数学归纳法在中学数学证明中的应用本科.docVIP

摘 要 数学归纳法是用来证明某些与自然数有关的数学命题的一种推理方法，同时也是数学命题证明的一种数学思想.针对与自然数有关的恒等式、代数不等式、三角不等式、数列问题、几何问题、整除性问题等的证明，在中学数学课堂教学及证明中具有广泛的运用，本文对它在中学数学不同类型证明中作简要分析，目的在于培养学生观察能力、逻辑思维能力、形象思维以及解决整体性问题的能力.数学归纳法作为由特殊概括出一般的一种思维方法，具有两种基本意义，首先数学归纳法是一种推理方法，称为归纳推理，它可以为我们提出猜想，为论证提供基础和依据．其次归纳是一种研究方法，归纳是一种又创造性的探索式思维方法，能开发智力，拓宽思路，引出猜想，它在发现问题和探索解题途径的过程中起着重要作用．数学归纳法可按照它的概括事物是否完全分为两种基本形式——不完全归纳和完全归纳．本文还介绍了在数学解题过程中归纳发现的思考方法：利用归纳法发现和提出数学猜想，利用归纳法发现问题的结论，运用归纳法发现解题途径等． 关键词：数学归纳法；不完全归纳法；完全归纳法；中学数学；应用 Abstract Mathematical induction is a kind of reasoning methods, which is used to prove some propositions related mathematical natural number, it is also a kind of mathematical proposition proof mathematical thoughts. According to the concerned with natural number , algebraic inequalities identities, triangular, inequality series problem, geometry problems, division of sexual problems ，it has widely applied to the classroom teaching and proof in high school. As different mathematical inductions have different types of proof in middle school, this paper makes a brief analysis aims to cultivate the students observation, logical thinking ability, visual thinking and solving integrity question ability. Mathematical induction, as summarized by the general as a special way of thinking, has two basic meanings, the first mathematical induction is a kind of reasoning, known as inductive reasoning, it can bring up us suppose ,Provide the basis and foundation for the argument. Second, induction is a research method, induction is a creative exploration of another type of thinking, can develop intelligence, broaden thinking, leads to speculation, it plays an important role in finding the problem and ways to explore the process of problem solving. Mathematical induction, in accordance with its general matter is completely divided into two basic forms - incomplete induction and complete induction. This article also describes the process of mathematics problem solving way of inductive methods of discovery: using mathematical i