International comparative studies on mathematics teaching and learning often provide unitary and harmonious images of classroom practices. This paper aims to complement those studies by describing the complex aspects of those practices. Adopting activity theory as a framework, this paper considers classroom teaching and learning of mathematics as an activity system embedded in socio-historical contexts, analyzes its contradictions, and makes a comparative analysis of different practices of mathematics teaching and learning in the same country. As a case in point, mathematics lessons in Japanese secondary schools are considered. The initial activity system of mathematics lessons in Japanese modern schools came from the whole-class instruction system and then gradually evolved into the problem-solving style lesson. The latter has been facing challenges, and then a new activity system has emerged from a new paradigm of school education. It is argued that activity systems analysis enables us to understand the contradictions prevailing in mathematics education and that comparative analysis of more than one system in the same culture can provide valuable insights.

关于数学教学和学习的国际比较研究往往提供课堂实践的统一和和谐的形象。本文旨在通过描述这些实践的复杂方面来补充这些研究。本文以活动理论为框架,将数学课堂教与学视为嵌入社会历史背景的活动系统,分析其矛盾,并对同一国家不同的数学教与学实践进行比较分析。例如，考虑了日本中学的数学课。日本现代学校数学课最初的活动体系来自全班教学体系，然后逐渐演变成问题解决式的课堂。后者一直面临挑战，继而在学校教育的新范式中出现了新的活动体系。有人认为，活动系统分析使我们能够理解数学教育中普遍存在的矛盾，并且对同一文化中的多个系统进行比较分析可以提供有价值的见解。