高一学生数学学习分化点的研究

发布时间：2018-07-12 12:43

本文选题：高一学生 + 分化点　；参考：《南京师范大学》2015年硕士论文

【摘要】：数学学习上总存在一些知识点,在学习过程容易导致学生产生分化,我们称之为“分化点”。分化点内容的掌握程度,直接影响学生的学习成绩,也是导致两极分化的重要因素。从数学实际教学过程来看,学困生的出现都可以追溯到具体某一个分化点的学习上。虽然一部分教师已经对高一数学分化点进行探索研究,但是大多按具体章节讨论,综合概括、归类分析较少；大部分研究集中在分化点的外在表现,涉及具体内容、成因分析,特别是心理成因分析较少。本文首先采用文献研究的方法,结合个人的理解对分化点的概念作了界定：在教学过程中,受知识本身的特点和学生心理特征的影响,被教师忽略的教学内容；或者是由于教学观念陈旧使得问题解决不彻底而引起学习困难的重难点内容；又或者是造成数学成绩大面积滑坡,影响学生后续知识学习和最终高考的知识点,都被称之为“分化点”。在此基础上,针对高一数学必修一和必修四的知识内容,对师生进行问卷调查、教师访谈、学生平时作业和测试的调查。通过对数据统计分析,本文得到高一学生数学学习(必修一和必修四)中分化点,从分化点自身的特点、学生的认知特征、教师的教学状况三方面分析了分化点的成因,并提出突破分化点的一般教学策略和不同类型分化点的教学策略。最后选择两个班学生作为研究样本,进行等组实验。通过问卷调查、成因分析、策略研究、等组实验等途径,本研究主要获得了以下几个基本结论：(1)认定高一学生数学学习(必修一和必修四)分化点通过师生的问卷调查、学生平时作业与测试的统计,认定高一学生数学学习(必修一和必修四)的分化点,具体是：子集、全集补集、交集、并集、函数的概念和图像、函数的简单性质、映射的概念、分数指数幂、指数函数、对数函数函数的零点、用二分法求方程的近似解、函数的模型及其应用、任意角的三角函数、同角三角函数关系、三角函数的诱导公式、三角函数的图像及性质、函数y=A sin(ωx+φ)的图像、平面向量的基本定理、向量的数乘、向量的应用、两角和与差的余弦正弦、二倍角的三角函数。(2)从分化点本身的特点、学生的认知特征、教师的教学状况分析高一学生数学学习分化点的成因在本研究中发现,从分化点本身来看,在认定的分化点所对应的知识内容分别是集合、函数、三角函数和平面向量；从学生的认知特征上看,存在着高一学生的认知结构还不够完善、学生的思维发展与学科思维之间有矛盾、学生的情意发展与认知发展还不够协调、学生学习的自我监控能力和自我意识不够强的因素；从教师的教学状况上分析,存在“角色分化”、“经验主义”、重结果轻过程、重知识轻方法等弊端。(3)本文按陈述性分化点、程序性分化点、过程性分化点提出突破分化点的教学策略通过对高一学生数学学习分化点的调查,结合成因分析,提出了教学策略,具体为针对陈述性分化点建议：促进学生对陈述性分化点内容组织和加工、促进学生“图式”的形成；针对程序性分化点提出：促进学生产生式系统的建构、促进学生自我监控能力的培养；针对过程性分化点,希望教师能为学生提供适当的情境,使他们亲身体验知识的建构过程。(4)结合“函数的概念和图像”分化点的研究给出范例,并就教学策略的有效性进行等组实验研究通过对“函数的概念和图像”分化点的调查与分析,提出概念教学环节中的三个阶段：概念习得阶段、概念应用阶段、反思提升阶段。进而通过等组实验研究发现：如果对分化点成因分析恰当,教学策略得当,学生的学习兴趣和学习成绩会有所提高,对分化点的突破也有正面影响。
[Abstract]:There are always some knowledge points in the study of mathematics. In the process of learning, it is easy to lead to students' differentiation. We call it "differentiation point". The degree of mastery of the content of the differentiation point directly affects the students' learning achievement. It is also an important factor that leads to the polarization. From the perspective of the practical teaching of mathematics, the emergence of the students of learning difficulties can be traced back to the concrete. Although some teachers have explored the differentiation point of high mathematics, most of them are discussed in specific chapters, comprehensive generalization, and less classification analysis. Most of the studies focus on the external performance of the differentiation point, involving specific content, cause analysis, especially the psychological cause analysis. The concept of the differentiation point is defined by the method of literature research and personal understanding. In the course of teaching, the teaching content is ignored by the teacher, which is influenced by the characteristics of knowledge itself and the psychological characteristics of the students; or the difficult and difficult content of the learning difficulties is caused by the obsolescence of the teaching concept, and the difficulty of learning is caused by the obsolescence of the teaching concept; or On the basis of this, a questionnaire survey for teachers and students, teachers' interviews, and the investigation of students' daily homework and testing are carried out on the basis of the data statistics. This paper analyzes the differentiation points in the students' mathematics learning (compulsory and compulsory four). From the characteristics of the differentiation point, the cognitive characteristics of the students and the teaching situation of the teachers, this paper analyzes the causes of the differentiation points, and puts forward the general teaching strategy and the teaching strategy of different types of differentiation points. Finally, it chooses two classes of students. As the research sample, we carry out the group experiment. Through the questionnaire survey, the genetic analysis, the strategy research, and other groups of experiments, the main conclusions are obtained as follows: (1) it is found that the students' mathematical learning (compulsory and compulsory) is determined by the questionnaire survey by teachers and students, and the students' daily homework and test statistics are found to be higher. The student mathematics learning (compulsory and compulsory four) differentiation point, specifically: subset, complete complete complement, intersection, combined, the concept and image of function, the simple property of function, the concept of mapping, fractional exponentiation, exponential function, logarithmic function zero point, the approximate solution of the equation with the two method, the function model and its application, the three of arbitrary angle. The angular function, the relation of the trigonometric trigonometric function, the induction formula of the trigonometric function, the image and properties of the trigonometric function, the image of the function y=A sin (omega x+ phi), the basic theorem of the plane vector, the number multiplication of the vector, the application of the vector, the cosine sine of the difference and the three angle function of the two fold angle. (2) the characteristics of the differentiation point itself, the cognitive characteristics of the students, and the teaching of the students. From the point of view of the differentiation point, the knowledge content corresponding to the differentiation point is set, function, trigonometric function and plane vector from the point of differentiation itself. From the cognitive characteristics of the students, the cognitive structure of the students in the high one is not perfect. There is a contradiction between the development of students' thinking and the thinking of the subject. The students' emotional development and cognitive development are not well coordinated, the self-monitoring ability and self consciousness of the students are not strong enough. From the teaching situation of the teachers, there are some disadvantages such as "role differentiation", "empiricism", heavy result light process, and heavy knowledge and light method. (3) In this paper, the teaching strategy is put forward through the investigation of the differentiation point of high school students and the analysis of the reasons for the differentiation point of the process differentiation point according to the point of the declarative differentiation, the procedural differentiation point and the process differentiation point. The formation of "schema" for students; to the point of procedural differentiation: to promote the construction of students' generation system and to promote the cultivation of students' self-monitoring ability. In the light of the process differentiation point, we hope that teachers can provide students with appropriate situations to experience the construction process of knowledge. (4) combining the "concept of function and image". The study of the point is given an example, and the experimental research on the effectiveness of the teaching strategy is carried out by the investigation and analysis of the differentiation point of "the concept and image of the function". The three stages of the concept teaching link are put forward: the phase of concept acquisition, the phase of concept application, and the reflection of the ascending order. The analysis of the causes of differentiation is appropriate. If the teaching strategies are appropriate, students' interest in learning and academic performance will be improved, and they will also have a positive impact on breakthroughs in differentiation.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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