设计应用问题的主要途径和原则

设计应用问题的主要途径和原则李星明（湖南省衡山县四中４２１３４１）近年来．中学数学开始重视数学应用题的教学与训练．进行应用题的教学，首先要有好的素材，应用问题质量的好坏直接关系到应用题教学的成败．本文就设计应用问题的主要途径和原则作粗浅探讨．１设计应...     

新课程高中数学教师适应性研究

普通高中新课程已于2004年秋季在山东、广东、海南和宁夏开始实验．这次课程改革在教学内容、教学理念、教学形式等方面都有很大的变化．课程内容力求体现时代性，反映数学学科及其应用的进展，渗透了现代数学思想，加强了与其他科学以及日常生活的联系，注重了信息技术与数学课程的整合．教学中，     

数学应用问题的建模方法初探

数学应用问题的教学已成为中学数学教学与研究的一个重要内容．解答数学应用问题的核心是建立数学模型．本文对如何建立数学模型和解答数学应用问题谈谈自己粗浅的认识，供同行参考．１数学应用问题的建模方法建立数学模型的一般方法步骤是：１．１认真审题，准确理解题意...     

教育统计与测评在高中数学教学管理中的应用研究

教育统计与测评是教育信息化背景下现代教育教学中不可或缺的重要手段,在教育教学评价中发挥着越来越大的作用．而教育统计与测评在高中数学教学管理中的应用研究却并不多见,这一现象严重制约了这一评价和管理手段的推行,更无法发挥其在数学教学管理中应有的作用．     

利用科研实践提高概率统计教学质量

将“应用式教学”理念引入概率论与数理统计课程的教学,并给出在实际科研项目中遇到的一些相关应用实例,旨在提高学生的学习热情,实现科研为教学服务的目的．     

数学方法论在数学教学中的应用

本文介绍了运用数学方法论的观点指导数学教学的一种崭新的数学教育方式,即应用数学的发展规律、数学的思想方法和数学中的发现、发明与创新的观点设计数学教学．     

信息技术与数学课堂整合的思考

近年来,飞速发展的信息技术渗透到了社会生活与工作的各个方面,信息素养已经成为当今社会每个公民必须具备的素养．为了跟时代接轨,世界各国纷纷将信息技术应用于数学课程．美国《标准》的“科技原则”提出“数学教学应该使用信息技术来帮助所有学生理解数学,并为越来越技术化的社会应用数学做好准备”．我国高中数学新课程理念中也强调要注重信息技术与数学课程的整合．     

大观念视角下的高中数学深度教学设计——以“直线与平面平行”的教学为例

<正>随着高中数学六大核心素养目标的提出,深度教学被推向新高度．大观念的挖掘和应用为实现深度教学搭建了“脚手架”,能够体现核心素养目标的本质要求．华东师范大学崔允漷教授指出:“整合应成为深度教学坚持的逻辑,以大观念为核心的整合是一种有效的教学方式．”基于此,本文中以“直线与平面平行”的教学为例,探讨如何基于大观念实现高中数学的深度教学设计．     

直角三角形的应用

二期课改非常重视培养学生应用所学数学知识的能力,对此提出了较高的教学目标．为了实现这样的教学目标,教师更应该研究教材、了解学生,在教学中注重学生获得数学知识的过程,即让学生做到知其然并知其所以然,只有这样才能真正提高学生的思维能力及应用数学知识的能力．     

解非常规数学题的教学探讨与研究

在数学教学中，解题教学对学生巩固理解与应用所学知识，培养良好的思维素质，增加其分析问题与解决问题的能力都极为重要．而在解题教学中，常规题与非常规题都有重要作用．本文拟在个人从事非常规题教学体验的基础上，探讨与这一课题有关的一些看法．毫无疑义，我们的教...     

Evaluating views of lecturers on the consistency of teaching content with teaching approach: traditional versus reform calculus

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both textbooks are presented in a rather formal language and generally highlight procedural knowledge. And, even though the examples in the reform book chosen are structured using multiple representations, only a small number of them incorporated the usage of instructional technology. The lecturers' views which were gathered indicated that, although, on the one hand, the example structures of the traditional textbook largely overlapped with the characteristics of the traditional approach, the example structures of the reform textbook, on the other hand, were found to be inconsistent with the characteristics of the reform approach, especially with regard to its environment and knowledge components. At the end of the paper, some suggestions for further studies are provided for book authors and researchers.     

Enhancing pre-service teachers’ fraction knowledge through open approach instruction

This study explores whether using the open approach instruction in teaching mathematics has a positive effect for enhancing pre-service teachers’ fraction knowledge. The test consisted of 32 items that were designed to examine pre-service teachers’ procedural and conceptual knowledge of fractions before and after receiving open approach instruction. The study was undertaken among students in four mathematics content and methods courses for the Elementary School Education program in a mid-western public university. The findings show that most of the teachers achieved improved learning outcomes through the open approach instruction.     

Solution representations of percentage change problems: the pre-service primary teachers’ mathematical thinking and reasoning

Solution representations can reveal how problem solvers communicate mathematical thinking and reasoning in problem-solving process. The present study examined the solution representations used by 20 pre-service teachers for the percentage change problems. The pre-service teachers were invited to solve a combination of simple and complex percentage change problems. The score for the majority of simple problems was 75% or above, but the score for the complex problems was below 75%. The highest percentage error occurred when the pre-service teachers encountered a percentage greater than 100% in the percentage change problems. Irrespective of their level of mathematics qualifications, the equation approach demonstrating two-step problem-solving process was the predominant strategy adopted by the pre-service teachers. The equation approach imposes low cognitive load and, therefore, is more accessible and efficient than the unitary approach. A few pre-service teachers used the unitary approach. The findings indicate that the pre-service teachers possessed relevant mathematical knowledge for percentage change problems. Furthermore, the inclusion of the equation approach in mathematics textbooks would provide an alternative perspective regarding the teaching and learning of percentage change problems.     

An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.     

Teaching of real numbers by using the Archimedes–Cantor approach and computer algebra systems

Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of CAS. In the case of real numbers, the Archimedes–Cantor approach satisfies this requirement. The name of Archimedes brings back the exhaustion method. Cantor's name reminds us of the use of Cauchy rational sequences to represent real numbers. The usage of CAS with the Archimedes–Cantor approach enables the discussion of various representations of real numbers such as graphical, decimal, approximate decimal with precision estimates, and representation as points on a straight line. Exercises with numbers such as e, π, the golden ratio ?, and algebraic irrational numbers can help students better understand the real numbers. The Archimedes–Cantor approach also reveals a deep and close relationship between real numbers and continuity, in particular the continuity of functions.     

A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the α-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA.     

2004年一个考研数学题

通过一个教研数学试题论述了能力培养和基础知识数学的重要性。     

Top-down approaches for integrated risk management: How accurate are they?

Banks and other financial institutions try to compute the necessary amount of total capital that they need for absorbing stochastically dependent losses from different risk types (e.g., credit risk and market risk). Two sophisticated procedures of this so-called integrated risk management are the top-down and the bottom-up approaches. When banks apply a more sophisticated risk integration approach at all, it is usually the top-down approach where copula functions are employed for linking the marginal distributions of profit and losses resulting from different risk types. However, it is not clear at all how accurate this approach is. Assuming that the bottom-up approach corresponds to the real-word data-generating process and using a comprehensive simulation study, it is shown that the top-down approach can underestimate the necessary amount of total capital for lower credit qualities. Furthermore, the direction and strength of the stochastic dependence between the risk types, the copula function employed, and the loss definitions all have an impact on the performance of the top-down approach. In addition, a goodness-of-fit test shows that, based on time series of loss data with realistic length, it is rather difficult to decide which copula function is the right one.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

一类增长网络模型的度分布

将主方程方法和马氏链首达概率方法应用于一个去边机制与时间相关的网络模型,得到这个模型度分布的精确表达式,并严格证明了度分布的存在性.