高中生代数符号理解与表示的调查及教学策略研究

发布时间：2018-03-11 01:39

本文选题：高中生　切入点：代数符号　出处：《山东师范大学》2016年硕士论文　论文类型：学位论文

【摘要】：数学教学中,概念、公式、定理都是靠数学符号来呈现的,而且大部分是代数符号。所以,学好代数符号在数学学习中显得尤为重要。代数符号不仅是数学知识的构成要素,更是学生进一步数学学习的有力工具。高中阶段的代数符号作为数学的基础知识,是学好高中数学的基石,也是学生高中以后后续学习的科学工具。大学阶段的数学对代数符号具有更高的要求,所以高中阶段就需要打下牢固的基础。但是,经过笔者的初步观察和与高中数学教师的交流后发现,现阶段高中生的代数符号学习能力水平情况并不理想,这种能力分为代数符号的理解能力与表示能力两个方面。一方面,学生不能充分理解代数符号,对于许多代数符号的意义学生记忆不牢、理解不清。另一方面,即使学生了解代数符号的意义,也不能够很好的对其进行表示及应用。所以,高中生代数符号理解与表示的研究具有重要意义,既能够丰富代数符号系统的理论研究,还可以通过对高中生代数符号学习能力现状的调查分析,对高中的数学教学提出一些建议和参考。首先,本文对高中生代数符号的理解与表示开展了大量的理论研究工作。在广泛查阅文献资料的基础上,介绍了代数符号的发展历史、高中生代数符号学习障碍的成因分析、高中生代数符号学习的特点,探讨了符号、数学符号、代数符号的定义以及代数符号的分类,还介绍了高中生代数符号理解过程的三个阶段:符号识别、语义分析、意义建构,高中生代数符号表示过程的三个阶段:明确意义、符号准备、规范书写,为后文的研究奠定了坚实的理论基础。其次,本文对高中生代数符号的理解与表示开展了细致地实证研究工作。本文基于高一的代数符号内容编制问卷,将高中生代数符号理解与表示的各个阶段作为测试维度,分别对高一学生,高二理科、高二文科学生进行测试,通过分析整理数据,在每个维度上比较高一与高二学生、理科生与文科生、男生与女生之间的差异并分析原因,找出高中生在理解与表示每个阶段上的学习困难。然后结合访谈,根据问卷的回答情况,和学生交流做题时的思维过程,发现学生的错误原因和学习障碍。接着访谈有经验的高级教师,从教师角度分析高中生代数符号理解与表示的学习困难与教学策略。借助excel软件,对高中生代数符号的理解与表示开展了全方面的深入研究工作。最后,本文综合理论分析与实证研究,从高中生代数符号理解与表示的现状和存在的学习困难两个方面,得出研究结论。从教师角度和学生角度,分别给出高中生代数符号的教学建议和学习策略。教学建议:把符号的定义教授清楚,点出符号的形式、意义、适用范围、记忆规律、做题时此符号的易错点,与易混符号的区别等;注意规范板书,要求学生规范书写;家庭作业要做出规范性的批改;强调学习方法的重要性,改错题的时候不能只强调表面的过程与答案准确,还应该让学生多从代数符号意义的理解上注意;讲完新课后要有对新符号的针对性训练;注意培养学生的良好数学学习习惯,注意渗透数学思想方法、题型意识;重视学生运用代数符号语言表达的能力。学习策略:把符号的定义理解清楚;把握符号的应用范围、运用方法,书写时注意规范、准确;听讲完毕自己要及时训练加强记忆;改错题时,采取学生之间互相讲题的策略;符号涉及的知识点也要特别注意;养成用代数符号语言表示文字语言的习惯。
[Abstract]:In mathematics teaching, concepts, formulas, theorems are presented by mathematical symbols, and most of them are algebraic symbols. Therefore, learn the algebraic symbols in mathematical learning is very important. Not only is the algebraic sign elements of mathematics knowledge, students learn mathematics is further powerful tool teaching. The high school stage as algebraic symbols the basic knowledge of mathematics, is to learn the foundation of high school mathematics, and high school students after subsequent learning scientific tools. University level mathematics has higher requirements on the algebraic symbols, so the high school stage to lay a solid foundation. However, after a preliminary observation of the author and the high school mathematics teacher exchange found algebra the symbol at the present stage of senior high school students learning ability level is not ideal, this ability is divided into two aspects of algebraic symbols of understanding and expressing ability. On the one hand, students can't To fully understand the significance of the students' memory for algebraic symbols, many algebraic symbols is not strong, clear understanding. On the other hand, even if the students understand the meaning of symbols is not algebra, can be good for the representation and application. Therefore, it is important to study the algebraic sign of understanding and representation of high school students, not only theoretical research the rich algebraic symbol system, but also through the investigation and Analysis on the status quo of the algebra learning ability of high school students, and puts forward some suggestions and reference to mathematics teaching in senior high school. First, the algebraic sign of senior high school students show understanding and carry out a lot of theoretical research. Based on extensive literature review, introduces the the history of the development of algebraic symbols, analysis of the causes of learning disabilities in senior high school students the characteristics of algebraic symbols, algebraic symbols learning of high school students, to explore the symbols, mathematical symbols, and the definition of algebraic symbols The classification of algebraic symbols, also introduced the three stages of high school students understand the process of algebraic symbols: symbol recognition, semantic analysis, meaning construction, algebraic symbols of high school students said that the three stages of the process: clear meaning, symbol preparation, specification writing, lay a solid theoretical foundation for the following research. Secondly, this paper with the representation of algebraic symbols of senior high school students understand and carried out detailed empirical research work. In this paper, algebraic symbols content questionnaire based on a high, high school students will understand and represent various stages of algebraic symbols as test dimensions, respectively on the high school students, high school of science, School of liberal arts students are finishing the test, through the analysis of data, in each the dimension and a relatively high school students, students of science and liberal arts students, the differences between boys and girls and analyze the reason, find out high school students in the understanding and representation of each stage of the learning difficulties. After the interviews, according to answer questionnaire, and students do the thinking process, found the cause of the error of students and learning disabilities. Then interviews senior teachers with experience, analysis of learning difficulties and teaching strategies of senior high school students understand and represent algebraic symbols from the perspective of teachers. With the help of Excel software, the algebraic sign of senior high school students understanding and representation to carry out the work of all aspects of the study. Finally, this paper comprehensive theoretical analysis and empirical research, from two aspects of understanding and representation of algebraic symbols and the existence of high school students with learning difficulties, come to the conclusion of the study. From the perspective of teachers and students of senior high school students were given the angle of algebraic symbols suggestions for the teaching and learning strategies. Suggestions: symbol definition Professor clear, point out the symbolic form, meaning, scope of application, the memory of the law, the symbol error prone title, easily confused with symbols of the region Don't wait; pay attention to the standardization of writing on the blackboard, students are required to write the standard; homework to make normative corrections; emphasize the importance of learning methods, when error correction problem can not only emphasize the process and answer surface accurately, but also let the student from the symbolic significance understanding note; new class have to finish a new symbol targeted training; pay attention to the cultivation of good mathematics study habits of the students, pay attention to the infiltration of mathematical thought and method, question consciousness; pay attention to students' use of symbol language expression ability. Learning strategies: the algebraic definition of symbols understood; grasp the scope of application, the use of symbols, pay attention to standardized, accurate writing; listen to timely completion strengthen the training of memory; error correction problem, take students to each other on the strategy of the knowledge involved; symbols also pay special attention to; used to develop algebraic sign language representation language learning Used.

【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

【参考文献】