As argumentation is an activity at the heart of mathematics, (not only) German school curricula request students to construct mathematical arguments, which get evaluated by teachers. However, it remains unclear which criteria teachers use to decide on a specific grade in a summative assessment setting. In this paper, we draw on two sources for these criteria: First, we present theoretically derived dimensions along which arguments can be assessed. Second, a qualitative interview study with 16 teachers from German secondary schools provides insights in their criteria developed in practice. Based on the detailed presentation of the case of one teacher, the paper then illustrates how criteria developed in practice take a variety of different aspects into account and also correspond with the theoretically identified dimensions. The findings are discussed in terms of implications for the teaching and learning about mathematical argumentation in school and university: An emphasis on more pedagogical criteria in high school offers one explanation to the perceived gap between school and university level mathematics.

中文翻译：

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学校里什么才算“好”论证？——教师如何给学生的数学论证打分

由于论证是数学的核心活动，（不仅）德国学校课程要求学生构建数学论证，并由教师进行评估。然而，目前尚不清楚教师在总结性评估环境中使用哪些标准来决定特定等级。在本文中，我们为这些标准借鉴了两个来源：首先，我们提出了可以评估论点的理论派生维度。其次，对来自德国中学的 16 名教师进行的定性访谈研究提供了他们在实践中制定的标准的见解。基于对一位教师的案例的详细介绍，该论文随后说明了实践中制定的标准如何考虑各种不同的方面，并与理论上确定的维度相对应。