共查询到20条相似文献，搜索用时 450 毫秒
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王晓勇 《数学学习与研究(教研版)》2012,(16):101-103
数学命题的研究一般是由两个大类——证明和反例组成的,数学发现也主要是提出问题和构造反例.本文结合实际的例子,着重就反例在初中数学课堂教学的价值等进行了探讨,使更多的人认识到反例教学的积极作用. 相似文献
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张菊 《中学数学研究(江西师大)》2003,(1):36-37
G·波利亚说:"类比和反例是获得发明的伟大源泉."通过类比使我们获得一系列的猜想,但当猜想实为谬误时,反例是最简捷的一种说明方法.反例和证明同等重要,一个数学真命题往往需要严密的证明,而假命题则靠反例加以鉴别,因此,在数学教学中,反例也有着极为重要的意义.本文谈谈反例在数学教学中发挥的作用. 相似文献
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张俊 《数学学习与研究(教研版)》2014,(1):41
在数学的天地里,证明和反例共同构成了壮观的数学大厦,作为问题另一方面的反例往往随着命题的否定而被遗忘.在教学过程中,教师对反例作用重视不够,教材中提到的也很少,其实反例同证明一样,在数学学习中具有同样重要作用. 相似文献
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杨占鹏 《数学学习与研究(教研版)》2013,(2):16
数学中的反例,是指符合某个命题的条件而又不符合该命题结论的例子.也就是说反例是一种指出某命题不成立的具体例子.在有关数学概念的教学中,举反例是一种即简便又有实效并极富科学性的方法.教学实践证明,恰当运用反例进行教学,有助于学生深刻理解和掌握所学基础知识,培养学生思维的缜密性、灵活性、发散性和创新性,反例教学在数学教学中起着非常重要的作用,值得我们对此进行研究. 相似文献
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浅谈数学分析中反例的作用 总被引：2，自引：0，他引：2
董海瑞 《太原大学教育学院学报》2009,27(Z1)
证明在数学中有重要的作用,但是从哲学的角度出发,作为问题的另一方面,也应清楚反例在数学中的重要性.要证明一个命题是错误的,极具有说服力而又简明的方法就是举出反例,去推翻它.文章浅谈了反例在数学分析中的作用. 相似文献
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在数学教学中,要判断一个数学命题是正确的,应由已知条件和已学过的公理、定义、定理等,严密推理得出结论;要否定一个命题,只要举一个反例即可。运用反例进行教学的方法称为反例法。反例法与证明法对数学学科的发展同样重要,是高中数学不可或缺的一种有效的教学方法。一、反例法在高中数学教学中的作用1.帮助学生准确理解基础知识 相似文献
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数学反例的教学价值 总被引：1，自引：0，他引：1
数学中并非每个命题都为真 .有的命题 ,虽从多方面进行了严密的推理 ,但仍不能得到结论 .因此 ,很自然地 ,人们对这个命题的真伪产生怀疑 ,从而设法否定这个命题 .怎样推翻一个命题呢 ?只要举出一个符合命题的条件而不符合该命题的结论的特例——反例 ,就可以了 .在数学史上 ,有不少著名命题被否定 ,都是反例的功劳 .反例是十分简明的否定 ,也是极有说服力的肯定 .反例的作用不仅用以否定命题而且也是发现数学真理的一种重要手段 .它在数学学习与研究中起着不可估量的作用 .美国当代数学家盖尔鲍姆说得好 :“数学由两大类——证明和反例组成… 相似文献
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和数学证明一样,数学反例在数学的发展中占有重要地位。因为对于数学问题的探索,反例的作用是证明所无法替代的。因此,数学反例历来是被人们重视的一个研究课题。本文试图从如何正确理解数学反例的含义,如何恰当看待数学反例的方法论意义两个方面作些初步探究。与有兴趣于此的朋友共同研讨。 一、数学反例的逻辑结构分析 相似文献
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王锦 《江西教育学院学报》2011,32(6):15-17
举反例是数学中一种重要思维方式,反例在数学中有很多作用,一个数学真命题的确定往往需要严密的证明,而对假命题的判定如用反例来说明则显得容易理解。文章通过具体的例子阐述了反例在数学教学中作用的体现,构造分析简单例子,总结归纳出反例构造的方法,为数学解题以及实际数学教学提供参考价值。 相似文献
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《学习科学杂志》2013,22(1):69-105
Several earlier studies have found the amount learned while studying worked-out examples is proportional to the number of self-explanations generated while studying examples. A self-explanation is a comment about an example statement that contains domain-relevant information over and above what was stated in the example line itself. This article analyzes the specific content of self-explanations generated by students while studying physics examples. In particular, the content is analyzed into pieces of constituent knowledge that were used in the comments. These were further analyzed in order to trace the source of knowledge from which self-explanations could be generated. The results suggest that there are two general sources for self-explanations. The first is deduction from knowledge acquired earlier while reading the text part of the chapter, usually by simply instantiating a general principle, concept, or procedure with information in the current example statement. The second explanation is generalization and extension of the example statements. Such construction of the content of the example statements yield new general knowledge that helps complete the students' otherwise incomplete understanding of the domain principles and concepts. The relevance of this research for instruction and models of explanation-based learning is discussed. 相似文献
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中国大学去行政化的哲学思考——基于建设两型社会背景 总被引：1，自引：0，他引：1
黎利云 《湖南师范大学教育科学学报》2010,9(5)
大学行政化与建设两型社会背道而驰。中国大学行政化无孔不入、事无巨细、压抑学术、严重浪费资源、助长不正之风,贻害无穷、备受诟病。它的出现与中国社会价值取向官本位化、中国大学历史较短自主性弱、大学官办背景浓厚等有很大关系,体制的落后与各界对大学的误解是根本原因。正确认识大学的本质以及政府与大学的关系、正确认识行政权力与学术权力的关系、政府在反思自己职能的基础上理性把握对大学管与不管的平衡点、取消大学行政级别、重拾大学精神、建立现代大学制度、完善法制、实现教育法治是中国大学去行政化的主要路径。 相似文献
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This paper describes the construction and research program of the Learning Through Collaborative Visualization (CoVis) Project, a testbed for exploring science education reform with telecommunications technology. The CoVis testbed is contrasted with other forms of educational research in an “ecology of paradigms,” which argues that testbeds are in fact a new setting for research with different requirements and challenges for the researcher. Two extended examples of telecommunications research are provided as examples of the kind of research that testbeds are well suited to explore. The first example is the evolution of videoconferencing in the CoVis testbed. The second example is the design and development of a networked groupware application called the Collaboratory Notebook. 相似文献
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马氏规则和反马氏规则表面相反,但两者有内在的统一性。本文从电子效应和反应历程两个方面作了讨论,并通过具体实例加以解释． 相似文献
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Although researchers have demonstrated that studying multiple examples is more effective than studying one example to facilitate
learning, the principles found in the literature for designing multiple examples remain ambiguous. This paper reviews variation
theory research on example design which sheds light on unclear issues regarding the effects of example variability. First,
the distinction of surface/structural should be replaced by critical/uncritical in example study. Aspects and features that
are critical to students’ understanding should be identified and compared in example design. Second, variation as well as
similarity among examples should be taken into consideration in example design. Certain patterns of variation and invariance
should be adopted to systematically determine the variability of examples. Third, students with different levels of prior
knowledge perceive different aspects of examples that are critical for their learning. Examples should be designed according
to aspects that are critical to specific students. 相似文献
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Timothy Patrick Fukawa-Connelly Charlene Newton 《Educational Studies in Mathematics》2014,87(3):323-349
Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in Educational Studies in Mathematics 69:77–79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the concept of an example space (Mason & Watson, 2008) and variation theory (Runesson in Scandinavian Journal of Educational Research 50:397–410, 2006) to create a lens to study how examples are used for pedagogical purposes in undergraduate proof-based instruction. We adapted the construct of an example space and extended its application to the constructs of example neighborhood, methods of example construction, and the functions of examples. We explained how to use our new lens to analyze the collection of examples and non-examples that the students had access to. We then demonstrate our method by analyzing the collection of examples and non-examples of a mathematical group the professor of an abstract algebra class presented during lectures or assigned to students in problem sets or exams. 相似文献
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Irit Peled 《Journal of Mathematics Teacher Education》2007,10(4-6):369-379
This article discusses the design of tasks for teacher education. It focuses on tasks that are used in a university course
for pre-service secondary school mathematics teachers. Special attention is given to tasks that use analogical thinking in
their construction or implementation. These tasks are categorized by type of teacher education goal and analyzed with respect
to the use of analogical thinking. Short examples are presented for three of the goal categories, while an elaborated example
is given for the fourth one. The detailed example describes the goals and design of a task sequence following an emergent
pedagogical need. Using the ad hoc constructed task-sequence the teacher educator avoids “telling” while demonstrating an
alternative instructional approach, and seizing the opportunity to bring up additional pedagogical issues. 相似文献
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对P-半单广群与对合亚交换广群作了进一步的研究,探讨了它们之间的逻辑联系及其与P-半单BCI-代数的关系,指明两种广群不具有必然的逻辑联系,举出了许多有用的反例. 相似文献
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随着经济的快速发展,中国大多数地区城市的主城区都将在不久的将来逐步进入后工业社会。自2007年全国开始的第一次污染源普查工作,从污染的来源上进一步证实了长三角的许多城区已经进入了后工业社会,长三角地区的城区生态建设也将为中国大多数城市城区的生态治理提供“范本”。本文选择比较有代表性的苏州市沧浪区（中心城区）为代表,分析进入后工业社会之后,城市政府应该改变执政理念,建设生态型城区。 相似文献