数学理性思维的作用及几点哲学思考

抽象思维和逻辑证明是数学中典型的理性思维.归纳理性思维的作用以及与哲学的联系,有助于我们更好地认识数学的功能.本文通过论述理性思维在数学的应用、发展以及保证科学研究的确定性与超前性、驳斥不可知论等方面的作用及数学与哲学的紧密联系,旨在说明理性思维对人才的培养有独特的作用,应该予以重视.     

Conceptual distinctions and preferential alignment across rational number representations

European Journal of Psychology of Education - Rational numbers can be represented in multiple formats (e.g., fractions, decimals, and percentages), and a rational number notation can be used to...     

有理数域Q上的矩阵为周期矩阵的一种简易判别法

对有理数域Q上矩阵的周期性的研究,得到了其为周期矩阵的一个充分条件,并由此给出了有理数域Q上的矩阵为周期矩阵的一种简易判别法,此法避开了繁难的求特征值和每个特征值的特征向量来判定矩阵能否对角化的过程．     

党校图书馆期刊文献利用率的若干思考

这篇文章揭示了影响党校图书馆期刊文献利用率的一些问题。并对如何提高党校图书馆期刊文献利用率提出了一些思考与建议。     

The role of rational number density knowledge in mathematical development

Many students still have not developed a robust understanding of rational number concepts at the end of primary school, despite several years of instruction on the topic. The present study aims to examine the patterns, predictors, and outcomes of the development of rational number knowledge in lower secondary school. Latent transition analysis revealed that rational number development from primary to lower secondary school (N = 362) appears to follow similar patterns as in younger students. In particular, a majority of students had poor knowledge of the density of the rational number set. Whole number magnitude knowledge appeared to be an important predictor of the development of rational number size knowledge, but not density knowledge. Finally, fraction density knowledge appeared to be related to concurrent algebra knowledge. Together these results point to an important role for density knowledge in mathematical development.     

Various ways to determine rational number size: an exploration across primary and secondary education

European Journal of Psychology of Education - Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is...     

Modeling the developmental trajectories of rational number concept(s)

The present study focuses on the development of two sub-concepts necessary for a complete mathematical understanding of rational numbers, a) representations of the magnitudes of rational numbers and b) the density of rational numbers. While difficulties with rational number concepts have been seen in students' of all ages, including educated adults, little is known about the developmental trajectories of the separate sub-concepts. We measured 10- to 12-year-old students' conceptual knowledge of rational numbers at three time points over a one-year period and estimated models of their conceptual knowledge using latent variable mixture models. Knowledge of magnitude representations is necessary, but not sufficient, for knowledge of density concepts. A Latent Transition Analysis indicated that few students displayed sustained understanding of rational numbers, particularly concepts of density. Results confirm difficulties with rational number conceptual change and suggest that latent variable mixture models can be useful in documenting these processes.     

有理数域(Q)上的矩阵为周期矩阵的一种简易判别法

对有理数域Q上矩阵的周期性的研究,得到了其为周期矩阵的一个充分条件,并由此给出了有理数域Q上的矩阵为周期矩阵的一种简易判别法,此法避开了繁难的求特征值和每个特征值的特征向量来判定矩阵能否对角化的过程．     

未确知有理数在商业银行社会责任评价中的应用

采用未确知有理数理论给出了一种评价商业银行社会责任履行程度的新方法。实例表明,该评价新方法较传统方法更有效、更实用。     

用同态映射讨论有理系数多项式可约性判定

从整系数多项式的不可约判定的充分条件E isenste in判别法的等价形式出发,借助同态映射,给出了判断整系数多项式不可约的新的判定条件.     

Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge

Spontaneous Focusing On quantitative Relations (SFOR) has been found to predict the development of rational number conceptual knowledge in primary students. Additionally, rational number knowledge has been shown to be related to later algebra knowledge. However, it is not yet clear: (a) the relative consistency of SFOR across multiple measurement points, (b) how SFOR tendency and rational number knowledge are inter-related across multiple time points, and (c) if SFOR tendency also predicts algebra knowledge. A sample of 140 third to fifth graders were followed over a four-year period and completed measures of SFOR tendency, rational number conceptual knowledge, and algebra knowledge. Results revealed that the SFOR was relatively consistent over a one-year period, suggesting that SFOR is not entirely context-dependent, but a more generalizable tendency. SFOR tendency was in a reciprocal relation with rational number conceptual knowledge, each being uniquely predictive of the other over a four-year period. Finally, SFOR tendency predicted algebra knowledge three-years later, even after taking into account non-verbal intelligence and rational number knowledge. The results of the present study provide further evidence that individual differences in SFOR tendency may have an important role in the development of mathematical knowledge, including rational numbers and algebra.     

覆盖粗糙集模型的增值算子及其性质

引进覆盖粗糙集模型的一对增值算子,并讨论它们的有关性质,即通过引理2和引理3,给出并证明了定理4.     

China's quest for world-class teachers: a rational model of national initiatives and institutional transformations

Teacher education has been undergoing significant transformations worldwide in recent decades, and China has made continuous efforts in its quest for world-class teachers. This paper aims at a comprehensive investigation of the complex policy process in China's national initiatives to nurture a world-class teaching force, with qualitative findings from a case study. It focuses on policy initiatives in China's unique sociocultural context, system transformations and developmental challenges from a rational prospective. Meanwhile, the challenges of institutional change and the limitations to change are examined within two frames – the contextually less amenable to change and the institutionally remediable. Policy implications for teacher education reform in the future are illustrated within these two frames. Lastly, this paper concludes that, along with its rising status, in terms of excellence in educational performance and students' academic achievement as shown in PISA 2009, China provides an alternative model for building a world-class teaching force and this may have multiple implications for the international community in an age of globalisation.     

A model for nurturing and assessing multidigit number sense among first grade children

Based on a synthesis of the literature and on the results of a two-year teaching program working with young primary children, a framework was developed, refined and validated for nurturing and assessing multidigit number sense. The major constructs incorporated in this framework were counting, partitioning, grouping, and number relationships. For each of these constructs, four different levels of thinking were established which, in essence, reflected a learning apprenticeship for multidigit number sense. At each level, and across all four constructs, learning indicators were developed and matched to distinctive problem tasks that went beyond the four basic operations.The framework was validated through data obtained from six case studies of grade 1 children. The thinking of these children was assessed and analyzed on the problem tasks for the four constructs and four levels. While the students were at different levels, all but one showed striking consistencies across the four constructs. Moreover, no student was able to solve a problem at a higher level when they had not solved a lower-level problem in the same category. The present framework for multidigit number sense covers only the lower primary grades, but research and instruction would benefit from an extended framework across the elementary grades.     

大学学科模型构建的理性审视

大学是以学科为赖以生存和发展核心的学术组织,学科模型是学科生存的基本样态,构建学科模型是大学学科建设的重要内容。理性审视大学学科模型的构建,则人才、基地和文化是大学学科的核心要素,也是构建大学学科模型的基本内核;国家与社会的需求以及学者的好奇心与兴趣是学科形成和发展的推动力;硬件和软环境是学科形成和发展的基本保障;科技创新、人才培养和引领文化是学科的主要任务与产出;而学科方向则是学科形成和发展的灵魂。     

Estimation of financial loss ratio for E-insurance: a quantitative model

In view of the risk of E-commerce and the response of the insurance industry to it, this paper is aimed at one important point of insurance, that is, estimation of financial loss ratio, which is one of the most difficult problems facing the E-insurance industry. This paper proposes a quantitative analyzing model for estimating E-insurance financial loss ratio. The model is based on gross income per enterprise and CSI/FBI computer crime and security survey. The analysis results presented are reasonable and valuable for both insurer and the insured and thus can be accepted by both of them. What we must point out is that according to our assumption, the financial loss ratio varied very little, 0.233% in 1999 and 0.236% in 2000 although there was much variation in the main data of the CSI/FBI survey.