小学数学化归思想方法的教学研究

发布时间：2018-09-18 16:29

【摘要】：数学思想方法是人类在漫长的数学实践中提炼出来的,是对数学知识的本质反映,是解决和研究数学问题,指导教学的手段、途径和方式.无论是建立数学概念、发现数学规律,还是解决数学问题都离不开数学思想方法.化归思想方法不仅是各类数学思想方法的基础,而且应用于大部分的数学内容中,统领着绝大多数的数学思想方法.论文在相关理论的指导下,界定了化归思想方法的含义,阐述了化归思想方法的特点,详细地说明了化归的原则:熟悉化原则、简单化原则、统一化原则.从小学数学教材中“数与代数”、“图形与几何”、“综合与实践”三大领域,对化归思想方法的知识载体进行了分析与整理.在上述研究基础上,给出了化归思想方法的教学原则:同步性原则、螺旋上升原则、系统性原则、直观性原则、活动性原则,设置了适合小学不同年级的化归思想方法教学的基本模式:“讲解——传授”、“引导——探究”、“自学——评价”,在此基础上提出了具体的教学策略:在研读教材中,发掘化归思想方法;在目标设计中,融入化归思想方法;在动手实践中,领悟化归思想方法;在问题解决中,掌握化归思想方法;在知识梳理中,深化化归思想方法,并结合具体实例进行了说明.基于上述教学策略,对“平行四边形的面积”与“三角形的面积”教学进行了详细的教学设计与分析.
[Abstract]:Mathematical thought and method is extracted from the long practice of mathematics and reflects the essence of mathematical knowledge. It is the means, ways and means of solving and studying mathematical problems and guiding teaching. Whether it is to establish mathematical concepts, find mathematical laws, or solve mathematical problems can not be separated from mathematical thinking. The thought method of transformation is not only the foundation of all kinds of mathematical thinking methods, but also applied to most mathematics contents, and dominates the vast majority of mathematical thinking methods. Under the guidance of relevant theories, this paper defines the meaning of the ideological method of conversion, expounds the characteristics of the ideological method of conversion, and explains in detail the principles of conversion: familiarization principle, simplification principle, unifying principle. From the three fields of "number and algebra", "figure and geometry" and "synthesis and practice" in primary school mathematics teaching materials, the knowledge carrier of thinking method of transformation is analyzed and sorted out. On the basis of the above research, the teaching principles of the thought method of transformation are given: synchronism principle, spiral ascending principle, systematic principle, intuitive principle, activity principle, and so on. This paper sets up the basic mode of thinking teaching suitable for different grades of primary school: "explanation-imparting", "guide-inquiry", "self-study-evaluation". On the basis of this, the author puts forward some specific teaching strategies: in the course of reading, Explore the ideological method of transformation and return; in the goal design, integrate the method of thinking of transformation and return; in the practical practice, comprehend the method of thinking; in solving the problem, grasp the method of thinking; in the process of combing knowledge, deepen the method of thinking; And combined with concrete examples to explain. Based on the above teaching strategies, the teaching design and analysis of the area of parallelogram and triangle are carried out in detail.
【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】：G623.5

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