数形结合在初中数学教学实践中运用的研究

发布时间：2018-12-31 15:08

【摘要】：《义务教育数学课程标准(2011)》在课程总目标中明确指出“学生经过义务教育阶段的数学学习后,要能够获得适应社会生活和进一步发展所必需的数学的基础知识、基本技能、基本思想和基本活动经验’。与旧课程标准总目标的双基相比,新课程标准明确指出学生要能够掌握数学的基本思想方法,其一个重要方面是要掌握数学结果形成过程中蕴涵的数学思想方法。因此注重数学思想方法在数学教学实践中的运用变得十分必要。“数学是研究数量关系和空间形式的科学”,因此“数”与“形”是数学主要研究的两类对象。数形结合是在中学数学教学中运用最为广泛的一种数学思想方法,它将“数”与“形”两个方面结合起来诠释数学知识。“数”是形的抽象概述,“形”是数的直观表现。初中阶段学生的抽象思维能力不强,对抽象数学知识的理解还有难度,所以在进行数学知识讲解时,应该从直观形象的模型出发帮助学生理解抽象的数学知识。数形结合思想方法能够把数学知识的直观和抽象两个方面结合,通过数与形的相互转化使抽象的问题具体化,复杂的问题简单化,最终使得数学问题得到很好的解决,所以研究数形结合思想方法在数学教学实践中的运用就变得十分有意义。本文以华东师大版数学义务教育教科书(7-9年级)为例,结合笔者的教学经验,详细探讨了在课堂上运用数形结合进行教学的作用。全文包含五个部分内容。本文首先简单的介绍了研究数形结合的背景和意义,并对数学思想方法和数形结合的相关概念进行了界定；然后探讨了数形结合研究的理论基础,指出对于数形结合在教学中运用的研究符合中学生心理认知特点；紧接着通过具体案例仔细分析研究了数形结合的运用对初中数学教学的作用；最后对于数形结合思想方法的教学提出了个人的建议。
[Abstract]:The Mathematics Curriculum Standard for compulsory Education (2011) clearly points out in the general goal of the curriculum that "after studying mathematics in the compulsory education stage, students should be able to acquire the basic knowledge of mathematics necessary for adapting to social life and further development." Basic skills, basic ideas, and basic activity experience. Compared with the general objective of the old curriculum standard, the new curriculum standard clearly points out that students should be able to master the basic thinking methods of mathematics, and one of its important aspects is to master the mathematical thinking methods contained in the forming process of mathematical results. Therefore, it is necessary to pay attention to the application of mathematical thought method in mathematics teaching practice. Mathematics is the science of studying quantitative relation and spatial form, so number and form are two main objects of mathematics research. The combination of number and form is one of the most widely used mathematical thinking methods in middle school mathematics teaching. It combines "number" and "form" to interpret mathematical knowledge. "number" is an abstract summary of form, and "form" is an intuitive representation of numbers. The abstract thinking ability of junior middle school students is not strong, and it is still difficult to understand abstract mathematics knowledge, so we should help students to understand abstract mathematics knowledge from the visual and visual model. The combination of numbers and shapes can combine the visual and abstract aspects of mathematical knowledge. Through the mutual transformation of numbers and shapes, the abstract problems can be concretized, the complex problems can be simplified, and finally the mathematical problems can be solved very well. Therefore, it is very meaningful to study the application of numeral-form combination thought method in mathematics teaching practice. Taking East China normal University mathematics compulsory education textbook (grades 7-9) as an example, combined with the author's teaching experience, this paper discusses in detail the role of the combination of numbers and shapes in the classroom teaching. The full text contains five parts. Firstly, this paper introduces the background and significance of the research on the combination of numbers and shapes, and defines the concepts of mathematical thinking and combination of numbers and shapes. Then it discusses the theoretical basis of the research on the combination of numbers and shapes, and points out that the research on the application of the combination of numbers and shapes in teaching accords with the psychological cognitive characteristics of middle school students. Then through a specific case study of the use of the combination of numbers and shapes in junior high school mathematics teaching role; finally for the teaching of thinking methods of the combination of numbers and shapes put forward personal suggestions.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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