redistricting problem in which blocks of a city must be assigned to schools according to diverse criteria. Previous approaches are reviewed and some desired properties of a good school districting plan are established. An optimization model together with a geographic information system environment are then proposed for finding a solution that satisfies these properties. A prototype of the system is described, some implementation issues are discussed, and two real-life examples from the city of Philadelphia are studied, one corresponding to a relatively easy to solve problem, and the other to a much harder one. The trade-offs in the solutions are analysed and feasibility questions are discussed. The results of the study strongly suggest that ill-defined spatial problems, such as school redistricting, can be addressed effectively by an interaction between objective analysis and subjective judgement.     

A survey of school timetabling research

Although there has been a fair amount of research in the area of school timetabling, this domain has not developed as well as other fields of educational timetabling such as university course and examination timetabling. This can possibly be attributed to the fact that the studies in this domain have generally been conducted in isolation of each other and have addressed different school timetabling problems. Furthermore, there have been no comparative studies on the success of different methodologies on a variety of school timetabling problems. As a way forward this paper provides an overview of the research conducted in this domain, details of problem sets which are publicly available and proposes areas for further research in school timetabling.     

Examination of the 8th grade students' TIMSS mathematics success in terms of different variables1

The aim of this study is to determine how the TIMSS mathematics success of the 8th grade students differentiates according to the school type, gender, mathematics report mark, parents' education level, cognitive domains and cognitive domains by gender. Relational survey method was used in the study. Six-hundred fifty two 8th grade students studying in the same city in Turkey participated in this study. In this study, a 45 question test that was made up by choosing TIMSS 2011 mathematics questionnaire was used as a data collection tool. Quantitative data analysis methods were used in the data analysis, frequency, percentage, average, standard deviation, independent sample test, one-way analysis of variance and post-hoc tests were applied to data by using SPSS packaged software. At the end of the study, it was determined that the school type, mathematics school mark, parents' education level and cognitive domains influenced the students' TIMSS mathematics success but their gender was a neutral element. Moreover, it was seen that schools which are really successful in national exams are more successful in TIMSS exam; students whose mathematics school marks are 5 and whose parents graduated from university are more successful in TIMSS exams than others.     

Planning Urban Recreational Facilities with Integer Goal Programming

Urban planners are often involved in the determination of where recreational facilities (i.e. pools, gymnasia, tennis courts, etc.) should be located within the city. This problem is complicated by the planners' desire to realize certain goals in the allocation process. They desire to build only facilities for which there are sufficient construction funds and which can be operated within a predetermined budget. In addition they desire to satisfy the demands of the residents of the city for different facilities. However, these demands are often conflicting since many urban areas are somewhat segregated with the inner city being predominantly minority/lower income and the outer city consisting of white/upper income groups. These different groups enjoy different types of recreation, and, thus, demand different facilities. Since this is basically an allocation problem with multiple conflicting objectives, goal programming surfaces as an appropriate solution technique. This paper describes an integer (0-1) goal programming model for the recreational allocation problem and demonstrates its use via a case example. The model results specify the facilities which should be constructed that best meet the conflicting goals.     

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.     

Preparing New Science Teachers for Urban Classrooms : Consensus Within an Expert Community

Preparing future science teachers for U.S. city classrooms is an important yet poorly understood process. The purpose of this study was to determine the philosophies and practices of university ‐based science educators associated with programs supplying teachers for metropolitan school systems. Through an iterative process of mailed questionnaires, 20 participants rated their views on issues pertinent to science teacher education. The responses to questionnaires were used in the creation of items for each subsequent round. The three rounds of questionnaires contained Likert ‐scale and open‐ended questions. For many issues, there was consistently high consensus among the expert panelists, including the presence of students for whom English is a second or new language, the importance of science education professors remaining connected to urban school issues, and practices often affiliated with reform (e.g., alternative assessment, nature of science). Several issues emerged as having low regard by the participants, including the role of student ethnicity on teaching strategies, providing instruction about reading strategies within science teacher preparation, and the value of professors having themselves taught science in urban settings.     

An Experiment in Teaching Elementary Ideas of Vectors

For a long time schools have been finding it difficult to appoint sufficient numbers of teachers of mathematics of the quality they would like. Qualifications of the teachers of arts subjects in a school are usually a good deal higher than those teaching sciences or mathematics. At the same time a revolution in the syllabus is taking place, and although the ‘Modern’ Syllabus is being encouraged there are very few competent teachers of it available.

In many schools the choice of a new textbook is handicapped by a lack of knowledge. This project, under the auspices of CAMET, is an attempt to provide a remedy.     

Modelling in Mathematics Classrooms: reflections on past developments and the future

This paper describes the development of mathematical modelling as an element in school mathematics curricula and assessments. After an account of what has been achieved over the last forty years, illustrated by the experiences of two mathematician-modellers who were involved, I discuss the implications for the future—for what remains to be done to enable modelling to make its essential contribution to the «functional mathematics», the mathematical literacy, of future citizens and professionals. What changes in curriculum are likely to be needed? What do we know about achieving these changes, and what more do we need to know? What resources will be needed? How far have they already been developed? How can mathematics teachers be enabled to handle this challenge which, scandalously, is new to most of them? These are the overall questions addressed. The lessons from past experience on the challenges of large-scale of implementation of profound changes, such as teaching modelling in school mathematics, are discussed. Though there are major obstacles still to overcome, the situation is encouraging.     

Memorable Experiences of a Science Field Trip

Potential immediate outcomes of a science field trip are the retention of knowledge associated with the program and an improved attitude toward the site visited during the trip. The length of associated memories regarding this experience are less clear. In an attempt to begin learning more about memorable experiences associated with a science field trip, a 1‐month and an 18‐month evaluation was conducted of elementary school students who had participated in an environmental science program at a community park in a midwestern city. Results of the evaluation found that students' memories were nonspecific and disassociated from information given by the field teacher. On the other hand, results from both tests yielded positive responses toward wanting to learn more about the subject matter and an interest in returning to the field trip site. This would indicate that, while not retaining specific objective‐oriented content, students did gain a positive reaction to returning that continued over the long‐term. Research related to memorable experiences is outlined, using a theory of long‐term memory developed by Tulving (1972) as a basic paradigm of correlation for the subsequent investigation.     

机场蓄车池出租车司机的选择决策研究 ——以首都机场为例

随着中国全面小康的逐步实现,乘客下飞机后乘坐出租车回市区已经成为大多数人的选择.着眼出租车送客至机场后的情景,以出租车司机的盈利最大化为目标,讨论出租车司机的两种决策选择——决策A是留在机场蓄车池等待回城区的乘客,决策B是空载回城找生意.控制时间相同的条件下,用机场接客的订单金额来估计决策A的收益,用司机单位时间内平均收益乘以经营时长来衡量决策B的收益.以北京市首都国际机场为例,从数学模型的角度为出租车司机提供决策条件,有效实现司机利润最大化.     

人口迁入与新增确诊数的趋势关系及因果量化分析

目前,很多地区新冠肺炎疫情已得到缓解,复工、复产已被多地政府部门提上日程.2月10日前后,全国各地返城复工人数增多,2月14日开始,广东、河南等地新增病例数出现了明显反弹,人口跨地区迁徙使疫情防控更加困难.目前全国返工、返校需求还远未得到满足,需要通过数据分析,对"返城复工"的风险进行评估.通过观察数据可以发现人口迁徙与新增确诊病例数有很强的正相关性,因此由"格兰杰因果检验"确定了人口迁徙与新增确诊病例数有显著的因果关系.     

Mathematics Teachers' Instructional Practices in an Era of High‐Stakes Testing

This study explored mathematics teachers' instructional practices in the context of high‐stakes testing. Data were obtained from a survey instrument given to a stratified sample of Mississippi and Tennessee teachers who teach the same content tested on their state's high school graduation examination. An analysis showed teachers using a balance of standards‐based and traditional practices and tools, including textbook‐based assignments, calculators, open‐response questions, supplementary materials, and multiple‐choice questions. Over 90% of teachers from both states felt that an “interest in helping my students attain test scores that will allow them to graduate high school” was a factor influencing their instructional practices. This was followed by an “interest in helping my school improve high school graduation examination scores,” and “belief these are the best instructional practices.”     

Science Attitudes of Selected Middle School Students in China: A Preliminary Investigation of Similarities and Differences as a Function of Gender

Evaluating the attitudes of science students is important for teachers, curriculum developers, and those working with preservice teachers. Although in the United States a great deal of attitudinal research has been conducted with regard to science education, in the People's Republic of China very little work concerning science attitudes has been completed. This study will report on an evaluation of Chinese boys' and girls' attitudes toward selected science topics. Students attended a middle school in the city of Shanghai. Analysis indicated that when the male and female Chinese students differ in their response patterns, females select more intense responses (“strongly agree” as opposed to “agree,”“strongly disagree” as opposed to “disagree”). Furthermore, the surveyed females often selected responses suggesting that they were more interested in the science topics and issues presented in the survey.     

The development of school mathematics textbooks in China since 1950

This paper provides an account of the development of school mathematics textbooks in China since 1950, the year following the founding of the People’s Republic. This development can be divided into several major periods consisting of (a) translating and modifying textbooks from the Soviet Union, (b) writing and editing unified textbooks, and (c) developing multiple versions of textbooks under curriculum standards that emphasize students’ personal development. Over the last 60 years, there have been many changes in the structure and content of developed textbooks; textbooks from each period exhibit their own characteristics which relate to specific political and cultural conditions. The debates on reform of compilation principles and of textbook structure and content still intertwine within the development of school mathematics textbooks. This development has resulted in the launching of a cross-national comparative study on mathematics textbooks in China which is intended to promote the development of mathematics textbooks considering cross-national perspectives.     

Affirmative action under common school priorities: The top trading cycles mechanism case

In school choice, there are two types of extensively used affirmative action policies based on majority quotas and minority reserves, respectively. This paper investigates the responsiveness of the top trading cycles school choice mechanism to these two types of affirmative action policies when all schools have the same priority order over students. Under the common school priority (within student type) condition, we show that the top trading cycles mechanism is minimally responsive to the minority reserves type of affirmative action policy, while a stronger majority quotas type of affirmative action policy may yield a Pareto inferior assignment for the minority.     

Application of network theory and AHP in urban transportation to minimize earthquake damages

Network theory and Saaty's analytic heirarchy process (AHP) are considered to be effective methods for estimating a city's traffic pattern during the emergency period of an earthquake, and for evaluating the urban transportation network of that city. A graph is created in which the nodes are land uses (or a group of land uses), crossroads or junctions represent the city, and the arcs are the streets. AHP is used to determine the priority of trips, and shortest path techniques identify the fastest routes for daily trips, and the safest ones during earthquakes. A pareto diagram then shows those streets that play an important role in satisfying both criteria. On the basis of the trip patterns obtained, the accessibility of a city may be estimated. This methodology helps to identify the weak points of the transportation network after an earthquake. However, it can also be used to analyse plans for the expansion of existing cities. The methodology was employed in the city of Rasht after the devastating earthquake in northern Iran in 1990.     

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.     

主成分分析在经济预测中的应用

在许多社会经济现象中，有这样的数学模型，它是不断地增长的，但又略有波浪式的起伏。要预测这类型的问题，既不能用一般的线性回归预测法，即使在ｎ＝２１时其相关系数高达０．９８８（甚至０．９９６），也能产生较大的预测误差。我们也不能用一般的曲线回归或多项式回归。包括很常用的龚珀资（Ｃｏｍｐｅｒｔｚ）曲线预测法也无济于事，因为龚法实际上是对具有Ｓ形数学模型的预测有效。它们都不符合波浪增长式且具有一定周期的数学模型。本文先就青岛市１９６２年至１９８２年这２１年人口资料进行分析探讨；再就１９７１年至１９９１年这２１年资料进行动态跟踪分析。并引进波浪增长曲线的作法。     

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.     

Modeling conceptions revisited

The previous issue of ZDM raised several fundamental issues on the role of modeling in the school curricula at micro and macro levels. In this paper we complement the approaches described there by discussing some of the issues and the barriers to the implementation of mathematical modeling in school curricula raised there from the perspective of the on going work of the models and modeling research group. In doing so we stress the need for critical literacy as well as the need to initiate a new research agenda based on the fact that we are now living in a fundamentally different world in which reality is characterized by complex systems. This may very well require us to go beyond conventional notions of modeling.