培养高中生数学类比推理能力的教学研究
发布时间：2018-11-20 17:43
【摘要】：类比推理能力在人类认识世界和改造世界中起着启发思想、拓宽思路、探索结论的作用。现在,我国也开始逐渐关注对学生数学类比推理能力的培养,但是单就硕博论文来看,我国对如何培养学生的数学类比推理能力的专项研究还不是很多,所提出的教学策略也不是很全面,教学步骤也不是很详细。本文从理论和实践两个方面对如何在教学中培养学生的数学类比推理能力进行了研究,得出了一些有价值的结论,可为一线数学教师提供参考。本文利用文献查找法,总结了与本文有关的三个类比推理心理学研究理论,即结构映射理论、实用图式理论和认知发展理论。利用问卷调查法,对盘山县高级中学的部分学生及教师进行了问卷调查,推理出我国高中生数学类比推理能力的现状以及教师对培养学生数学类比推理能力的意识。本文以三大理论为指导,结合调查结果,总结了培养高中生数学类比推理能力的教学策略和教学步骤。经上述研究,本文得出一些结论:我国高中生的数学类比推理能力总体来说还比较低,其中由有限到无限的类比推理能力最低,由特殊到一般的类比推理能力好与其他类比推理能力。造成该现象的原因是,学生还没有形成类比推理步骤。教师对培养学生的数学类比推理能力意识比较薄弱,是因为我国现在还没有一套科学、明确、详尽的培养高中生数学类比推理能力的教学步骤和相应的教学素材。针对以上问题笔者认为教师应该利用数学知识结构的相似性、性质的相似性和研究方法的相似性以及类比问题所处情境和类比问题的呈现形式来培养学生的数学类比推理能力。教师在培养学生数学类比推理能力时应该按照提出目标问题、检索源问题、类比对应部分、得出类比结论、验证类比结论、习得类比结论这六步进行。
[Abstract]:The ability of analogical reasoning plays an important role in understanding and transforming the world. Now, our country has begun to pay more and more attention to the cultivation of students' ability of analogical reasoning in mathematics. However, from the point of view of the thesis, there are not many special researches on how to cultivate students' ability of analogical reasoning in mathematics. The proposed teaching strategy is not very comprehensive, teaching steps are not very detailed. This paper studies how to cultivate students' ability of analogical reasoning in mathematics teaching from two aspects of theory and practice, and draws some valuable conclusions, which can be used as a reference for first-line mathematics teachers. In this paper, three theories of analogical reasoning psychology, namely, structural mapping theory, practical schema theory and cognitive development theory, are summarized by using the method of literature search. By using the method of questionnaire, some students and teachers of Panshan High School were surveyed, and the present situation of Chinese senior high school students' ability of mathematical analogical reasoning and their awareness of cultivating students' ability of mathematical analogical reasoning were inferred. Under the guidance of three major theories and combined with the results of the investigation, this paper summarizes the teaching strategies and teaching steps for cultivating the ability of mathematical analogy reasoning of senior high school students. Through the above research, this paper draws some conclusions: the ability of mathematical analogy reasoning of senior high school students in our country is still relatively low in general, among which the ability of analogy reasoning from limited to infinite is the lowest. The ability of analogy reasoning from special to general is good with other analogical reasoning ability. The reason for this phenomenon is that the students have not yet formed the analogical reasoning steps. Teachers' awareness of cultivating students' ability of analogical reasoning in mathematics is relatively weak, because there is not a set of scientific, clear and detailed teaching steps and corresponding teaching materials for cultivating students' ability of analogical reasoning in mathematics in our country. In view of the above problems, the author holds that teachers should use the similarity of mathematical knowledge structure, the similarity of nature, the similarity of research methods, the situation of analogical problems and the presentation of analogical problems to cultivate students' ability of mathematical analogical reasoning. When developing students' ability of analogical reasoning in mathematics, teachers should follow the six steps of raising objective problem, searching source problem, analogy corresponding part, drawing analogy conclusion, verifying analogy conclusion, and acquiring analogy conclusion.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2345559
[Abstract]:The ability of analogical reasoning plays an important role in understanding and transforming the world. Now, our country has begun to pay more and more attention to the cultivation of students' ability of analogical reasoning in mathematics. However, from the point of view of the thesis, there are not many special researches on how to cultivate students' ability of analogical reasoning in mathematics. The proposed teaching strategy is not very comprehensive, teaching steps are not very detailed. This paper studies how to cultivate students' ability of analogical reasoning in mathematics teaching from two aspects of theory and practice, and draws some valuable conclusions, which can be used as a reference for first-line mathematics teachers. In this paper, three theories of analogical reasoning psychology, namely, structural mapping theory, practical schema theory and cognitive development theory, are summarized by using the method of literature search. By using the method of questionnaire, some students and teachers of Panshan High School were surveyed, and the present situation of Chinese senior high school students' ability of mathematical analogical reasoning and their awareness of cultivating students' ability of mathematical analogical reasoning were inferred. Under the guidance of three major theories and combined with the results of the investigation, this paper summarizes the teaching strategies and teaching steps for cultivating the ability of mathematical analogy reasoning of senior high school students. Through the above research, this paper draws some conclusions: the ability of mathematical analogy reasoning of senior high school students in our country is still relatively low in general, among which the ability of analogy reasoning from limited to infinite is the lowest. The ability of analogy reasoning from special to general is good with other analogical reasoning ability. The reason for this phenomenon is that the students have not yet formed the analogical reasoning steps. Teachers' awareness of cultivating students' ability of analogical reasoning in mathematics is relatively weak, because there is not a set of scientific, clear and detailed teaching steps and corresponding teaching materials for cultivating students' ability of analogical reasoning in mathematics in our country. In view of the above problems, the author holds that teachers should use the similarity of mathematical knowledge structure, the similarity of nature, the similarity of research methods, the situation of analogical problems and the presentation of analogical problems to cultivate students' ability of mathematical analogical reasoning. When developing students' ability of analogical reasoning in mathematics, teachers should follow the six steps of raising objective problem, searching source problem, analogy corresponding part, drawing analogy conclusion, verifying analogy conclusion, and acquiring analogy conclusion.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
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