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

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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.