巧用无穷小数列求数列极限

介绍利用无穷小数列进行“变量”替换在求数列极限中的一些应用,并举例说明这一方法     

初中数学竞赛微型讲座——换元法

知识精要 1．认识换元法在解决某些数学问题时,根据问题的特征或关系引进适当的新的辅助元来替换原问题中的数、字母、式子等,从而使原问题变得更简单易解,这种通过用变量替换来解决问题的方法就叫换元法．它是一种基本而重要     

也谈三角代换在代数中的应用

1982年第11期《数学通报》发表的“三角代换在代数中的应用”一文是从如何进行代换及其应用两方面交织在一起介绍的,比较全面。本文着重谈一下如何进行代换的问题。变量代换法是数学中常用的解题方法,学生比较熟悉。但是,这种代换对于变量来说,是命题中已知条件认可的。即没有改变原变量的允许值范围。否则,会破坏变形的等价性。这一点却往往被学生所忽视。     

将数学实验的思想和方法融入大学数学教学

大学数学教学中应注重理论联系实际,注重数学思想和方法的讲授,强调应用案例中融入数学实验思想的新教学方法.改革课堂教学方法,探索新的教学模式,加强学生的实践性教学环节,培养学生的应用和创新能力.最后,本文给出了几个例子显示了数学实验与大学数学教学结合的效果.     

数学建模与学生自主实践能力培养的探索与实践

培养创新人才是新时期大学数学教育的重要目标,在大学数学教学中融入数学建模的思想和方法是培养学生科研能力的有效途径.结合多年指导学生数学建模竞赛和学生科研活动的经验与体会,深入分析数学建模在学生自主实践能力培养中的重要作用,将数学建模实践活动纳入学生课外科技创新活动,为更广泛地开展学生数学建模科技创新活动提供了新的思路.     

数学方法论(MM)在我国大学数学教学中的应用

综述了数学方法论在我国大学数学教学中的应用及其取得的成果.由一项数学教育实验所确证的"数学方法论的数学教育方式"(简称MM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,既教证明又教猜想,使教学、研究、发现同步.它不仅提升了学生的一般科学素养,增进了社会文化修养,形成和发展了数学品质,从而全面提高了学生素质;而且也培养与造就了一批既能胜任教学,又能从事科研的数学教师.     

数学思想方法在文科教学中的运用

最近,在首届“大学数学课程报告论坛”上,与会学者、教授认为,数学在许多社会科学领域得到越来越广泛的应用,文科的数学教学需要加强,文科生要学好数学.作为直接向大学输送人才的中学,如果能巧妙运用数学思想方法,取数学思想方法之长,补高中文科教学之短,可使教学内容化抽象为形象,化枯燥为生动,化深奥为浅显,化复杂为简明,不但调动学生的学习积极性和主动性,帮助他们理解和记忆,有利于学生了解数学应用及其应用的可能性,而且用思维方面所起的作用来了解数学,学会运用数学思想方法,培养学生的数学应用素质和意识.一、用数学思想方法揭示知识…     

求参数的范围(连堂讲稿)

[复习说明 ]含参数的数学问题中一个方面是已知该数学问题具有某种特性 ,依此求参数的范围(或参数的值 ) .此类问题遍及函数、方程、不等式、数列、三角、解几等等 ,历来是高考试卷中的一个热点 ,亦是高考复习中的一个热点 .学生容易把它与“分类讨论”混淆在一起而造成解题思维受阻 .本专题的复习难点是帮助学生克服见参数就分类的思维定势 .复习重点是探求不等式与解几中的参数范围 .[内容提要 ]求参数范围的常用思路是 :( 1 )分离变量 ,考虑代数式的取值范围及最值 ;( 2 )引进函数 ,利用函数的相关性质 ;( 3)变量替换 ,促进合理迁移 ;( 4…     

巧用极限思想解题

函数的极限是高中数学的重要内容之一，它研究变量在无限变化中的变化趋势，是从有限中认识无限、从近似中认识精确、从量变中认识质变的一种数学思想方法．极限和极限的思想是高等数学的基本思想方法，几乎所有的概念都离不开极限，作为进一步升入高校学习的工具，它的应用越来越备受重视．研究极限、极限的思想在中学数学中的应用．对培养学生的数学思维能力是非常重要的．     

变量代换在解题中的应用

在高中数学的学习中,学生大多采用题海战术,盲目刷题,不注重解题方法,导致在面对复杂抽象的数学题时,很难自主完成,久而久之对数学产生了抵触心理,影响学习效果.变量代换法是一种常见且应用广泛的解题方法,可以简化题目,帮助学生克服恐惧.本文中主要介绍幂函数代换、一元一次函数代换、有理函数代换、数列代换、分式代换、均值代换、三角代换这七种变量代换法在解题中的应用.     

用贝叶斯公式解释化验结果

借助概率论中的贝叶斯公式理论和方法,对现实中人们对有关化验结果的疑惑进行了详细的解释,从而使人们能更科学地理解化验结果,深刻感知数学在解决实际问题的作用.     

Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections Beyond Formal Classroom

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real‐world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and their applications to solving problems arising in real‐world situation. Clearly, it is assumed that the teachers themselves are able to make such connections. On the other hand, research shows that mathematics teachers find it difficult to make those connections. In this paper, we present the results of the study that investigated the ways in which exploring mathematics in informal sites, and in particular science museum, assist teachers with making connections between school mathematics and its applications in real world.     

Exploring Polygon Rings

Some topics in mathematics are unique because they can be explored by learners from the early grades through the advanced grades. One such topic is polygon rings. As suggested in the Curriculum and Evaluation Standards for School Mathematics ( National Council of Teachers of Mathematics. 1989 ), students can learn mathematics by actively engaging in the activities outlined in this article. The activities integrate problem solving, reasoning, and communication, and they offer a fascinating look at the beauty of the structure of mathematics.     

Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions,domain restrictions,and the arcsine function

Prospective secondary mathematics teachers are typically required to take advanced university mathematics courses. However, many prospective teachers see little value in completing these courses. In this paper, we present the instantiation of an innovative model that we have previously developed on how to teach advanced mathematics to prospective teachers in a way that informs their future pedagogy. We illustrate this model with a particular module in real analysis in which theorems about continuity, injectivity, and monotonicity are used to inform teachers’ instruction on inverse trigonometric functions and solving trigonometric equations. We report data from a design research study illustrating how our activities helped prospective teachers develop a more productive understanding of inverse functions. We then present pre-test/post-test data illustrating that the prospective teachers were better able to respond to pedagogical situations around these concepts that they might encounter.     

Journey toward Teaching Mathematics through Problem Solving

Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving? A group of teachers began the journey of learning to teach through problem solving while taking a Teaching Elementary School Mathematics graduate course. This course was designed to engage teachers in problem solving during class meetings and required them to do problem solving action research in their classrooms. Although challenged by the course problem solving work, teachers became more comfortable with the mathematics and recognized the importance of group work while problem solving. As they worked with their students, teachers were more confident in their students' abilities to be successful problem solvers. For some teachers, a strong problem solving foundation was established. For others, the foundation was more tentative.     

例谈数形结合在高数解题中的应用

通过微分中值的等式证明、求渐近线方程、定积分中的换元法、几何图形的描绘以及曲线积分的计算等例题,说明将代数运算或证明与几何直观相结合给解高等数学问题带来的好处．     

探索错误资源在高等数学教学中的应用

学生在学习高等数学的过程中,难免会犯一些错误.这些错误,实际上是一种宝贵的教学资源.本文探讨了高等数学教学中如何利用这些错误资源,提高学生分析问题和解决问题的能力.     

在军事院校大一新学员高等数学的教学中融入数学文化的思考与体会

军事院校的高等数学的教学有其固有的特点,大学数学的部分内容进入中学课堂,对高等数学的教学产生了一定的积极影响,在此过渡基础上军校的高等数学的教学中融入数学文化,不仅增强了趣味性有利于克服脱节现象,而且在教学内容、教学理念、教学方法上也得到衔接与提升,有助于培养军事院校大学生的综合素质与创新能力.