独立学院数学课程体系的探索

为解决独立学院数学教学中能力强的学生"吃不饱",能力欠佳的学生"吃不消"的问题,提出了"基础+提高"统筹优化的数学课程体系."基础"模块的教学坚持为后续专业课服务,并穿插教书中"育人"理念;"提高"模块作为公共选修范畴,具有自主性、多元化特点,并突出人才培养的阶梯式发展.通过近5年的教学改革与实践,新课程体系有效地提高了学生学习数学的兴趣,降低了期末考试的不通过率,并造就一批有创新意识的人才.     

Journal of Mathematical Research with Applications

<正>Aims and Scope Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,is one of the transactions of China Society for Industrial and Applied Mathematics,and is a bimonthly journal.JMRA is dedicated to publishing first-rate original research papers in all areas of mathematics with applications,and making research findings available to a wide scientific world,as JMRE has for many years.In line with the name change,the new scope of Journal of Mathematical Research with Applications will not include the articles on mathematical methodology and mathematical philosophy.Copyright Information     

Middle-school students’ concept images of geometric translations

This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.     

The continuum as a formal space

A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined. Received: 11 November 1996     

基于熵的投资组合模糊优化模型

本文对基于信息熵的证券投资组合模型，根据模糊决策理论，在模糊环境下对模型进行求解，将投资者的主观意见反映在模糊情况的组合投资模型中，并通过实例，验证了该模型解法的可行性和有效性。     

教育专业规划的一个定量分析问题

本依据教育专业规划的定量分析方法，讲述了规划一所中学的办学模型的数学手段，提出了需考虑的主要因素，介绍了这些因素的量化方法，所应用的数学模型。     

Ways of talking and ways of positioning: Students’ beliefs in an inquiry-oriented differential equations class

As part of developmental research for an inquiry-oriented differential equations course, this study investigates the change in students’ beliefs about mathematics. The discourse analysis has identified two different types of perspective modes - i.e., discourse of the third-person perspective and discourse of the first-person perspective - in the students’ mathematical narratives, depending on their ways of positioning themselves with respect to mathematics. In the third-person perspective discourse, the students positioned themselves as passive recipients of mathematics that has been established by some external authority. In the first-person perspective discourse, the students positioned themselves as active mathematical inquirers and produced mathematics by interweaving their own mathematical ideas and experiences. Over the semester, students’ mathematical discourse changed from third-person perspective narratives to first-person perspective narratives. This change in their discourse pattern is interpreted as an indication of change in their beliefs about mathematics. Finally, this article discusses the instructional features that promote the change.     

高等级公路路线方案的多目标量化优选

应用最小二乘法准则,并改进了层次分析法判断矩阵的构成,获得考虑专家评价水平的诸影响因素权向量;基于集值统计法和属性数学原理,建立了对高等级公路路线方案量化综合评价优选模型,并给出了计算实例.     

补孔措施目标井层优选方法

油井补孔措施就是增加射开新的油层,是保证油井高产、油田持续开发的重要增产措施.而补孔措施效果好坏,主要取决于目标井层的选择是否合适.分析了影响油井补孔措施效果的因素,认为主要包括两方面共7个因素,一方面是井因素,包括全井含水率和全井日产油量共2个因素,另一方面是小层因素,包括小层渗透率、小层孔隙度、小层有效厚度、小层含油饱和度和小层地层压力共5个因素.在此基础上,建立了油井补孔措施目标井层优选方法,该方法以模糊数学为基础,通过综合评判对侯选井层打分,从而优选补孔措施目标井层.实际应用结果表明,利用该方法优选补孔措施目标井层,可靠性高,补孔措施实施后效果好.这种方法具有较高的学术与实用价值.