自然数的平方和公式推导

The Formula Derivation of the Sum of Squares of Natural Numbers

摘要: 解题是数学学习的一个核心内容和一种最基本的活动形式。罗增儒教授曾指出“数学教育中真正发生数学的地方都无一例外地有数学解题活动”。因此数学教学应“以解决问题为导向”，解决问题的过程是学习新知识、发展智力和提高能力的过程，而“一题多解”恰恰是解题教学中最常用、最有效的一种教学手段与技术。本文针对解题灵活性的要求，通过“自然数的平方和公式推导”的一题多解，完善学生数学知识框架，提升思维的发散性和系统性。让学生感受到学习数学的乐趣，从而进一步提高学生数形结合能力以及代数运算的能力以及空间解析能力等，激发学生学习数学的兴趣。

Abstract: Problem solving is a core content and the most basic form of activity in mathematics learning. Professor Luo Zengru once pointed out that “all places where mathematics truly occurs in mathe-matics education have mathematical problem-solving activities”. Therefore, mathematics teaching should be “problem-solving oriented”. The process of problem-solving is the process of learning new knowledge, developing intelligence, and improving abilities. “Multiple solutions to one problem” is precisely the most commonly used and effective teaching method and technique in problem-solving teaching. In view of the requirement of flexibility in solving problems, this paper improves students’ mathematical knowledge framework, improves their divergent and systematic thinking, makes students feel the fun of learning mathematics, and further improves students’ ability to combine numbers with shapes, algebraic operations and spatial analysis, and stimulates students’ interest in learning mathematics through multiple solutions to one problem of “square sum formula derivation of natural numbers”.