A Study on Mathematics Curriculum for Learning Functions Which Takes Account of the Articulation between Elementary and Secondary Schools and of the Applications of Functions

本研究是在这样一种假设下进行的，即许多初中生发现函数学习困难的主要原因之一是他们对函数概念的理解不发达。参考前人关于学习函数的相关著作，对学生学习函数的课程进行了记录和分析。分析表明，即使是小学生也表现出了许多行为，这些行为被认为是对功能理解程度较高的指标。这些分析和理论思考表明，目前的课程缺乏的是功能的对象化，而不是某些推理模式的便利化。这些结果表明，在开发数学课程时应考虑对象化方面的问题。

This study was conducted under the assumption that one of the main reasons why many junior high-school students find difficulty in learning functions is their undeveloped understanding of the concept of function. Lessons for students learning functions were recorded and analyzed referring to the previous related works about learning functions. The analyses showed that even primary students demonstrated many behaviors which are considers as indices of rather developed understanding of functions. These analyses and the theoretical considerations suggested that what lacks in today's curriculum is the objectification of functions, rather than the facilitation of certain modes of reasoning. These results show that the aspect of objectifying should be considered in developing mathematics curriculum.