不定方程在初等数学中的教学研究摘要 不定方程在中学数学中的应用相当广泛，是中学数学中的一个重要组成部分 .评估学生掌握不定方程相关知识的程度，寻找如何提高学生使用不定方程解决问题能力的方法，在学生未来步入高等数学研究的过程中也是至关重要的.通过收集历年江苏高考中出现的不定方程题目，可以发现此考点多在数列的存在性问题中出现.对收集的题目进行归纳，得出不定方程题型的考察方式及考察侧重点.分析发现考察题目可分为两大类：非整解不定方程和整解不定方程，主要为整解类问题.再结合函数及数论知识从中总结出解决不定方程问题的处理方法.以缓解在处理此类问题无从下手的局面.关键词 不定方程 初等数学 数论 整数解 数列 1Teaching research of indefinite equation in Elementary MathematicsAbstract Indefinite equation is widely used in middle school mathematics, and it is an important part of middle school mathematics. It is also very important for students to evaluate their knowledge of the indefinite equation and find out how to improve their ability of using the indefinite equation to solve problems. By studying the teaching of indefinite equation in primary mathematics, it is very important to improve students' mathematical literacy and increase their mathematical knowledge. Therefore, in the future mathematics teaching process, students should be able to think independently about the discovery, development and application of indefinite equations according to the thought method of problem-solving.Key words Indefinite Equation Elementary Mathematics 2目 录1.引言..............................................................11.1 选题意义............................................................................................................................11.2 研究综述............................................................................................................................11.3 研究意义..........................................................................
