【作者】 红梅；

【导师】 代钦；

【作者基本信息】 内蒙古师范大学 ， 学科教学（专业学位）， 2014， 硕士

【摘要】 目前，数学思想和方法的教学成为教学过程的重要目标之一，类化也是数学思想方法之一，渗透在数学的各个内容之中。函数作为数学的主要内容之一，它的思想贯穿于整个高中数学之中。在高中数学教学中，可以利用类化研究，这样有利于学生数学思维能力的发展及巩固所学的知识。本研究以高中函数内容为例，研究类化教学，并从函数的九个维度来类化研究，把函数的九个维度应用到每一类函数当中，这样从整体上把握了高中函数的性质，对以后研究函数提供理论与实践基础。本文共分四章，具体内容如下：一、导论。主要阐述了本文的研究目的、意义、国内外的研究现状、研究的方法以及创新之处。二、高中函数的概念、函数要素的类化。对求函数解析式、定义域、值域都做了系统的类化。三、函数性质的类化。分别对函数图象及其图象变换、函数对称性问题、函数单调性问题、函数周期性问题以及函数模型的应用等五个个方面做了类化研究。四、结束语。通过对高中函数的类化研究，得到以下几点启示：第一，在数学教学过程中，教师应尽可能多地向学生展示数学思想和方法，让学生感觉到学数学是一种培养学生思维逻辑的过程。第二，教师教学有两层意义，教师的教和学生的学。所以，作为一线教师要在分析学生学习的心理特点的基础上，研究类化的方法在教学中加以应用。只有充分了解学生，基于学生的思维特点展开教学，才是有意义的教学。第三，类化是一种思想，也是一种方法。在教学过程中遵循反复渗透的原则，培养学生形成良好的习惯，对所学的知识进行类化。第四，类化研究在数学教学中的应用，主要体现在解决问题方面。教师应当善于将问题进行分类，将复杂的问题简单化，帮助学生摆脱题海战术的局面；同时引导学生注重知识之间的转化，鼓励学生利用类化来巩固所学知识。更多还原

【Abstract】 Nowadays, the teaching of mathematics thoughts and methods hasbecome one of the important goals of mathematics teaching. Themathematical generalization is one of the mathematical thoughts, whichpermeates in almost all the knowledge points in mathematics. Function is amajor section in mathematics, which runs through the whole mathematicalteaching in high school. In high school mathematic teaching, we couldimplement mathematical generalization research in order to train, improvestudents’ mathematical thinking abilities and help students to strengthen whatthey have been learning in mathematics.This research uses high school function as an example to illustrate how toimplement mathematical generalization teaching in high school. Theresearch focuses on function’s nine latitudes and their applications in everyfunctions appeared in high school’s mathematics, which grasps the nature ofthe high school’s function. This research provides the theoretical andpractical basis for the future research of functions. The research is dividedinto five sections. The specific content is as follows:Section one IntroductionThis section mainly introduces the purpose, significance, status, methodand innovation of this mathematical generalization research.Section two The generalization of high school functions’ definitions andelementsThis section systematically generalizes high school functions’ analysisformulas, domains of definition and ranges.Section three Generalization of properties of functions in five aspectsThis section focuses on the research of generalization of properties offunctions in aspects of functional images and the image transformation,symmetrical characteristics, monotonicity of a function, periodicity offunctions and function model.Section four Conclusion Based on this research, we could conclude the following:1. In the process of mathematics teaching, teachers should show thestudents as much mathematical thought and mathematical methods tolet the student as possible, which lets students feel that learningmathematics is a process of cultivating students’ logical thinking.2. The teaching has two meanings–teachers’ teaching and students’learning. Teachers need to research how to implement generalizationmethods in their teaching practice. Moreover, students’ learningpsychological characteristics also need to be put into considerationsince any teaching method that is suitable for students’ thinkingpatterns could be regarded as effective teaching methods.3. Generalization is a philosophy, and it is a principle that should befollowed in the teaching practice, which cultivates students’ habits ofgeneralizing whatever they are learning in their school days.4. The implementation of research on generalization in mathematicalteaching mainly serves for how to solve problems in daily lives.Teachers need to be able to generalize problems and simplify thecomplicated ones, which helps students to get out of the boring andheavy workbooks and endless exercises. Moreover, teachers need touse the generalization method to help students to make knowledgetransformation as a means of consolidating the knowledge they havebeen learning.更多还原