球积术案例及其分析

Cases and analysis of calculating the volume of the sphere

目的以数学史上的4种球积术为例,说明数学史在中学数学教学中应用的意义。方法案例研究和比较分析。结果 4种历史上的球积术方法体现出两种数学传统下数学家对相同问题的不同处理,对其在数学课堂的适当应用既可以更好地增进学生对具体知识的理解,也可以提高学生的数学修养。结论开发数学史的教学案例,并将其有效地应用于数学教学中,对于数学教育目标的实现具有重要帮助。

Aim To illustrate the effect and significance of the application of the history of mathematics to mathematical class of middle schools.Methods Case study and comparative analysis.Results The 4 historical methods of calculating the volume of the sphere indicate mathematician′s different treatment to a same problem under two different mathematical traditions.The proper application of these methods to mathematical class will not only strengthen students′ understanding of concrete knowledge,but also improve their mathematical accomplishment.Conclusion It will be greatly helpful for realizing the target of mathematical education that HPM cases are constructed and applied effectively to mathematical class.