Developing qualitative research methods for improvement of mathematics teaching

本研究旨在发展中小学数学教学中的质的研究方法。调查由三部分组成。第一部分是课堂上的理论思考，涉及到质的研究方法。理论框架受到了抹大拉·兰伯特著作的影响。它的核心概念是，数学课堂是一个由以下事件组成的系统，作为分析单位：教学以建立课堂文化；教学时备课；教学时学生独立工作；教学时引导全班讨论；教学故意将课程内容联系起来。第二部分是六、七年级教学实验的设计。六年级和七年级分别选择正比例和线性方程。在两所公立学校进行了教学实验。每节课都录下了音频和视频，以备日后分析。第三部分包括对每个事件的定性分析；建立课堂文化的教学；备课时的教学；教学中有意地将课程内容联系起来。对每个事件的描述和解释表明，这些事件条件反射地构成了整堂课。这一新观点将为改进数学教学提供良好的理论基础。

The research aims at developing qualitative research method in teaching mathematics in elementary and secondary school levels. The investigation consists of three parts. First part addresses theoretical consideration in classroom, which involves qualitative research methodology. The theoretical framework has been influenced by the writings of Magdalene Lampert. Central to its formulations is the notion that mathematics classroom is a system which constitutes of the following events as unit of analysis : teaching to establish a classroom culture ; teaching while preparing a lesson ; teaching while students work independently ; teaching while leading a whole-class discussion ; teaching to deliberately connect content across lessons. Second part addresses design of teaching experiment at sixth and seventh grades. Direct proportion and linear equation are chosen for sixth and seventh grades respectively. Teaching experiments are implemented at two public schools. Every lesson was audio-video taped for later analysis. The third part involves qualitative analysis of each event ; teaching to establish a classroom culture ; teaching while preparing a lesson ; teaching to deliberately connect content across lessons. Description and interpretation of each event shows that these events reflexively constitute entire lesson. The emergent perspective would be promising theoretical underpinning for improvement mathematics teaching.