初中数学归纳推理实证研究
发布时间：2018-10-29 09:16
【摘要】：现代学校教育是通过各个学科的教学来实现对整体人的培养的,每个学科都有自己的核心任务。数学教育的职责使命是培养和造就有探索能力的人才。探索能力不仅包括分析问题和解决问题的能力,也包括发现问题的能力,而发现问题的能力是探索能力的最关键要素。归纳、类比等归纳逻辑推理思维都是发现问题的基本手段,这种数学核心素养强调数学教育不再仅仅是灌输、传承,而是更加侧重于启发以及对数学思想方法的理解。在过去很长的一段时间里,中国基础教育阶段的数学教育重视演绎推理,教授训练学生验证掌握已有的完善的数学结论,而同时却忽略了归纳推理(1),数学教育的偏失和不完善,其结果必然弱化数学学科的育人价值,影响学生创造力的发展。本文围绕初中数学中归纳推理实证研究这个核心,具体研究如下问题:第一,采用文本分析法,借助文献梳理演绎推理与归纳推理的关系,同时梳理归纳推理国内外研究的现状,在分析国内小学和高中数学中归纳推理研究结论的基础上,探索初中数学中的归纳推理和演绎推理的关系。第二,通过文本分析的方法,对初中教学大纲和数学课程标准中归纳推理内容以及北师大版与人教版教材归纳推理内容呈现分别进行量化比较研究。第三,对师生的归纳推理能力以及师生对归纳推理的认同感和课堂教学现状进行调查研究,第四,对调查研究结果进行归因分析。通过研究,主要有以下发现:第一,初中数学中的归纳推理和演绎推理应该是双螺旋式发展。第二,通过对两个版本数学教材中与归纳推理能力培养的相关内容呈现的量化对比研究,并结合教学实践发现两个版本教材关于归纳推理呈现没有达到《义务教育课程标准(2011年版)》(以下简称《标准(2011年版)》)的要求。第三,选取北京市、黑龙江省十所学校初中阶段学生1446人和在职初中数学教师212人,运用了试题测试法和问卷调查法。通过对初中数学教师和学生完成的调查问卷、测试题进行的统计分析结果看,师生对归纳推理的理解不清晰,对《标准(2011年版)》的要求模糊。部分老师和学生的归纳推理能力比较薄弱,亟待提高。第四,通过聚焦访谈,87%初中数学老师虽然认同归纳推理的重要价值,但是在教学中不知道如何操作,导致在初中课堂教与学过程中目标不明确效果不好。综合上述情况,呼吁教材编写部门再修改教材时严格按着《标准(2011年版)》对归纳推理的要求,并能提供更多更鲜活的案例供老师们学习参考。也建议教育行政部门和学校真正重视初中阶段学生归纳推理能力的培养。本文对调查研究结果进行了归因分析,也从多个角度提供了一些案例,希望引起更多的讨论和研究。
[Abstract]:Modern school education realizes the cultivation of the whole person through the teaching of each subject, and each subject has its own core task. The duty mission of mathematics education is to cultivate and bring up people with the ability to explore. The ability to explore includes not only the ability to analyze and solve problems, but also the ability to find problems, and the ability to discover problems is the most important element of the ability to explore. Induction, analogy and other inductive logical reasoning thinking are the basic means to find problems. This kind of mathematics core accomplishment emphasizes that mathematics education is no longer just indoctrination, inheritance, but more emphasis on inspiration and understanding of mathematical thinking methods. For a long time in the past, mathematics education in basic education in China attached importance to deductive reasoning, and the professors trained students to verify and master the existing mathematical conclusions, while neglecting inductive reasoning (1). The deviation and imperfection of mathematics education will inevitably weaken the educational value of mathematics subject and affect the development of students' creativity. This paper focuses on the core of the empirical research on inductive reasoning in junior high school mathematics, and studies the following problems: first, using text analysis, combing the relationship between deductive reasoning and inductive reasoning with the help of literature. At the same time, combing the current situation of inductive reasoning at home and abroad, on the basis of analyzing the research conclusions of inductive reasoning in primary and high school mathematics in China, this paper explores the relationship between inductive reasoning and deductive reasoning in junior high school mathematics. Secondly, through the method of text analysis, the contents of inductive reasoning in middle school syllabus and mathematics curriculum standard, and the presentation of inductive reasoning content in Peking normal University edition and human education edition are studied respectively. Thirdly, the author investigates the ability of inductive reasoning of teachers and students, the identity of teachers and students to inductive reasoning and the present situation of classroom teaching. Fourthly, the attribution analysis of the investigation results is carried out. The main findings are as follows: first, inductive reasoning and deductive reasoning in junior high school mathematics should be double spiral development. Second, through the quantitative comparative study of the two versions of mathematics textbooks and the related contents of the training of inductive reasoning ability, Combined with teaching practice, it is found that the presentation of inductive reasoning does not meet the requirements of "compulsory Education Curriculum Standard (2011 Edition) > (hereinafter referred to as" Standard (2011 Edition) >). Thirdly, 1446 junior middle school students and 212 in-service junior high school mathematics teachers in Beijing, Heilongjiang Province, were selected, and the methods of test and questionnaire survey were used. Through the questionnaire of mathematics teachers and students in junior high school and the statistical analysis of the test questions, we can see that the teachers and students do not have a clear understanding of inductive reasoning, and the requirements of < Standard (2011) > are vague. The inductive reasoning ability of some teachers and students is weak and needs to be improved. Fourth, through focused interviews, 87% of junior high school mathematics teachers agree with the important value of inductive reasoning, but do not know how to operate in the teaching, resulting in the middle school classroom teaching and learning process is not clear effect. In the light of the above situation, the author calls upon the textbook compiling department to strictly follow the requirements of inductive reasoning when revising the textbook according to the Standard (2011 Edition), and can provide more and more vivid cases for teachers to learn for reference. It is also suggested that the educational administration and schools should really pay attention to the cultivation of students' inductive reasoning ability in junior middle school. In this paper, the attribution analysis of the research results is made, and some cases are provided from many angles, hoping to arouse more discussion and research.
【学位授予单位】：东北师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：G633.6
，
本文编号：2297276
[Abstract]:Modern school education realizes the cultivation of the whole person through the teaching of each subject, and each subject has its own core task. The duty mission of mathematics education is to cultivate and bring up people with the ability to explore. The ability to explore includes not only the ability to analyze and solve problems, but also the ability to find problems, and the ability to discover problems is the most important element of the ability to explore. Induction, analogy and other inductive logical reasoning thinking are the basic means to find problems. This kind of mathematics core accomplishment emphasizes that mathematics education is no longer just indoctrination, inheritance, but more emphasis on inspiration and understanding of mathematical thinking methods. For a long time in the past, mathematics education in basic education in China attached importance to deductive reasoning, and the professors trained students to verify and master the existing mathematical conclusions, while neglecting inductive reasoning (1). The deviation and imperfection of mathematics education will inevitably weaken the educational value of mathematics subject and affect the development of students' creativity. This paper focuses on the core of the empirical research on inductive reasoning in junior high school mathematics, and studies the following problems: first, using text analysis, combing the relationship between deductive reasoning and inductive reasoning with the help of literature. At the same time, combing the current situation of inductive reasoning at home and abroad, on the basis of analyzing the research conclusions of inductive reasoning in primary and high school mathematics in China, this paper explores the relationship between inductive reasoning and deductive reasoning in junior high school mathematics. Secondly, through the method of text analysis, the contents of inductive reasoning in middle school syllabus and mathematics curriculum standard, and the presentation of inductive reasoning content in Peking normal University edition and human education edition are studied respectively. Thirdly, the author investigates the ability of inductive reasoning of teachers and students, the identity of teachers and students to inductive reasoning and the present situation of classroom teaching. Fourthly, the attribution analysis of the investigation results is carried out. The main findings are as follows: first, inductive reasoning and deductive reasoning in junior high school mathematics should be double spiral development. Second, through the quantitative comparative study of the two versions of mathematics textbooks and the related contents of the training of inductive reasoning ability, Combined with teaching practice, it is found that the presentation of inductive reasoning does not meet the requirements of "compulsory Education Curriculum Standard (2011 Edition) > (hereinafter referred to as" Standard (2011 Edition) >). Thirdly, 1446 junior middle school students and 212 in-service junior high school mathematics teachers in Beijing, Heilongjiang Province, were selected, and the methods of test and questionnaire survey were used. Through the questionnaire of mathematics teachers and students in junior high school and the statistical analysis of the test questions, we can see that the teachers and students do not have a clear understanding of inductive reasoning, and the requirements of < Standard (2011) > are vague. The inductive reasoning ability of some teachers and students is weak and needs to be improved. Fourth, through focused interviews, 87% of junior high school mathematics teachers agree with the important value of inductive reasoning, but do not know how to operate in the teaching, resulting in the middle school classroom teaching and learning process is not clear effect. In the light of the above situation, the author calls upon the textbook compiling department to strictly follow the requirements of inductive reasoning when revising the textbook according to the Standard (2011 Edition), and can provide more and more vivid cases for teachers to learn for reference. It is also suggested that the educational administration and schools should really pay attention to the cultivation of students' inductive reasoning ability in junior middle school. In this paper, the attribution analysis of the research results is made, and some cases are provided from many angles, hoping to arouse more discussion and research.
【学位授予单位】：东北师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：G633.6
，
本文编号：2297276
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