Developing qualitative research methods for improvement of mathematics teaching

本研究旨在发展中小学数学教学的质性研究方法。调查由三个部分组成。第一部分是课堂上的理论思考，涉及到定性研究方法。理论框架受到了玛格达琳·兰伯特著作的影响。其表述的核心概念是，数学课堂是一个系统，它由以下事件作为分析单元构成：教学以建立课堂文化；边备课边教学；在学生独立学习的同时进行教学；在带领全班讨论的同时进行教学；教学要有意识地将各课的内容联系起来。第二部分是六、七年级教学实验设计。六年级和七年级分别选用正比例和线性方程。教学实验在两所公立学校实施。每节课都有录音录像供以后分析。第三部分对各事件进行定性分析；建立课堂教学文化；边备课边教学；教学要有意识地将各课的内容联系起来。对每个事件的描述和解释表明，这些事件反身性地构成了整个课程。涌现视角将为改进数学教学提供有希望的理论基础。

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.