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.     

Rethinking the role of algorithms in school mathematics: a conceptual model with focus on cognitive development

Starting from the context of mathematics learning in the East and West, this paper discusses the position and role of algorithms within school mathematics and argues that learning of algorithms has suffered from an alleged dichotomy between procedures and understanding, in that algorithms have been associated with low-level cognition. The paper first introduces a broad perspective about algorithms in school mathematics, and then, partially drawing on Bloom’s taxonomy and Säljö’s categorization of learning, proposes a model for the learning of algorithms with focus on students’ cognitive development. The model consists of three cognitive levels: (1) Knowledge and Skills, (2) Understanding and Comprehension, and (3) Evaluation and Construction. The model suggests that the learning of algorithms does not simply imply a low level of cognition, and provides a new perspective and framework to analyse the learning of algorithms. Following the model, we present examples to demonstrate the three levels and discuss related teaching strategies. We propose that the model can be used as an analysis tool to reconceptualize the role of algorithms in school mathematics and pose some questions for further research and scholarly discourse in this direction.     

An epistemic model of task design in dynamic geometry environment

Dynamic geometry environment (DGE) has been a catalytic agent driving a paradigm shift in the teaching and learning of school geometry in the past two decades. It opens up a pedagogical space for teachers and students to engage in mathematical explorations that niche across the experimental and the theoretical. In particular, the drag-mode in DGE has been a unique pedagogical tool that can facilitate and empower students to experiment with dynamic geometrical objects which can lead to generation of mathematical conjectures. Furthermore, the drag-mode seems to open up a new methodology and even a new discourse to acquire geometrical knowledge alternative to the traditional Euclidean deductive reasoning paradigm. This discussion paper proposes an epistemic model of techno-pedagogic mathematic task design which serves as a theoretical combined-lens to view mathematics knowledge acquisition. Three epistemic modes for techno-pedagogic mathematical task design are proposed. They are used to conceptualize design of dynamic geometry tasks capitalizing the unique drag-mode nature in DGE that opens up an explorative space for learners to acquire mathematical knowledge.     

Controlled sequential factorial design for simulation factor screening

Screening experiments are performed to eliminate unimportant factors efficiently so that the remaining important factors can be studied more thoroughly in later experiments. This paper proposes controlled sequential factorial design (CSFD) for discrete-event simulation experiments. It combines a sequential hypothesis testing procedure with a traditional (fractional) factorial design to control the Type I error and power for each factor under heterogeneous variance conditions. We compare CSFD with other sequential screening methods with similar error control properties. CSFD requires few assumptions and demonstrates robust performance with different system conditions. The method is appropriate for systems with a moderate number of factors and large variances.     

A comparative analysis of learning curves: Implications for new technology implementation management

New technology implementation projects are notoriously over time and budget resulting in significant financial and strategic organizational consequences. Some argue that inadequate planning and management, misspecification of requirements, team capabilities and learning contribute to cost and schedule over runs. In this paper we examine how learning curve theory could inform better management of new technology implementation projects. Our research makes four important contributions: (1) It presents a comparative analysis of learning curves and proposes how they can be used to help ERP implementation planning and management. (2) Based on empirical data from four ERP implementation projects, it provides illustrations of how managers can apply the curves in different project situations. (3) It provides a theoretical basis for empirical studies of learning and ERP (and other IT) implementations in different organizational settings. (4) It provides empirical justification for the development of learning curve theory in IT implementation.     

Pancake网络的t/k-诊断度及其算法

由于大型多处理机系统规模的不断扩大, 其组件脆弱性也随之增加, 因此故障容错性能对于多处理机系统尤为重要. t/k-诊断分析是一种能极大提高多处理机系统自我诊断性能的系统级故障诊断策略,该诊断策略能识别至多t个故障处理机节点, 其中可能包含至多$k$个被误诊的处理机. 首先给出了Pancake网络P_n(n\geq 5) 的容错性分析, 其后证明了P_n在PMC模型下是((k+1)n-3k-1)/k-可诊断的, 其中1\leq k\leq 3, 最后还给出复杂度为O(NlogN)的快速诊断算法来识别所有的故障节点.     

Increasing the total net revenue for single machine order acceptance and scheduling problems using an artificial bee colony algorithm

The order acceptance and scheduling (OAS) problem is an important topic for make-to-order production systems with limited production capacity and tight delivery requirements. This paper proposes a new algorithm based on Artificial Bee Colony (ABC) for solving the single machine OAS problem with release dates and sequence-dependent setup times. The performance of the proposed ABC-based algorithm was validated by a benchmark problem set of test instances with up to 100 orders. Experimental results showed that the proposed ABC-based algorithm outperformed three state-of-art metaheuristic-based algorithms from the literature. It is believed that this study successfully demonstrates a high-performance algorithm that can serve as a new benchmark approach for future research on the OAS problem addressed in this study.

     

A definition of subjective possibility

Based on the setting of exchangeable bets, this paper proposes a subjectivist view of numerical possibility theory. It relies on the assumption that when an agent constructs a probability measure by assigning prices to lotteries, this probability measure is actually induced by a belief function representing the agent’s actual state of knowledge. We also assume that the probability measure proposed by the agent in the course of the elicitation procedure is constructed via the so-called pignistic transformation (mathematically equivalent to the Shapley value in game theory). We pose and solve the problem of finding the least informative belief function having a given pignistic probability. We prove that it is unique and consonant, thus induced by a possibility distribution. This result exploits a simple informational ordering, in agreement with partial orderings between belief functions, comparing their information content. The obtained possibility distribution is subjective in the same sense as in the subjectivist school in probability theory. However, we claim that it is the least biased representation of the agent’s state of knowledge compatible with the observed betting behaviour.     

Reduced-order model predictive control of a fish schooling model

We study the problem of model predictive control (MPC) for the fish schooling model proposed by Gautrais et al. (2008). The high nonlinearity of the model attributed to its attraction/alignment/repulsion law suggests the need to use MPC for controlling the fish schooling’s motion. However, for large schools, the hybrid nature of the law can make it numerically demanding to perform finite-horizon optimizations in MPC. Therefore, this paper proposes reducing the fish schooling model for numerically efficient MPC; the reduction is based on using the weighted average of the directions of individual fish in the school. We analytically show how using the normalized eigenvector centrality of the alignment-interaction network can yield a better reduction by comparing reduction errors. We confirm this finding on the weight and numerical efficiency of the MPC with the reduced-order model by numerical simulations. The proposed reduction allows us to control a school with up to 500 individuals. Further, we confirm that reduction with the normalized eigenvector centrality allows us to improve the control accuracy by factor of five when compared to that using constant weights.     

Science Self‐Efficacy and School Transitions: Elementary School to Middle School,Middle School to High School

This study examined the science self‐efficacy beliefs of students at the transition from elementary school (Grade 6) to middle school (Grade 7) and the transition from middle school (Grade 8) to high school (Grade 9). The purpose was to determine whether students' perceived competence is impacted at these important school transitions and if the effect is mediated by gender and ethnicity. Science self‐efficacy was measured through a modified Self‐Efficacy Questionnaire for Children, which was adapted to focus specifically on science self‐efficacy. Multiple ordinary least squares regression was used to analyze the data. Two models were developed, one using ninth grade as the comparison group and the other using sixth grade as the comparison group. In each model, the independent variables (grade level, gender, and ethnicity) were regressed on the dependent variable, science self‐efficacy. The most striking finding was the large and significant decline in science self‐efficacy scores for ninth graders at the transition to high school. We also found that females and Hispanic students had lower scores across grades as compared to males and Caucasians. How these results relate to existing studies, and implications for practice and future research are discussed.     

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.     

代数系列课程习题讨论课的改革与实践

通过作者多年教学实践和总结 ,提出代数习题讨论课对培养学生分析解决问题的能力 ,初步的研究创新意识和提高代数课的教学质量是一个很有益的教学环节 .     

双瓶颈路段家庭出行者早高峰出行问题研究

针对一次连续出行中两个路段各存在一个瓶颈的双瓶颈路段,研究了家庭出行者早高峰期间先后经过双瓶颈到达学校和工作地的出行行为。首先建立了无收费下的用户均衡模型,接着考虑了拥挤收费模型,并就学校工作地开始时间差值大小的不同展开讨论,分析得出对应系统总出行成本最优时的收费值和收费时窗。研究发现收费管理能够有效降低系统总成本,并且学校和工作地开始时间差较小时的系统总成本更低,最后,通过数值算例验证了高峰时长保持不变,且得出了使得系统出行成本最优时的收费方案。     

The new math as an international phenomenon

The new math was a several-decade-long movement to update school mathematics that began in the mid twentieth century in many countries around the world. It took many forms, but much of it involved the preparation of new instructional materials, including textbooks. Much of the new math activity in Europe and North America was stimulated by conferences and seminars of the Organisation for Economic Cooperation and Development (OECD) in the early 1960s. Although the initial reform efforts addressed secondary school mathematics courses that prepared pupils for tertiary education, those efforts quickly spread to primary school mathematics, to pupils not headed to tertiary education, and to non-OECD countries. Mathematicians and schoolteachers were divided about the direction that the new math reforms took. Although the new math is often deemed a failed endeavor, it changed not only school mathematics but also the way people and countries viewed school mathematics.     

常系数线性微分方程组的基解矩阵的一种新求法

在求解常系数线性微分方程组时,关键是基解矩阵的计算.给出了利用哈密顿—凯莱定理计算基解矩阵的一种方法,并通过实例说明了这种方法的特点和在简化计算方面的有效性.     

Effects of variation theory approach in teaching and learning of algebra on urban and rural students’ algebraic achievement and motivation

This study investigates the effect of utilizing variation theory approach (VTA) on students' algebraic achievement and their motivation in learning algebra. The study used quasi-experimental non-equivalent control group research design. It involved 114 Form Two students in four intact classes (two classes were from an urban school, another two classes from a rural school). The first group of students from each school learnt algebra in class which used the VTA, while the second group of students in each school learnt algebra through conventional teaching approach. Two-way analysis of covariance and two-way multivariate analysis of variance (MANOVA) were used to analyse the data collected. The result of this study indicated that the use of VTA has significant effect on both urban and rural students' algebraic achievement. There were evidences that VTA has significant effect on rural VTA students' overall motivation in its five subscales: attention, relevance, confidence, satisfaction and interest but it was not so for urban VTA students' motivation. This study provides further empirical evidence that utilization of variation theory as pedagogical guide can promote the teaching and learning of Form Two Algebra topics in urban and rural secondary school classrooms.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

基于多任务委托—代理理论的高校教师激励机制研究

对高校教师的激励是高等教育中一个非常重要的环节,对高校教师合理的激励机制设计是提高高等教育水平的制度保证.从教师激励工作中高校管理者作为委托人与高校教师作为代理人二者信息不对称的角度出发,运用博弈论与委托代理理论,将高校教师工作进行教学努力和科研努力的划分,运用多任务委托代理理论对教师激励机制进行研究,建立模型进行分析,并结合西安科技大学现实提出合理化建议,以求达到既提高教学质量又提高科研产出水平的目的.     

Exploring the Use of New Representations as a Resource for Teacher Learning

An important goal of mathematics education reform is to support teacher learning. Toward this end, researchers and teacher educators have investigated ways in which teachers learn about mathematical content, pedagogical strategies, and student thinking as they implement reform. This study extends such work by examining how one elementary school and one high school teacher learned from students' interpretations of new conceptually based representations contained in instructional materials aligned with the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Results indicated that teaching with new representations provided a rich context for teacher learning at both the elementary and high school level, and three dimensions were identified along which such learning occurred. The results suggest that pedagogical content knowledge with respect to representations is an important facet of teacher cognition that should be studied in greater depth.