一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

运用新课程的理念提高数学复习课的课堂效率

如何提高数学复习课的教学效率?这是当前数学教学中值得研究的问题."复习",如果只是基础知识的简单罗列,难免使学生厌倦;如果只是习题解法的演示,又会令学生深陷题海无所适从……,对复习课的目标和功能的认识,决定了复习课内容的选择、教学的模式和教学的效果.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

一个基于复制变异准则的蛋白质作用网络的构建模型

本文主要根据生物学的复制和变异的基本原理,提出了具有反偏爱复制特性的一个蛋白质作用网络的新的演化模型.通过计算,发现所得的网络与实测的蛋白质作用网络的某些拓扑性质能够很好的吻合.生成的网络不仅是稀疏的,而且具有小世界性和无标度(scale-free)性质.     

例谈题目“提示”信息的有效利用

解题的一个重要环节是"审题",审题的目的就是希望从题目中提取有用的解题信息.一些创新性的试题,常在题干中设置了明显的"提示"信息,而对于解题者而言,如何利用好题目的这些"提示"信息,将是成功解题的关键.     

在向量解题中强化学生的解题意识

向量在近几年高考中越来越重要,其工具性作用已渗透以数学的各个分支.解答题中主要是以向量为载体的综合问题,体现向量"搭台",其他知识"唱戏"的特点.近年来高考中小题综合化的特点,已被大家所共识.选填题中对向量知识的考查更加灵活多变,对学生能力要求较高,可是只要是题型新颖一点或能力要求高点的题就成为学生得分的"事故多发地带".……     

员工配置资源行为的优化研究:自适应组织的视角

组织目标必须通过约束体系规范员工行为得以实现.进行组织约束下员工行为的定量研究,这对保证组织健康稳定发展非常必要.员工自身适应组织目标,服从组织的约束体系,配置好自有的资源,使得自身行为得以优化的研究较少.本文简要回顾了经济学理论、组织行为学、人力资源管理等方面对员工配置资源行为优化的研究及应用.界定了组织资源,并将其分为三种类型.在约束体系给出的基础上,将组织对员工行为的控制、要求或激励转为员工在之上或之下的运行约束;认为约束体系具有离散、悬河效应的特点;得出了评价组织约束体系的两种算法.讨论了员工资源及行为.尝试构造了基于员工适应组织约束下,员工的多目标、非线性,既有连续又有离散约束条件的配置资源行为优化的定量模型,并在基于员工利益最大化的前提下,对模型求解最优解的几种情况进行了研究.希望能够填补员工自身适应组织目标,行为优化定量模型这方面研究的空白.     

简议数列综合题的求解策略

数列在中学数学中占有极为重要的地位,它不仅广泛应用于实际,而且还融于高中数学的各个章节构成精彩纷呈的综合题,因此数列的综合题是高考中久考不衰的热点,且常考常新,并以此为压轴题者也屡见不鲜.本文拟就数列的几类主要综合题求解的基本策略简议如下:……     

让我们的课堂充满探索与交流——一个定值问题的诱思教学实录

新课程倡导"数学学习过程应该表现为一个探索与交流的过程--在探索的过程中形成自己对数学的理解,并在与他人的交流过程中逐渐完善自己的想法."     

Revival of a classical topic in differential geometry: the exploration of envelopes in a computerized environment

Learning mathematics in a technology-rich environment enables us to revive classical topics which have been removed from the curriculum a long time ago. Both theoretical issues and applications can be studied with an experimental process. We present how envelopes of 1-parameter families of plane curves and some of their applications can be presented early in the curriculum either for pre-service teachers or for in-service teachers. This approach may be useful for students in an engineering curriculum. Working with technology yields important effects, such as reviving classical topics, broadening perspectives on already known topics, and enhancing the learner's experimental skills, where conversion between various registers of representation is an important issue.     

Development of Theme-based,Interdisciplinary, Integrated Curriculum: A Theoretical Model

Interest in interdisciplinary, integrated curriculum development continues to increase. However, teachers who have been given primary responsibility for developing these materials are often working with little guidance. A model for developing theme-based, interdisciplinary, integrated curriculum is presented in this article. The model includes two phases, a theme creation phase and an activity refinement phase. Validity criteria from the interdisciplinary curriculum literature are used to assess the power of potential themes. An integration continuum model is used to facilitate refinement of activities included in the theme-based instruction. The curriculum development model is used to clarify the meaning of the terms theme-based, interdisciplinary, and integrated. The model is intended to be used by curriculum developers to facilitate the creation of powerful interdisciplinary lessons.     

Inquiry Learning of High School Students Through a Problem‐Based Environmental Health Science Curriculum

The purpose of this study was to examine the degree to which high school students improved their inquiry capabilities in relation to scientific literacy through their experience of a problem‐based environmental health science curriculum. The two inquiry capabilities studied were scientific questioning and approaches to inquiry into their own questions. A total of 129 high school students taught by two teachers in one school wrote responses to environmental health issues at the beginning and at the end of a 10‐week long inquiry curriculum. An additional group of 46 students of one of the two teachers learned an alternative curriculum and participated as a comparison group. The students using the inquiry curriculum performed significantly better than those using the alternative curriculum in posing active inquiry questions and generating hypothesis‐driven approaches to inquiry into their questions. The inquiry curriculum students also improved significantly from the pretest to the posttest in both measures of inquiry capacity. Among the students who were less prepared for inquiry in the beginning, 68% improved inquiry‐questioning capability, while among the students who were more prepared for inquiry, 36% improved in generating hypotheses‐driven approaches. Implications for curriculum design and implementation were provided along with further research suggestions.     

Re-sourcing curriculum materials: in search of appropriate frameworks for researching the enacted mathematics curriculum

This article provides a commentary to the eight papers of this issue of ZDM entitled “Researching the enacted mathematics curriculum.” It is structured around three main questions concerning (1) the layers of the curriculum addressed in the eight papers; (2) an identification of the main theoretical framework used, and an appreciation of this as compared to another European framework; and (3) challenges for future research on the enacted mathematics curriculum. The author outlines her views derived from a particular European perspective.     

A Literature Review of Science and Mathematics Integration

Integrated curricula has gained a great deal of acceptance among educators. Many educators provide testimonials about the effectiveness of units they teach, and many professional organizations stress integration across the curriculum. However, few empirical studies exist to support the notion that an integrated curriculum is any better than a well-designed traditional curriculum. Some educators question integration across the curriculum, because in the effort to integrate topics, science and mathematics content becomes superficial and trivial. This paper presents a review of the literature on integrated curricula. It concludes with a call to action for members of School Science and Mathematics Association.     

应用型本科院校《计算方法》课程教学模式研究

《计算方法》课程对于培养学生数值计算思想、应用科学计算解决实际问题的能力起着重要的作用.针对当前该课程的教学中存在的诸多问题,探讨了应用型本科院校的计算方法课程教学模式.     

Mathematics for All: Perspectives and Promising Practices

The Core-Plus Mathematics Project (CPMP, 1995) is one of four comprehensive curriculum development projects that, in 1992, were awarded 5-year grants by the National Science Foundation to design, evaluate, and disseminate innovative high school curricula that interpret and implement the recommendations of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics ( NCTM, 1989 ) and Professional Standards for Teaching Mathematics ( NCTM, 1991 ). This article describes CPMP perspectives on a new curriculum organization for high school mathematics, identifies implications of these perspectives for promoting access and equity for all students, and reports some of the supporting oral data from an ongoing formative evaluation of the curriculum.     

Developing Interdisciplinary Units: A Strategy Based on Problem Solving

While the benefits of the interdisciplinary unit are well documented, it presents a complex challenge to teachers in the natural and social sciences, mathematics, and humanities. Teachers must become active curriculum designers who shape and edit the curriculum according to students' needs. This paper describes knowledge for teachers as curriculum designers and a framework for interdisciplinary unit development. The framework addresses a metacurricular process (problem solving) that will be the unit centerpiece, the development of this central process related to the learner, and the tasks that teach explicit learning and thinking skills attached to the central process. An example of the framework in action is also described. As the faculty and curriculum coordinators for an innovative summer academy for minority students in northern Arizona have used this framework, they have evolved from a group that created a good idea to interest students with parallel subject development in separate classrooms to humanities/mathematics/science teams united in one team/classroom, in which content is integrated through the actions of the problem solving process.     

New challenges in the 2011 revised middle school curriculum of South Korea: mathematical process and mathematical attitude

The ‘future-oriented middle school mathematics curriculum focused on creativity and personality’ was revised in August of 2011 with the aim of nurturing students’ mathematical creativity and sound personalities. The curriculum emphasizes: contextual learning from which students can grasp mathematical concepts and make connections with their everyday lives; manipulation activities through which students may attain an intuitive idea of what they are learning and enhance their creativity; and reasoning to justify mathematical results based on their knowledge and experience. Since students will not be able to engage in the intended mathematical process with the study-load imposed by the current curriculum, the newly revised curriculum modifies or deletes some parts of the contents that have been traditionally taught mechanically. This paper provides a detailed overview of the main points of the revised curriculum.     

The Impact of Enacted Mathematics Curriculum Models on Prospective Elementary Teachers' Course Perceptions and Beliefs

This paper communicates the impact of prospective teachers' learning of mathematics using novel curriculum materials in an innovative classroom setting. Two sections of a mathematics content course for prospective elementary teachers used different text materials and instructional approaches. The primary mathematical authorities were the instructor and text in the textbook section and the prospective teachers in the curriculum materials section. After one semester, teachers in the curriculum materials section (n= 34) placed significantly more importance on classroom group work and discussions, less on instructor lecture and explanation, and less on textbooks having practice problems, examples, and explanations. They valued student exploration over practice. In the textbook section (n= 19), there was little change in the teachers' beliefs, in which practice was valued over exploration. These results highlight the positive impact of experiences with innovative curriculum materials on prospective elementary teachers' beliefs about mathematics instruction.