結(jié)構(gòu)觀點下的高中數(shù)學(xué)教學(xué)設(shè)計分析
發(fā)布時間：2018-12-13 04:12
【摘要】：SOLO分類摘要結(jié)構(gòu)觀點在數(shù)學(xué)上的研究自法國布爾巴基學(xué)派提出,隨后作為認知心理學(xué)的核心觀點,對美國“新數(shù)”時期及歐亞一些國家的課程改革有很大影響.然而隨著“新數(shù)”運動失敗,數(shù)學(xué)結(jié)構(gòu)主義連同教學(xué)理論日漸被淡化.現(xiàn)在為什么還要去研究這一觀點?我國從2001年開始第八次課程改革,今天對這次改革的反思之一是:數(shù)學(xué)課程結(jié)構(gòu)松散.由于結(jié)構(gòu)觀點對數(shù)學(xué)教育的影響,結(jié)合新課標(biāo)理念和高中數(shù)學(xué)本身的結(jié)構(gòu)特點,因此基于結(jié)構(gòu)觀點去探究教學(xué).本研究經(jīng)文獻整理分析,發(fā)現(xiàn)結(jié)構(gòu)觀點對學(xué)生理解以及教學(xué)上有較大意義.在數(shù)學(xué)上的體現(xiàn)為,一方面它傾向于從整體去分析數(shù)學(xué)知識,并按照某個分類將數(shù)學(xué)知識納入一個結(jié)構(gòu)體系中,有利于增加學(xué)生對數(shù)學(xué)理解的廣度.另一方面,數(shù)學(xué)內(nèi)容顯示出一定的結(jié)構(gòu)特征,根據(jù)某一類的結(jié)構(gòu)特點分析解決問題,有利于挖掘問題中蘊含的數(shù)學(xué)本質(zhì),提高學(xué)生理解的深度.在教學(xué)上,發(fā)現(xiàn)學(xué)習(xí)和理論分別在學(xué)生對問題進行結(jié)構(gòu)性理解,以及評價學(xué)生理解的結(jié)構(gòu)水平上作用明顯.教學(xué)設(shè)計之前,先分析了人教A版高中數(shù)學(xué)教材,發(fā)現(xiàn)當(dāng)前高中數(shù)學(xué)是以“數(shù)量關(guān)系和空間形式”為研究對象的知識結(jié)構(gòu)體系,在該體系下,按“代數(shù)結(jié)構(gòu)(?)數(shù)量關(guān)系;拓撲結(jié)構(gòu)(?)空間關(guān)系;序結(jié)構(gòu)(?)序關(guān)系”,去分析概念、法則和方法的結(jié)構(gòu)特點,將數(shù)學(xué)結(jié)構(gòu)具體化.其次,通過對西昌市某中學(xué)的學(xué)生問卷調(diào)查,主要調(diào)查結(jié)構(gòu)理解的意識、做法及學(xué)習(xí)結(jié)果3個方面,發(fā)現(xiàn)學(xué)生普遍有一定結(jié)構(gòu)性意識,但缺乏行動,理解水平較低.并分別對成都市及周邊8位及西昌市2位教師進行訪談,訪談內(nèi)容圍繞“對教材、教學(xué)、評價及對學(xué)生的幫助”展開,發(fā)現(xiàn)教師普遍用結(jié)構(gòu)觀去理解教材,但較少將該觀點用在教學(xué)中.因此,根據(jù)結(jié)構(gòu)觀點,對概念型——橢圓、法則型——正弦定理這兩部分進行教學(xué)設(shè)計分析,通過這兩個案例,去尋找方法,探究教學(xué),幫助學(xué)生理解.總結(jié)出基于結(jié)構(gòu)觀點進行教學(xué)設(shè)計的關(guān)鍵點:(1)教學(xué)上,從整體入手,聯(lián)系已有認知和經(jīng)驗;(2)“探索發(fā)現(xiàn)”應(yīng)貫穿整個教學(xué);(3)挖掘數(shù)學(xué)內(nèi)容本身的結(jié)構(gòu)特點;(4)設(shè)計評價應(yīng)有層次性,幫助學(xué)生自查理解的廣度和深度.
[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.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6
本文編號：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.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：G633.6
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