中英高中数学概率与统计内容难易程度的比较研究

发布时间：2017-12-27 08:57

本文关键词：中英高中数学概率与统计内容难易程度的比较研究　出处：《东北师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：在世纪之交2001年,我国专门针对课程改革制订了各门学科的指导纲要或课程标准,这标志了我国的基础教育重新开启了一个新的篇章——新课程改革时代。教材特色也是教材质量的又一重要部分。所以本篇论文选取中英两国具有代表性的高中数学教科书的“概率与统计”这一内容作为研究的对象,对该部分内容的难易程度进行比较研究。本篇论文在认真研读中国人教A版高中数学教材和英国SMP版高中数学教材的基础上整理出中国人教A版、英国SMP版高中数学的“概率与统计”的知识点。再结合中国《普通高中数学课程标准实验2003版》,英国《英国国家数学课程标准》以及相的应参考书确定相应的知识点的深度和广度;结合教材例题确定相应习题性质、习题背景和含有知识点数量。最终依据由史宁中教授主持的国家社会科学基金项目组确立的高中数学教材难度的的定量模型N=α1·G/T+α2·S/T+α3·X/T通过这个数学模型,对中英两国高中数学教材进行量化分析,分别确定中国人教A版,英国SMP版“概率与统计”的内容广度、内容深度和习题综合难度及教材总难度,得到以下几个结论：1.以内容广度来看,中国人教A版高中数学“概率与统计”包含68个知识点；英国SMP版高中数学“概率与统计”包含35个知识点。在概率与统计的学习中,中国教材人教版教材涉及内容广泛,更加注重知识的全面性,,英国教材重视知识点的实用性；2.以内容深度来看,中国人教A版高中数学“概率与统计”知识团深度为149；英国SMP版高中数学“概率与统计”知识团深度为75。在树状图上两版教材均显现出倒“U”型,两国教材均是处于理解水平的知识点最多。总的来说,中国人教A版的知识团总深度远远大于英国SMP版教材；3.以习题综合难度来看,中国人教A版高中数学“概率与统计”综合难度为392；英国SMP教材“概率与统计习题的综合难为320。总的来说,在教材的习题难度上,中国教材是“多且难”的,SMP版教材是“少且易”的；4.以教材总难度方面来看,中国人教A版高中数学“概率与统计”的总难度为3.16；英国SMP版高中数学“概率与统计”的总难度为2.64。相比之下,中国人教A版高中数学的教材“概率与统计”内容部分广而深,习题多且难；英国SMP版高中数学教材“概率与统计”内容窄而浅,习题少且易。
[Abstract]:At the turn of the century, in 2001, our country set up guidelines and curriculum standards for various disciplines, which marked a new chapter in our basic education -- the era of new curriculum reform. The characteristics of the textbook are also an important part of the quality of the teaching materials. So this paper selects the content of "probability and statistics" of representative high school mathematics textbooks in China and Britain as the object of study, and makes a comparative study of the difficulty of this part. On the basis of careful reading of Chinese A version of high school mathematics textbook and British SMP version of high school mathematics textbook, this paper collated the knowledge points of "probability and statistics" of Chinese A edition and SMP edition of high school mathematics. Combined with the Chinese "experimental mathematics curriculum standards of senior high school English 2003 edition", "national mathematics curriculum standard" and the reference book should determine the appropriate knowledge of the depth and breadth; combined with the textbook examples determine the nature, background and the corresponding Exercises Exercises contains number of knowledge points. Based on the history by Professor Ning in the National Social Science Fund Project Group established the high school mathematics teaching difficulty of the quantitative model of N= alpha 1 - alpha 2 - alpha 3 G/T+ S/T+ X/T with this model, the two high school mathematics textbooks are analyzed, respectively to determine the Chinese teach A version, British SMP version of "probability and statistics" content, depth and breadth of content and teaching exercises comprehensive difficulty difficulty, and get the following conclusions: 1. the content of breadth of view, Chinese A version of high school mathematics teaching "probability and statistics" contains 68 knowledge points; mathematical probability and statistics for the British version of SMP contains 35 high knowledge points. In the probabilistic and statistical learning, Chinese textbooks PEP extensive contents, pay more attention to comprehensive knowledge, English textbooks, pay attention to practical knowledge; 2. in the depth of content, Chinese A version of high school mathematics teaching of probability and statistics knowledge group depth of 149 SMP; the British version of high school mathematics "probability and statistics" knowledge group depth is 75. In the tree on the two edition show inverted "U" type, the two textbooks are in the level of understanding of knowledge points up. Generally speaking, the total depth of the Chinese A version is far greater than that of the British SMP textbook. 3., in terms of the comprehensive difficulty of exercises, the comprehensive difficulty of Chinese A version of high school mathematics "probability and statistics" is 392, and that of the UK SMP textbook is 320. In general, in the exercise of difficulty, Chinese "textbook is more and more difficult," SMP "version of the textbook is less easy"; 4. textbooks in the total difficulty, difficulty Chinese teach A version of high school mathematics "probability and statistics" is 3.16; the total SMP of the UK version of the high difficulty "mathematical probability and statistics for 2.64. In contrast, the contents of "A" version of high school mathematics textbook "probability and statistics" are extensive and deep, and the exercises are much more difficult. The SMP version of high school mathematics textbooks in the UK is narrow and shallow, and exercises are few and easy.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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