HPME视角下的椭圆教学设计与研究

发布时间：2018-04-21 20:39

本文选题：HPM + PME　；参考：《华中师范大学》2017年硕士论文

【摘要】：近年来,国际上数学史与数学教育(HPM)领域、数学教育心理(PME)领域迅速发展,越来越多的学者和研究者不再着手于理论研究,而将视线投放在课堂教学实践当中,而将HPM、PME结合进行课堂教学实践将会给高中数学课堂带来不一样的教学方向。高中圆锥曲线的教学是高中数学的重点之一,同样是平面解析几何的核心,而椭圆的教学是高中圆锥曲线的开始,其概念的引入和标准方程的推导是现在所说的平面解析几何中用代数方式去探究几何方面问题的基本思想。本研究借鉴已有研究,选择以椭圆教学作为载体,从数学史与数学教育心理(HPME)的角度进行教学设计,并在实际课堂中践行HPME教学设计。本研究整理了数学史与数学教育、数学教育心理的相关理论,在此基础上,搭建HPM和PME的沟通桥梁,从一个新的视角——HPME的领域指导教学实践。研究选择了两所重点高中的四个班进行椭圆及其标准方程的教学实践,一个班进行正常教学,其余三个班分别进行实验教学,分为1班、2班、3班。本研究问题:如何将HPM、PME结合起来进行基于HPME的教学;探究基于HPME的椭圆教学实践对学生的知识理解水平以及情感、态度与价值观的影响;探究基于HPME的椭圆教学实践对教师的专业知识发展的启示。本研究采用多种研究方法收集数据,包括访谈、问卷测试,课堂实录分析。通过对数据的量化分析,以及对访谈、课堂实录的质性分析,得到研究结论。通过教学前后的问卷测试,考查学生对椭圆概念理解及认知水平的变化。经过和教师的沟通与交流,分析教师的专业发展。通过课堂教学实录对影响课堂教学效果的要素进行分析,并且知道如何将HPM、PME结合进行教学设计。本研究的主要结论有:(1)学生对椭圆概念的理解表现出较多的相似性,对它的灵活运用有待提高,理解层次大多处于A、B水平,尚达不到灵活运用水平。(2)对比分析,正常教学及实验班教学之后,发现采用HPME教学方式的学生的理解水平显著高于其它方式,因此采取HPME下的教学方式,有助于加深学生对所学知识的理解。(3)教师在经历了 HPM、PME以及HPME实践后,他们的HPM、PME的知识以及教学实践素质得到很大的提升。(4)HPM、PME在课堂数学教学设计中可以有效结合,以此提高教学效果。
[Abstract]:In recent years, the field of mathematics history and mathematics education (HPMM) and the field of psychology of mathematics education (PMEs) have developed rapidly. More and more scholars and researchers are no longer engaged in theoretical research, but focus their attention on classroom teaching practice. The combination of HPMPME and classroom teaching practice will bring different teaching direction to high school mathematics classroom. The teaching of high school conic curve is one of the key points of high school mathematics, it is also the core of plane analytic geometry, and the teaching of ellipse is the beginning of high school conic curve. The introduction of the concept and the derivation of the standard equation are the basic ideas of the algebraic approach in plane analytic geometry. Based on the previous research, this study chooses elliptical teaching as the carrier to carry out the teaching design from the angle of mathematics history and mathematics educational psychology, and practice the HPME teaching design in the actual classroom. This study collates the related theories of mathematics history and mathematics education, mathematics education psychology, on the basis of which, builds the communication bridge between HPM and PME, and guides the teaching practice from a new angle of view. The study selects four classes of two key high schools to carry on the ellipse and its standard equation teaching practice, one class carries on the normal teaching, the other three classes carry on the experiment teaching separately, divides into one class two classes and three classes. The research questions are as follows: how to combine the HPME teaching, explore the influence of the elliptical teaching practice based on HPME on the students' knowledge understanding level, emotion, attitude and values; This paper probes into the enlightenment of elliptical teaching practice based on HPME to the development of teachers' professional knowledge. This study uses a variety of research methods to collect data, including interviews, questionnaire tests, classroom analysis. Through the quantitative analysis of the data and the qualitative analysis of the interview and classroom record, the research conclusion is obtained. The students' understanding of ellipse and their cognitive level were tested by questionnaire before and after teaching. Through the communication and communication with teachers, the professional development of teachers is analyzed. This paper analyzes the factors that affect the effect of classroom teaching through classroom teaching record, and knows how to combine HPMPME with teaching design. The main conclusions of this study are as follows: (1) the students' understanding of elliptic concept shows more similarity, and its flexible application needs to be improved. Most of the understanding levels are at the level of Aneb, but they are still not up to the level of flexible application. After normal teaching and experimental class teaching, it is found that the understanding level of the students who adopt the HPME teaching method is significantly higher than that of the other methods. Therefore, the HPME teaching method is adopted. It is helpful to deepen the students' understanding of what they have learned. (3) after the teachers have experienced the practice of HPMPME and HPME, their knowledge and teaching practice quality have been greatly improved. HPMPME can be effectively combined in the design of classroom mathematics teaching. In order to improve the teaching effect.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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