例谈数学思维的批判性

发展中学生的数学思维能力 ,特别是对思维品质的培养 ,是中学数学教学的一项重要任务 .近年来 ,高考中也注意了“加强对思维品质的考查” ,“无疑 ,对学生思维的灵活性、批判性、创新性等思维品质的考查是命题人员的新的探索与追求” .①所谓思维的批判性 ,就是善于发现问题 ,提出疑问 ,辨别是非的一种思维品质 .批判性的思维是一种实事求是、周到缜密的思维 .例 1　判断命题 :“设两曲线Ｃ1 ∶ｆ1 (ｘ ,ｙ) =0和Ｃ2 ∶ｆ2 (ｘ ,ｙ) =0有交点 ,则经过Ｃ1 和Ｃ2 交点的曲线的方程是 ｆ1 (ｘ ,ｙ) λｆ2 (ｘ ,ｙ) =0 ( ) ,其中λ∈Ｒ”的真假…     

论高三数学总复习中的过程教学功能

前苏联数学教育家斯托利亚尔指出 :“数学教学是思维活动的教学” .既然是活动 ,就有它的过程 ,思维活动的教学就是数学过程的教学 .因此 ,我们必须进行过程教学的探索 ,把学生学习知识的过程当作认识事物的过程来进行教学 .数学知识的形成过程一般经历知识发生过程 (形成感性认识 ) ,发展深化过程 (由感性认识向理性认识发展过程 ,形成数学结论或数学思想方法 )和知识应用过程 (应用理性认识解决数学问题形成能力 ,即实践过程 )三个阶段 ,每个阶段都存在相应的思维过程 .过程教学的实质 ,就是要在教学过程中 ,充分揭示每个阶段中的思维活动…     

要帮助学生完善解题结构——通过解题教学培养数学意识的思考

“问题是数学的心脏”,学数学离不开解题。通过解题培养学生的数学意识——数学思维方式是数学教学的一项根本任务。现实情况是相当一部分学生(甚至是即将高中毕业的学生)在解题上还处在盲目阶段:解题程序上缺乏必要的规范训练;思路探寻上主要是记题型,记套     

论数学解题创新的教学原则与策略

1　数学解题创新的基本内涵创新作为解决问题的最高形式 ,它有不同层次的表现形式 :一种是特殊才能的创新性 ,如科学家、发明家、艺术家等特殊人物在发现新事物、揭示新规律、获取新成果、建立新理论、创造新方法、发明新技术、研制新产品、解决新问题、创出新成绩的过程中所表现出来的创新性 (也称真创造 ) ;另一种是自我实现的创新性 ,是指相对于个体开发的可能性和自我潜在能力的创新性 ,如学生通过对已掌握的知识的分析、重组、联想、猜测等思维过程产生的自己从未有过的想法、见解和解决问题的方法 (也称类创造 ) .无论是真创造还是类…     

浅谈如何在数学教学中培养学生的解题反思能力

几乎所有的国家都把提高学生的问题解决的能力作为数学教学的重要目标之一.但解题后的反思是解题能力不可或缺的重要组成.本文就笔者在教学实践中如何培养学生解题反思能力谈几点看法.1挖掘教材例题本身价值,重视“三基”教学,培养解题反思能力首先,教材中素材的选取,反映了相应数学内容的本质,充分考虑了学生的心理特征和认知水平,有助于学生对数学的认识和理解,激发他们学习数学的兴趣.其次,课程内容的呈现,反映了数学发展的规律,以及人们的认识规律,体现从具体到抽象、特殊到一般的原则,使学生能够从中发现问题、提出问题,经历数学的发现…     

数学解题中的优化假设举例

在解题教学中注重优化假设的数学思想与方法 ,探索解题的思路和规律 ,能培养学生的直觉思维、发散思维和想象力 .在各类的数学问题中 ,有许多的题目可由条件和结论的特殊性与一般性的辩证关系 ,采用优化假设思想 ,创设新的解题思路 ,优化解题过程 .优化假设通过恰当的假设处理问题 ,优化出新的解题方法与思路 .优化假设是科学的发现、创造的方法之一 ,在优化假设过程中 ,体现了假设、猜想、优化等数学思想 ,渗透了数学其他的方法和思路 ,在高考和数学竞赛题中有许多数学问题能采用此方法给予解决 .1　假设条件特殊化优化解题思路一个命题成…     

解题反思——深化数学理性思维的重要方法

数学教学的核心任务是培养学生的思维能力．但是，当前的教学现状，由于受高考升学率的影响，有些教师盲目追求“题海战术”，用大量的练习来强化训练学生，忽视了数学理性思维的锤炼和深化．这样既加重了学生的课业负担，影响了学生的身心健康，而且事倍功半，收效甚微．众所周知，学习数学的过程与数学解题紧密相关，而数学能力的提高在于解题的质量而非解题的数量，因而重在研究解题的方向和策略，要善于帮助学生在解题过程中不断总结经验、积累解题的思维方法．因此，对于解决了的数学问题我们不要急于收工，苦能加以反思，质疑问难，启发学生发现问题和提出问题，便可以举一反三，深化学生的理性思维，培养学生分析问题和解决问题的能力，促进学生创新性思维能力的提高．     

数学问题解答

2007年9月号问题解答（解答由问题提供人给出）1691AABC中，AB-AC，D在BC上且BD=2DC；E在AD上且∠ABE=∠CAE．     

不可忽视的几项高三数学教学微观原则

高三数学教学(高考数学总复习)的宏观教学原则有:目的性、计划性、针对性、渐进性、系统性、综合性、有效性等.在长期的高三教学实践中,笔者深刻地认识到尚有下述几项不可忽视的微观教学原则,对其遵循与否必将直接影响学生的升学成绩.一、解题教学须暴露审题与觅径的思维过程的原则解题教学是高三数学教学的主要表现形式.常听学生说:"老师上课讲题讲得很清楚很有条理,板书也很详细,老师讲的每一个解题步骤及其理论依     

数学问题解答

2007年11月号问题解答(解答由问题提供人给出)(浙江省义乌市群星中学闵飞322000)证明(1)设直线AI1交BD于P,交BC于G,直线AI2交CD于Q.由AI1平分∠BAD知AADB=DBPP,由AI2平分∠CAD知AADC=DCQQ,又AB=AC,所以DBDP=DCQQ.所以PQ∥BC,所以∠BGP=∠GPQ过I1,I2作PQ的垂线,垂足为X、Y.记⊙I     

数学教学中审美能力的培养

本探讨审美与审美能力的概念，系统论述了在数学教学中审美感受能力的培养；审美鉴赏能力的培养；审美想象能力韵培养和审美创造能力的培养，也只有将这四个方面密切结合，才能在数学教学中培养审美能力。     

奇素数幂中的优美指数猜想

对于不小于7素数p,设1≤k≤p-1,则使用同余方法可证明方程n=pkp-1d（n）无正整数解,从而pkp-1不是优美指数,进而可以肯定＂存在无穷多个正整数不是优美指数＂.     

美容院顾客满意度影响因素的实证分析

本文通过对国内外美容行业现状的分析,以长沙市美容院顾客满意度的问卷调查结果为依据,利用统计研究的方法进行分析,得出了几个影响顾客满意度的关键因素,指出美容院行业在产品和销售服务等方面存在多种管理经营缺陷。     

The Construction of Denumerable q-Processes in Random Environments-The Existence and Uniqueness

The concepts of Markov process in random environment, q-matrix in random environment, and q-process in random environment are introduced. The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.     

Developing a market-based approach to managing the US strategic petroleum reserve

The Strategic Petroleum Reserve has not been used effectively to manage the consequences of oil shocks in the United States. The main reason is that political decision makers tend to hoard the reserves during crises and bureaucratic processes delay the sale of the reserves. Also, the enabling legislation focused on ameliorating shortages whereas disruptions result price spikes rather than shortages. We develop a Markov game of the buildup and drawdown of the reserve in which a public player aims to maximize consumer welfare at the same time private holders of inventory maximize their profit. The methodological contribution in this paper is the development of financial options to implement the public player’s optimal policy. We use the solution of this game to calculate the number and value of options necessary for the private marketplace to trigger the optimal buildup and drawdown of the reserve.     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)

This article is a continuation of [9]. Based on the discussion of random Kol-mogorov forward (backward) equations, for any given q-matrix in random environment,Q(θ) = (q(θ; x, y), x, y ∈ X), an infinite class of q-processes in random environments sat-isfying the random Kolmogorov forward (backward) equation is constructed. Moreover,under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed.     

Rationalising the use of Twitter by official organisations during risk events: Operationalising the Social Amplification of Risk Framework through causal loop diagrams

Communication of health risk events is a complex and challenging task. The advent of information and communication technology along with the following popularisation and widespread uptake of social media are reshaping the field of risk communication. Guided by key tenets of the Social Amplification of Risk Framework, this study developed a causal loop diagram, capturing the perceptions of professionals in health organisations regarding the role of Twitter during risk events. The aim of this paper is to explore the use of the causal loop diagram and its role with rationalising the use of Twitter in risk communication strategies. A key finding of the model is the central role of trust and its interrelationship with other factors during a risk event. A contribution is made to operational research through the novel use of soft system dynamics in risk communication, to risk communication through the investigation of the new medium Twitter and also to research on the Social Amplification of Risk Framework by providing a means through which to operationalise the framework.     

The interplay of various Scandinavian mathematical journals (1859–1953) and the road towards internationalization

The merger of various Nordic mathematical journals in 1953 into Mathematica Scandinavica (for research) and into Nordisk Matematisk Tidsskrift (for the more elementary topics, from 1979 NORMAT) confirmed increasing cooperation between matured Scandinavian mathematical communities. The merger originated from practical considerations including the wish to have a critical mass for economically viable publications.The present paper presents the basic steps in the development of several Scandinavian mathematical journals from 1859, the year of the foundation of the first general mathematical journal in a Scandinavian language, the Danish Mathematisk Tidsskrift, through various converging and diverging tendencies, towards the events of the year 1953.     

Planning sustainable community health schemes in rural areas of developing countries

In this research, we consider the planning of community health schemes by non-governmental or faith-based organisations in rural areas of developing countries, from both top-down and ground level viewpoints. We conclude that both types of planning approach are valid and necessary for sustainability of such developments. With top-down planning in mind, we describe our hierarchical models especially designed for location of community health facilities, with objectives pertaining to both efficiency and equity of provision. As an additional case study, we present modelling of the location of a maximal number of self-sustainable primary healthcare workers in a rural region of India.