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在中学数学教学中与自然数n有关的恒等式的证明方法历来都是采用数学归纳法。本文介绍一种构造性证明方法。此法简单自然。并具特色。以下以几例说明这种方法。 相似文献
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解题是学习数学的必经过程,它是对已有知识、方法,采取调动、重组、变换、类比、限定、推广等手段进行再创造的过程.其中,构造性的思想方法就是这种创造性活动的一个组成部分.笔者从几年来的解题实践经验中体会到:构造性的思想方法首先要明确所求结论,即为什么结论而构造;其次再弄清楚已知条件的主要特征;然后根据这些主要特征,决定应对策略,实施对应的构造方法.以下是中学数学中几种常见的构造性的思想方法,即构造法. 相似文献
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本文试图通过实例说明与自然数有关的不等式的构造性证明的常见方法。既希望学生对中学数学各部分内容之间的联系和渗透有所加强和重视,也希望能开阔学生视野,培养他们良好的思维品质和创造性解决问题的能力,从而对优化解题有所启示。 相似文献
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刘国锋 《商情·科学教育家》2009,(9)
纵观近几年来国内外的一些中学数学竞赛试题,其中,鸽巢原理在解中学数学竞赛试题中占有一定的地位,利用鸽巢原理及其推论解中学数学竞赛题,可以把问题分为四种类型.这仅仅是类型,是数学竞赛中要用到的技巧,而不是题目本身. 相似文献
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本文通过例题解析形式,阐述了在中学数学解题中常用的数形结合、整体性、分类讨论、类比联想、逆向思维、化归转化和构造性等七种思想方法。 相似文献
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解数学题的过程就是将已知条件通过适当的转化、逐步地归结为结论的过程,其中构造性的解题方法，很好地体现了数学发现、类比、化归的思想，还渗透着猜想、试验、探索归纳、概括、特殊化等重要的数学思想．不等式的证明是高中数学教学的一个难点内容．本文以例说明不等式的各种构造性证明方法，以供中学数学教学参考。1．构造方程某些不等式的条件可与关于某一变元的方程联系起来，应用二次方程根的判别式，或讨论方程根的范围给予证明．例1已知α、β、T∈(-π/2,π/2),求证:(tga-tgβ)~2≥(tgr--2tga)(2tgβ-tgr)．证若tgr-2tga=0,则原不… 相似文献
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赖章荣 《中学数学教学参考》2007,(5):58-59,60
1方法概述
在数学中,要证明某类对象的存在性一般有两种方法：一种是构造出这类对象的具体例子,这种方法叫做构造性方法;另一种是应用反证法,即假定这类对象不存在,然后通过推理得出矛盾,从而由排中律就可证明这类对象的存在性,这种方法叫做非构造性方法（或纯粹存在性证明方法）． 相似文献
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《中学数学教学参考》2007,(9)
1 方法概述在数学中,要证明某类对象的存在性一般有两种方法:一种是构造出这类对象的具体例子,这种方法叫做构造性方法;另一种是应用反证法,即假定这类对象不存在,然后通过推理得出矛盾,从而由排中律就可证明这类对象的存在性,这种方法叫做非构造性方法(或纯粹存在性证明方法).例如,古希腊毕达哥拉斯学派的成员发现了不可公度的量,证明了无理数的存在性;利用辗转相除法 相似文献
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Konstantinos A. Sdrolias Triandafillos A. Triandafillidis 《Educational Studies in Mathematics》2008,67(2):159-169
Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often
proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary
school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary
school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict
school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies
about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts
taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean
view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements
in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities
and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether
a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels. 相似文献
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Götz Krummheuer Marianne Leuzinger-Bohleber Marion Müller-Kirchof Melanie Münz Rose Vogel 《Educational Studies in Mathematics》2013,82(2):183-199
Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world. 相似文献
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在设计香港"三三制"新高中数学课程上存在着不少挑战,包括学习差异随学制的变动而进一步扩大,加深教与学上的困难等.为了更全面兼顾学习者本身在修读高中数学上不同的需要,己发表的有关数学科新高中课程建议内容可作更深入的讨论和修订. 相似文献
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新课程改革背景下,职业中专数学教学模式也应该创新,要适应新课程改革的需求,深化教育改革,创新教学体制。文章就新课程改革背景下职业中专数学教学有效性进行研究,分析现阶段中职数学课堂教学中存在的问题,提出提升中职数学课堂教学有效性的策略。 相似文献
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数学思想、数学活动与小学数学教学 总被引：4，自引：0，他引：4
ZHENG Yu-xin 《课程.教材.教法》2008,(5)
将"基本(数学)思想"与"基本(数学)活动经验"明确纳入"数学课程目标"之中有一定的合理性。以小学数学教学为背景对此作进一步分析:我们不仅应当针对不同的教学对象对此作出更为具体的界定,从而切实防止简单移植的现象,而且也应很好地处理具体知识内容的学习与基本数学思想的学习以及过程与结果之间的关系,而不应将此绝对地割裂开来。 相似文献
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韩国的数学教师职前教育体制有如下特点:类型多样的教师职前培养机构、严格的公立学校数学教师聘任制度、定期的教师教育机构评估制度.小学数学教师教育课程具有综合性、多样化特点;中学数学教师教育课程更重视学科知识.韩国数学教师职前教育对中国的数学教师教育有如下启示:建立多元的办学体制,致力于专业化的数学教师培养;以教师聘任制度和教师教育机构评估制度促进数学教师培养质量的提高;在学科课程和教学法课程之间寻求恰当平衡. 相似文献
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This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of them had been taught using a reform curriculum in middle school and 26 (59%) had been taught using a more traditional curriculum. Using Di Martino and Zan’s three-dimensional model for attitude, we found that the high-school seniors who had been taught using the reform curriculum in middle school harbored attitudes toward mathematics that differed significantly from the attitudes of those who had been taught using a traditional curriculum in middle school. Our analysis of the student interviews culled seven themes that provide fine-grained information about the students’ attitudes toward mathematics. Significantly greater percentages of reform students than traditional students had a relational Vision of mathematics as opposed to an instrumental Vision; however, there was no significant difference between the proportions of reform and traditional students who had a positive Emotional Disposition toward mathematics or a positive Perceived Competence in mathematics. 相似文献
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Vaughan Prain Peter Cox Craig Deed Jeffrey Dorman Debra Edwards Cathleen Farrelly Mary Keeffe Valerie Lovejoy Lucy Mow Peter Sellings Bruce Waldrip Zali Yager 《British Educational Research Journal》2013,39(4):654-676
Personalised learning is now broadly endorsed as a key strategy to improve student curricular engagement and academic attainment, but there is also strong critique of this construct. We review claims made for this approach, as well as concerns about its conceptual coherence and effects on different learner cohorts. Drawing on literature around differentiation of the curriculum, self‐regulated learning, and ‘relational agency’ we propose a framework for conceptualising and enacting this construct. We then report on an attempt to introduce personalised learning as one strategy, among several, to improve student academic performance and wellbeing in four low SES regional secondary schools in Australia. We report on a survey of 2407 students’ perceptions of the extent to which their school provided a personalised learning environment, and a case study of a programme within one school that aimed to apply a personalised approach to the mathematics curriculum. We found that while there were ongoing challenges in this approach, there was also evidence of success in the mathematics case. 相似文献
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In this paper, we describe the work by a team of university and public school mathematics educators to design mathematics
assessment tasks that are effective for students who have been identified at risk in mathematics, through their failure on
a state mathematics assessment. We have developed assessment tasks that have the very best chance to elicit the most mathematical
knowledge possible, but are closely tied to the school curriculum and practical enough to be administered by classroom teachers.
We offer some perspectives on the need for alternative mathematics assessment for at-risk students, along with the dangers
inherent in this undertaking. Some practical design considerations are discussed and examples of student responses to a mathematics
assessment scenario are given. Finally, policy issues related to authentic assessment are discussed. 相似文献
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校本课程的理论研究与实践在我国的基础教育中越来越受到人们的重视，新一轮课程改革对校本课程的开发提出了新的要求．校本课程有显性和隐性两种模式．教师和学校在某种程度应当成为国家课程实施过程中的自主开发者、编制者和评价者．实施校本课程的基本要求和原则有：目标一致性原则、适宜性原则等． 相似文献