This paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: ‘mathematical knowledge for teaching’ and ‘mathematics didactic knowledge’. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical knowledge for teaching is viewed as a utilitarian-pragmatic approach rooted in English-speaking traditions as it focuses on its use in teaching and represents a practice-based conceptualization of knowledge domains required for mathematics teaching. Mathematics didactic knowledge, on the other hand, is considered normative-descriptive as it is formulated based on didactic principles and broader theoretical perspectives, providing a theory-driven conceptualization of knowledge domains rooted in traditions of German-speaking didactics of mathematics. The paper further highlights similarities and differences in these two constructs through an examination of two central knowledge domains: specialized content knowledge (part of mathematical knowledge for teaching) and subject matter didactic knowledge (part of mathematics didactic knowledge).

本文比较和对比了英语和德语中关于数学教师知识话语中广泛使用的两种方法：“教学用数学知识”和“数学教学知识”。有人提出，这些构造基于不同的理论和概念立场和起源。用于教学的数学知识被视为植根于英语传统的功利实用方法，因为它侧重于其在教学中的使用，并代表了数学教学所需知识领域的基于实践的概念化。另一方面，数学教学知识被认为是规范描述性的，因为它是基于教学原则和更广泛的理论视角制定的，提供植根于德语数学教学传统的理论驱动的知识领域概念化。本文通过对两个核心知识领域的考察，进一步强调了这两种结构的异同：专业内容知识（教学数学知识的一部分）和主题教学知识（数学教学知识的一部分）。