Development and evaluation of articulated curriculum based on mathematical activity

研究界越来越多地达成共识，认为有必要开发基于小学和中学数学活动的清晰课程。课程开发的三个层次是：预期课程、实施课程和实现课程。本研究共分三个部分。第一部分论述了预期课程，其中包括一个理论框架的指示，开发良好的衔接课程的基础上的数学活动。这一理论框架受到了现实主义数学教育理论基础的影响。其公式的核心是这样一个概念，即数学是一种通过数学手段进行的组织活动。第二部分是实施课程，包括六、七年级比例函数教学单元的设计。第三部分是关于课程的实现，包括对金泽市两所公立学校实施的教学实验的描述和分析。每节课都被录制成音频视频，供以后分析。该分析涉及对参与者观察期间发生的事件的描述和解释。数学课堂的定性分析发现了数学活动的几种具体模式。这些研究表明，教师和学生如何结构，使用和阐述比例函数，因为他们通过六年级和七年级。这些结果为开发基于数学活动的衔接课程提供了一些基本原则。

There has been a growing consensus among research community about the necessity for developing well-articulated curriculum based on mathematical activity that encompass elementary and secondary school level. The research focuses on the three levels of curriculum development : intended curriculum, implemented curriculum, and attained curriculum. The investigation consists of three parts. First part addresses intended curriculum, which involves an indication of the theoretical framework for developing well-articulated curriculum based on mathematical activity. The theoretical framework has been influenced by the theoretical underpinnings of Realistic Mathematics Education. Central to its formulations is the notion that mathematics is an organizing activity by mathematical means. Second part addresses implemented curriculum, which involves design of teaching unit for proportional function at sixth and seventh grades. The third part addresses attained curriculum, which involves description and analysis of teaching experiment, which are implemented at two public schools located at Kanazawa city. Every lesson was audiovideo taped for later analysis. The analysis involves description and interpretation of an episode that occurred during a participant observation. Qualitative analysis of mathematics classroom detected several specific patterns of mathematical activity. These researches showed how do teacher and students structure, use and elaborate proportional function as they go through sixth and seventh grades. These results suggest some basic principles for developing articulated curriculum based on mathematical activity.