Assessment - in what forms it ever takes place - has to be grounded on theoretical considerations of different levels and qualities. Among them most salient is that the content domain tested has been structured according to processes of teaching and learning. Then, tasks are the essential tool to assess the relevant content structures. The classification of tasks by appropriate marks and features is therefore a relevant issues and a big challenge when setting up educational assessment in mathe- matics. This paper focuses on the studies PISA （ an International Comparison taking mathematical literacy as target, including an ample national option in Germany） and COACTIV （a representative study in Germany on teachers＇ knowledge in mathematics and mathematical pedagogy）. Both studies aim to realize differentiated assessment, taking aspects of content and task analysis in- to consideration. Differentiated outcomes then allow getting information which is suitable for developing the teaching and learning in the classroom further, in two respects： Students＇ knowledge can be assessed in categories that point directly to issues of the teaching and learning in the classroom, and the influence teachers＇ knowledge has on students＇ learning progress can he tapped in a way that shows which didactical actions in the classroom could be effective.%评估——无论采用何种形式——不得不建立在对不同水平和质量的理论思考基础之上。其中至关重要的是测验内容领域要依据教与学的过程来构建。其次,任务是评估相关内容结构的核心工具。因此,在设计对数学的教育评估时,按照合理的标识和特征对任务进行分类就成为一个息息相关的问题,也是一个巨大的挑战。本文重点研究PISA（国际学生评估项目的缩写,是以数学素养为目标的国际比较研究,包括在国家层面德国所做的许多调整）和COACTIV（德国教师数学知识和数学教学知识的一个代表性研究）。两者都旨在实现区分性评估（differentiated assessment）,都考虑了评价内容和任务分析的不同方面。区分性评估结果使得我们能够获取有用的信息,进一步推动课堂教与学的发展。这些信息主要表现为两个方面：评估学生不同类型的知识,这些知识类型直接指向课堂教学与学习中存在的各种问题;探索教师知识对学生学习进展的影响,表明哪种教学行为是有效的。
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