中英初中数学教材中几何部分推理方式的比较研究

发布时间：2018-05-29 21:33

本文选题：推理方式 + 中英教材　；参考：《东北师范大学》2015年硕士论文

【摘要】：众所周知,在现代的教育教学中,培养中学生数学推理能力是数学课程的重要目标,更是中学数学教学非常重视的问题。目前国内的很多学者、教育家都在寻找提高中学生推理能力的办法。本研究从教材出发,通过查阅文献,文本分析,内容比较等方法,对中国人教版初中数学教材与英国SMP教材中几何部分的推理方法进行比较研究。研究发现：1.中国人教版初中数学教材定理、命题和例题的推理方式中,演绎推理的比重远远大于合情推理。2.英国SMP教材中定理、命题和例题的推理方式中,合情推理所占的比重大于演绎推理。3.中国人教版初中数学教材中的演绎推理的推理方式以传递推理和演绎定理为主,它们的比重各占演绎推理的40%左右。教材中的合情推理的推理方式中,主要是归纳推理,比重占到70%。4.英国SMP教材中演绎推理中主要的推理方式是假言推理,推理结构相对简单。在合情推理中占主要地位的是归纳推理。其比重在合情推理中占到79%。5.两版教材在图形的周长、面积,立体图形的体部分,采用相同的推理方式,都是合情推理,其比重都高达80%以上。在图形的相似和全等知识部分英国SMP教材以合情推理为主,而人教版数学教材以演绎推理为主。6.人教版教材与SMP教材在例题中只涉及到演绎推理,而没有合情推理。基于以上研究结果,提出相关教材的编写建议。
[Abstract]:As we all know, in modern education and teaching, cultivating students' mathematical reasoning ability is an important goal of mathematics curriculum, and it is also a very important problem in middle school mathematics teaching. At present, many domestic scholars and educators are looking for ways to improve the reasoning ability of middle school students. Based on the teaching materials, this paper makes a comparative study on the reasoning methods of the geometry part of the Chinese junior middle school mathematics textbook and the British SMP textbook by consulting the literature, text analysis, content comparison and so on. The study found that 1: 1. The proportion of deductive reasoning in Chinese junior middle school mathematics textbook theorem, proposition and example reasoning is much larger than that of reasonable reasoning. The proportion of rational reasoning in SMP textbooks is greater than that in deductive reasoning. Transfer reasoning and deductive theorem are the main ways of deductive reasoning in Chinese junior middle school mathematics textbooks, which account for about 40% of deductive reasoning. In the reasoning mode of reasonable reasoning in textbooks, the proportion of inductive reasoning accounts for 70.4. The main way of deductive reasoning in English SMP textbooks is hypothetical reasoning, and the inference structure is relatively simple. Inductive reasoning dominates the rational reasoning. Its proportion in reasonable reasoning accounts for 79. 5. The two editions of textbooks are reasonable reasoning in the perimeter, area and body part of three-dimensional graphics, and the proportion of them is as high as 80%. In the part of similarity and complete knowledge of graphics, the SMP textbook in England is mainly based on reasonable reasoning, while the human teaching version of mathematics textbook is mainly based on deductive reasoning. In the example, the teaching materials of human education and SMP only involve deductive reasoning, but not reasonable reasoning. Based on the above research results, the author puts forward some suggestions on the compilation of relevant textbooks.
【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

【参考文献】