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<正>一、目标定位计数问题是数学中的重要研究对象之一,分类加法计数原理、分步乘法计数原理是排列组合问题的最基本的原理,是推导排列数、组合数公式的理论依据,也是求解排列、组合问题的基本思想.本节课内容是学生在已有的利用列举法进行计数的基础上,进一步研究计数的规律,归纳出两种基本计数原理.从思想方法的角 相似文献
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容斥原理是组合数学的一个基本的计数原理.通过给出容斥原理的两种等价形式,来探讨容斥原理在排列组合、数论、图论以及代数中有关解决有限集合计数问题方面的应用. 相似文献
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陈昭亮 《中学数学教学参考》2008,(17)
对应是数学中非常基本的思想方法,它的应用极其广泛,数学竞赛中的许多问题都与它有关,特别是运用对应进行计数是解决组合数学中计数问题的有力手段.在组合计数中,要计算某个有限集合A的元素个数|A|,如果直接求解比较困难,这时可考虑在 相似文献
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计数问题是数学中的重要研究对象之一.小到我们生活中的琐碎往事,每日的课程安排,大到国家人口普查和经济状况的统计都涉及到计数问题.在我们中学的数学之旅中,加法原理和乘法原理或是解决计数问题最基本、最重要的方法,它们为学习排列、组合、二项式定理及其应用,也为解决很多实际问题提供了 相似文献
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计数问题是数学中的重要研究对象之一．分类加法计数原理、分类乘法计数原理是解决计数问题的最基本、最重要的方法，它们为解决很多实际问题提供了思想和工具．下面笔者结合2010年数学高考试题从以下几个方面加以说明． 相似文献
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《数理化学习(高中版)》2007,(13)
计算办某件事共有多少种办法的问题称作计数问题,课本中的排列与组合就是两类常见的计数问题.学习计数问题要掌握两个基本方法——分类原理与分步原理,两类基本问题——排列问题与组合问题,区分两个基本方法和两类基本问题是正确计数的前提. 相似文献
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<正>一、教材分析1.地位和作用两个基本计数原理是处理计数问题的最基本、最重要的方法,它为后面学习排列、组合、随机变量的概率等内容提供了思想和理 相似文献
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组合数学中的计数问题 ,是数学竞赛题中的熟面孔 ,很多同学认为只要凭借单纯的课内知识就可左右逢源 ,使问题迎刃而解 .其实具体解题时 ,却会使你挖空心思 ,也无所适从 .对于这类问题往往首先要通过构造法描绘出对象的简单数学模型 ,继而借助在计数问题中常用的一些数学原理方可得出所求对象的总数或范围 .1 运用分类计数原理与分步计数原理分类计数原理与分步计数原理 (即加法原理与乘法原理 )是关于计数的两个基本原理 ,是解决竞赛中计数问题的基础 .下面提出的三个问题 ,注意结合排列与组合的相关知识 ,构造出相应的模型再去分析求解 .… 相似文献
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成军 《中学生数理化(高中版)》2013,(8):59
《全日制普通高中数学课程标准》明确指出,计数问题是数学中的重要研究对象之一,在本模块中,学生将学习计数基本原理、排列、组合及其应用,了解计数与现实生活的联系,会解决简单的计数问题.从近几年高考命题来看,计数问题的试题难度有下降的趋势.在本模块的教学中,学生一听就会,而 相似文献
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研究了有限集论中的一类组合计数问题,利用容斥原理得出了此类问题的计数公式,从而发展了文献[1]的计数理论。 相似文献
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Education Governance in Transition: An introduction 总被引：1，自引：0，他引：1
Sverker Lindblad Ingolfur Asgeir Johannesson Hannu Simola 《Scandinavian Journal of Educational Research》2013,57(3):237-245
The purpose of this article is to present concepts and research problems dealing with education governance and social inclusion and exclusion. Education restructuring, as a recent international movement, is regarded as a combination of transitions in governing and new managerialism. Social inclusion and exclusion is conceived of as a duplet concept, mutually defining each other. The relation between new governance - deregulation, decentralisation, privatisation and steering by goals and results - and social inclusion/exclusion is conceptualised as an equity problematic and a knowledge problematic. It is argued that there is a need to understand the system of reason in order to capture the implications of education governing in transition. 相似文献
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母函数是组合数学中非常重要的计数工具.本文摒弃常用的使用加法原则、乘法原则及基本公式求解排列组合的方法,利用母函数对排列组合问题进行了分析和求解. 相似文献
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虞峰 《番禺职业技术学院学报》2011,(3):20-23
文章通过分析当前高职高等数学课程存在的问题,提出按照＂必须、够用＂的原则,以纵向内化整合和横向外化整合为课程改革基本思路,构建以＂问题教学、实验教学＂相结合的高职院校高等数学课程体系。 相似文献
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The inability to develop, strengthen, and access associations in memory that allow for the rapid and accurate retrieval of answers to basic addition problems is a distinguishing characteristic of a mathematics learning difficulty. The ‘two-factor theory of math fact learning’ (Robinson, Menchetti, & Torgesen, 2002) proposes that a weakness in semantic or phonological processing relating to number underlies such difficulty. The empirical support for this theory has been limited. In this study the basic addition performance of five adolescent students still reliant on counting was examined. A regression analysis of reaction times to counting trials revealed counting-speed to be an important factor in helping to explain why practice had not led to retrieval. The findings are discussed in terms of advancing the two-factor theory of math fact learning and implications for instruction are considered. 相似文献
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Smita Guha 《International Journal of Early Years Education》2006,14(1):15-34
The objective of this small study was to elicit responses from early childhood teachers in India on mathematics learning strategies and to measure the extent of finger counting technique adopted by the teachers in teaching young children. Specifically, the research focused on the effective ways of teaching mathematics to children in India, and examined teachers’ approach to number counting. In India, children were taught by their parents or by their teachers to use fingers to count. The qualitative study conducted by the researcher further enriched the topic with first‐hand comments by the teachers. Although the finger counting method was not the only process that teachers would adopt, it was embedded in the culture and taken into consideration while infusing mathematics skills. The teachers confirmed adopting the Indian method of finger counting in their teaching strategy; some specified that the method helped children to undertake addition and subtraction of carrying and borrowing, as counting by objects could not be available all the time. Although the study is limited by its small sample to the unique mathematics learning experience in India, it provides readers with a glimpse of culturally responsive teaching methods and an alternative mathematics teaching strategy. 相似文献
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分析研究了国际数学奥林匹克竞赛中的代数不等式问题,认为:它已成为发展中的奥林匹克数学的重要组成部分.这类问题的解决,体现了人的数学探索能力、创造性思维能力、灵活分析问题与解决问题的能力,实质是融数学机智、数学精神、数学文化、数学气质、数学修养于一体的人的全面发展. 相似文献
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Bharath Sriraman 《Interchange》2006,37(1-2):151-178
This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use
of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly
diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the
Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich
mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual
counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse.
In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting
problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos.
The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher
education are discussed. 相似文献