HPM视角下的高中数学问题提出课堂教学研究

发布时间：2018-01-08 21:19

本文关键词：HPM视角下的高中数学问题提出课堂教学研究　出处：《聊城大学》2017年硕士论文　论文类型：学位论文

【摘要】：数学史与数学教育关系(HPM)的研究是国际数学教育的新潮流之一,特别的,在将数学史如何运用到数学课堂教学方面,都还处于研究阶段。在我国数学课程改革的过程中,运用数学史于教学以及“问题提出”都是热点问题。问题提出的教学不仅可以促进学生对数学基础知识、基本技能的掌握,而且对于学生更好的理解数学,提高对数学学习的兴趣,培养学生的创新精神等都有极大的帮助。而历史中经典“问题提出”是帮助学生理解数学,发现数学间联系的重要手段。本文是在数学史与数学教育关系的视角下,以认识理论为指导,通过深入了解历史上“问题提出”的发展过程,及各问题间的联系,复现数学历史发展中经典问题提出的连续性,探寻数学问题提出和创造的轨迹。结合现代思维特点、心理学等相关理论探究历史中的“问题提出”与现代“问题提出”教学结合的策略。因此,本文作了如下工作。(1)通过查阅文献,介绍了“问题提出”的研究背景,分析了HPM视角下历史问题提出对学生认识数学、思维发展、问题认知的促进作用。界定了问题、数学问题、问题提出等相关概念。(2)根据数学史上现实问题的提出和数学概念理论的发展过程的研究,再现了数学发生发展的原生态,呈现了许多问题发现与提出的方法,实际分析了可借鉴的思维因素。总结了数学史中问题提出在教学中的意义。(3)对高中数学问题提出的课堂教学现状进行调查分析,分别从教师和学生两方面了解到教师对问题提出教学的实施情况及影响学生问题提出的因素,并给出了相关建议。(4)分析数学史在教学中的缺失原因,结合其教育意义,进一步地对历史上经典问题提出进行案例分析,并总结了经典数学问题提出与学生创造性思维的培养、数学思想方法的学习、身心全面发展等方面关系。(5)运用现代心理学中学习迁移理论,利用数学思维连续性、数学广泛应用型特点,结合现代教育的人文教育理念,对数学史上“问题提出”中的背景、方法进行综合分析。最后从学生的学习特点和知识建构规律,从数学课堂实际出发,提出了HPM视角下的“问题提出”教学策略。
[Abstract]:The research on the relationship between mathematics history and mathematics education is one of the new trends of international mathematics education, especially how to apply mathematics history to mathematics classroom teaching. Both are still in the research stage. In the course of mathematics curriculum reform in China, the use of mathematics history in teaching and "problem raising" are hot issues. The teaching of questions can not only promote students' basic knowledge of mathematics. The mastery of basic skills, and for students to better understand mathematics, improve the interest in mathematics learning. It is of great help to cultivate students' spirit of innovation. However, the classic question put forward in history is to help students understand mathematics. This paper is based on the relationship between mathematics history and mathematics education, under the guidance of cognitive theory, through the in-depth understanding of the history of the "problem put forward" development process. And the relationship between the problems, repeat the history of mathematics in the development of classical problems put forward the continuity, explore the mathematical problems put forward and create the track, combined with the characteristics of modern thinking. Psychology and other related theories explore the strategy of combining "problem" with "modern" problem in history. Therefore, this paper has done the following work. This paper introduces the research background of "problem raising", analyzes the role of historical question raising in promoting students' cognition of mathematics, thinking development and problem cognition from the perspective of HPM, and defines problems and mathematical problems. According to the practical problems raised in the history of mathematics and the study of the development process of the mathematical concept theory, the original ecology of the occurrence and development of mathematics is reappeared. There are many methods to find and propose problems. This paper analyzes the thinking factors which can be used for reference, and summarizes the significance of putting forward problems in the history of mathematics in teaching.) the present situation of classroom teaching of mathematics problems in senior high schools is investigated and analyzed. From the two aspects of teachers and students to understand the implementation of teachers to put forward problems and the factors that affect students' problems, and give the relevant suggestions. 4) analyze the reasons for the lack of mathematics history in teaching. Combined with its educational significance, this paper makes a case study on the classical problems in history, and summarizes the relationship between the classical mathematical problems and the cultivation of students' creative thinking and the study of mathematical thinking methods. The comprehensive development of body and mind. 5) apply the theory of learning transfer in modern psychology, make use of the continuity of mathematical thinking, the characteristics of extensive application of mathematics, and combine the humanistic education idea of modern education. This paper analyzes the background and method of "problem raising" in the history of mathematics. Finally, from the characteristics of students' learning and the law of knowledge construction, it starts from the reality of mathematics classroom. This paper puts forward the teaching strategy of "question put forward" from the perspective of HPM.
【学位授予单位】：聊城大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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