结构观点下的高中数学教学设计分析
发布时间：2018-12-13 04:12
【摘要】：SOLO分类摘要结构观点在数学上的研究自法国布尔巴基学派提出,随后作为认知心理学的核心观点,对美国“新数”时期及欧亚一些国家的课程改革有很大影响.然而随着“新数”运动失败,数学结构主义连同教学理论日渐被淡化.现在为什么还要去研究这一观点?我国从2001年开始第八次课程改革,今天对这次改革的反思之一是:数学课程结构松散.由于结构观点对数学教育的影响,结合新课标理念和高中数学本身的结构特点,因此基于结构观点去探究教学.本研究经文献整理分析,发现结构观点对学生理解以及教学上有较大意义.在数学上的体现为,一方面它倾向于从整体去分析数学知识,并按照某个分类将数学知识纳入一个结构体系中,有利于增加学生对数学理解的广度.另一方面,数学内容显示出一定的结构特征,根据某一类的结构特点分析解决问题,有利于挖掘问题中蕴含的数学本质,提高学生理解的深度.在教学上,发现学习和理论分别在学生对问题进行结构性理解,以及评价学生理解的结构水平上作用明显.教学设计之前,先分析了人教A版高中数学教材,发现当前高中数学是以“数量关系和空间形式”为研究对象的知识结构体系,在该体系下,按“代数结构(?)数量关系;拓扑结构(?)空间关系;序结构(?)序关系”,去分析概念、法则和方法的结构特点,将数学结构具体化.其次,通过对西昌市某中学的学生问卷调查,主要调查结构理解的意识、做法及学习结果3个方面,发现学生普遍有一定结构性意识,但缺乏行动,理解水平较低.并分别对成都市及周边8位及西昌市2位教师进行访谈,访谈内容围绕“对教材、教学、评价及对学生的帮助”展开,发现教师普遍用结构观去理解教材,但较少将该观点用在教学中.因此,根据结构观点,对概念型——椭圆、法则型——正弦定理这两部分进行教学设计分析,通过这两个案例,去寻找方法,探究教学,帮助学生理解.总结出基于结构观点进行教学设计的关键点:(1)教学上,从整体入手,联系已有认知和经验;(2)“探索发现”应贯穿整个教学;(3)挖掘数学内容本身的结构特点;(4)设计评价应有层次性,帮助学生自查理解的广度和深度.
[Abstract]:The mathematical study of SOLO classification abstract structure was put forward by the Bourbachian School of France, and then as the core view of cognitive psychology, it had a great influence on the curriculum reform in the "New number" period in the United States and in some countries in Europe and Asia. However, with the failure of the movement of "new numbers", mathematical structuralism and teaching theory have been downplayed day by day. Why study this idea now? China began the eighth curriculum reform in 2001. One of the reflections on the reform today is that the mathematics curriculum structure is loose. Because of the influence of structure viewpoint on mathematics education, combining the idea of new curriculum standard and the structural characteristics of mathematics itself in senior high school, this paper probes into teaching based on structural point of view. Through literature analysis, the author finds that the structural view is of great significance to students' understanding and teaching. In mathematics, on the one hand, it tends to analyze mathematics knowledge from the whole, and bring mathematics knowledge into a structural system according to a certain classification, which is helpful to increase the students' understanding of mathematics. On the other hand, the mathematical content shows certain structural characteristics, according to the structural characteristics of a certain type of structural analysis to solve the problem, is conducive to mining the mathematical nature of the problem, improve the depth of understanding of students. In teaching, it is found that learning and theory play a significant role in the structural understanding of the problem and the evaluation of the structural level of the students' understanding. Before the teaching design, the author analyzes the teaching material of senior high school mathematics, and finds out that the mathematics of senior high school is the knowledge structure system of "quantity relation and space form", under this system, according to the "algebraic structure" (?) Quantitative relation; topological structure (?) Spatial relation; order structure (?) To analyze the structural characteristics of concepts, laws, and methods, and to concretize mathematical structures. Secondly, through the questionnaire survey of students in a middle school in Xichang City, we found that the students generally have certain structural consciousness, but lack of action and low level of understanding. Interviews with 8 teachers in and around Chengdu and 2 teachers in Xichang City were conducted. The interviews were carried out around "teaching, evaluation and help to students". It was found that teachers generally use the concept of structure to understand the teaching materials. However, this point of view will be used in teaching. Therefore, according to the structural point of view, this paper analyzes the teaching design of the two parts of the concept type-ellipse, the rule-sinusoidal theorem, through these two cases, to find out the method, to explore the teaching, and to help the students to understand. The key points of teaching design based on structural point of view are summarized as follows: (1) in teaching, starting from the whole, connecting with existing cognition and experience; (2) "exploring and discovering" should run through the whole teaching; (3) excavating the structural characteristics of mathematics content itself; (4) Design evaluation should be hierarchical to help students to check the breadth and depth of understanding.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
本文编号：2375855
[Abstract]:The mathematical study of SOLO classification abstract structure was put forward by the Bourbachian School of France, and then as the core view of cognitive psychology, it had a great influence on the curriculum reform in the "New number" period in the United States and in some countries in Europe and Asia. However, with the failure of the movement of "new numbers", mathematical structuralism and teaching theory have been downplayed day by day. Why study this idea now? China began the eighth curriculum reform in 2001. One of the reflections on the reform today is that the mathematics curriculum structure is loose. Because of the influence of structure viewpoint on mathematics education, combining the idea of new curriculum standard and the structural characteristics of mathematics itself in senior high school, this paper probes into teaching based on structural point of view. Through literature analysis, the author finds that the structural view is of great significance to students' understanding and teaching. In mathematics, on the one hand, it tends to analyze mathematics knowledge from the whole, and bring mathematics knowledge into a structural system according to a certain classification, which is helpful to increase the students' understanding of mathematics. On the other hand, the mathematical content shows certain structural characteristics, according to the structural characteristics of a certain type of structural analysis to solve the problem, is conducive to mining the mathematical nature of the problem, improve the depth of understanding of students. In teaching, it is found that learning and theory play a significant role in the structural understanding of the problem and the evaluation of the structural level of the students' understanding. Before the teaching design, the author analyzes the teaching material of senior high school mathematics, and finds out that the mathematics of senior high school is the knowledge structure system of "quantity relation and space form", under this system, according to the "algebraic structure" (?) Quantitative relation; topological structure (?) Spatial relation; order structure (?) To analyze the structural characteristics of concepts, laws, and methods, and to concretize mathematical structures. Secondly, through the questionnaire survey of students in a middle school in Xichang City, we found that the students generally have certain structural consciousness, but lack of action and low level of understanding. Interviews with 8 teachers in and around Chengdu and 2 teachers in Xichang City were conducted. The interviews were carried out around "teaching, evaluation and help to students". It was found that teachers generally use the concept of structure to understand the teaching materials. However, this point of view will be used in teaching. Therefore, according to the structural point of view, this paper analyzes the teaching design of the two parts of the concept type-ellipse, the rule-sinusoidal theorem, through these two cases, to find out the method, to explore the teaching, and to help the students to understand. The key points of teaching design based on structural point of view are summarized as follows: (1) in teaching, starting from the whole, connecting with existing cognition and experience; (2) "exploring and discovering" should run through the whole teaching; (3) excavating the structural characteristics of mathematics content itself; (4) Design evaluation should be hierarchical to help students to check the breadth and depth of understanding.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
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