初中生数学归纳推理能力的调查研究

发布时间：2018-05-21 15:32

本文选题：数学归纳推理能力 + 教材编排　；参考：《哈尔滨师范大学》2015年硕士论文

【摘要】：数学归纳推理能力是发现数学问题,进行数学探索的一种重要能力,也是影响学生思维品质和创造能力的基本因素之一。数学新课程标准中也指出:“在数学教学过程中,不断地引导学生经历观察发现、归纳类比和抽象概括等思维过程。”因此,数学归纳推理能力是中学生必须要掌握的基本技能之一,义务教育阶段更是培养学生数学归纳推理能力的关键时期。通过仔细研读相关文献资料,笔者发现:对于初中生数学归纳推理能力的发展现状如何?在日常教学工作中对于初中生数学归纳推理能力的培养是否得到重视?教材编排、教育评价以及教学实践中还存在哪些不足和疏漏之处?这些问题还值得探讨。本文在前人研究的基础上,按照以下步骤对初中生的数学归纳推理能力进行了调查研究:首先,在研读文献、与专家讨论的基础上,分析了问题提出的背景和研究意义,然后从心理学、教育学和数学教育学三个维度确定了研究的理论基础,并对相关概念进行了界定。其次,自制学生数学归纳推理能力测试卷和教师访谈问题,并随机抽取了黑龙江省鸡东县第三中学八年级的230名学生和5名教师,分别对其进行调查和访谈,发现初中生数学归纳推理能力普遍偏低;接着梳理了现行三个最新版本的初中数学教材,包括人教版初中数学教材、北师大版初中数学教材、苏科版初中数学教材,并对这三个版本的教材中有关归纳推理的内容进行统计和分析,发现初中数学教材中关于归纳推理的内容在整体内容中所占比重相对较少,且分布不均衡。然后又搜集国内21个省份或城市最近五年(2010年——2014年)的中考数学试题,并分析了这些中考试题对归纳推理内容的考察形式和分值比例,了解到归纳推理并没有得到普遍的重视。最后,基于研究结论,提出发展初中生数学归纳推理能力的建议,包括教师教学的建议,初中数学教材中归纳推理内容所占比例与编排特点的建议,归纳推理在中考数学试题中考察的建议。
[Abstract]:Mathematical inductive reasoning ability is an important ability to find mathematical problems and to explore mathematics. It is also one of the basic factors that affect students' thinking quality and creative ability. It is also pointed out in the new mathematics curriculum standard: "in the course of mathematics teaching, students are constantly guided to the thinking process of observation and discovery, inductive analogy and abstract generalization." Therefore, the ability of mathematical inductive reasoning is one of the basic skills that must be mastered by middle school students, and the compulsory education stage is the key period for cultivating students' ability of mathematical inductive reasoning. Through a careful study of the relevant literature, the author found: for junior high school students, how about the development of mathematical inductive reasoning? In the daily teaching work for junior high school students to cultivate the ability of inductive reasoning has been paid attention to? What are the shortcomings and omissions in teaching material arrangement, educational evaluation and teaching practice? These problems are worth exploring. On the basis of previous studies, this paper investigates junior high school students' ability of inductive reasoning according to the following steps: firstly, on the basis of reading literature and discussing with experts, the paper analyzes the background and significance of the questions raised. Then, the theoretical basis of the research is determined from the three dimensions of psychology, pedagogy and mathematics pedagogy, and the related concepts are defined. Secondly, the self-made test paper of students' mathematical inductive reasoning ability and the question of teacher interview, and randomly selected 230 students and 5 teachers from the eighth grade of the third middle school in Jidong County, Heilongjiang Province, to investigate and interview them, respectively. Found that junior high school students generally low ability of inductive reasoning, and then combed the current three latest versions of junior high school mathematics textbooks, including the personal version of junior high school mathematics textbooks, Beijing normal University version of junior high school mathematics textbooks, Su version of junior high school mathematics textbooks. The contents of inductive reasoning in these three versions of textbooks are statistically analyzed, and it is found that the contents of inductive reasoning in junior high school mathematics textbooks account for relatively small proportion in the whole content, and the distribution is not balanced. Then it collects the mathematics test questions of 21 provinces or cities in China in the last five years (2010-2014), and analyzes the forms and the proportion of scores of these questions to the content of inductive reasoning. It is understood that inductive reasoning has not received universal attention. Finally, based on the conclusions of the research, the author puts forward some suggestions for developing junior high school students' ability of inductive reasoning, including the suggestions of teachers' teaching, the proportion of the contents of inductive reasoning and the characteristics of arrangement in junior high school mathematics textbooks. The suggestion that inductive reasoning should be investigated in the mathematics examination of the middle school.
【学位授予单位】：哈尔滨师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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