What mathematical knowledge is required for teaching has been researched by many, with Ball et al. (J Teach Educ 59(5):389–407, 2008) and their practice-based theory of mathematical knowledge for teaching (MKT) primary among them. However, what is required in terms of mathematical knowledge for teacher educator training has been researched much less. The present study builds on an emerging framework on mathematical knowledge for teaching teachers (MKTT) by Zopf (Mathematical knowledge for teaching teachers: the mathematical work of and knowledge entailed by teacher education, University of Michigan, Ann Arbor, 2010) augmented with more recent developments in the field. The empirical basis for the study stems from an implementation of a short course on history in mathematics education at the Danish School of Education, and in particular on two case studies involving three teacher educator students participating in that course. Based on analyses of their developments in terms of MKTT, we point to the potential of using history in both teacher and teacher educator training, and in particular historical source material. As part of the analyses, we also consider the teacher educator students’ development of disciplinary knowledge of mathematics, especially in relation to developing and making use of knowledge of the epistemology of mathematics and mathematical work. We assert that the cases we present here address Zopf’s call for case studies from different teacher education contexts as well as investigations of novice teacher educators, and further contribute to the developing theory of MKTT.

中文翻译：

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为教师教学发展数学知识：数学史在教师教育工作者培训中的潜力

Ball等人已经研究了教学所需的数学知识。（J Teach Educ 59（5）：389–407，2008）及其基于实践的数学知识教学理论（MKT）成为其中的主要内容。但是，对于教师教育者培训所需要的数学知识的研究却很少。本研究建立在Zopf提出的关于教师教学的数学知识（MKTT）的新兴框架（教师教学的数学知识：教师教育的数学工作和知识，密歇根大学，安阿伯，2010年）之后，该领域的发展。这项研究的经验基础来自丹麦教育学院开设的数学教育历史短期课程，特别是涉及两个案例研究，涉及三个老师教育的学生参加了该课程。基于对他们在MKTT方面的发展的分析，我们指出在教师和教师教育者培训中特别是历史源资料中使用历史的潜力。作为分析的一部分，我们还考虑了教师教育学生对数学学科知识的发展，特别是在发展和利用数学和数学工作的认识论知识方面。我们断言，这里介绍的案例满足了Zopf的要求，即从不同的教师教育环境中进行案例研究，以及对新手教师教育者的调查，这进一步为MKTT的发展理论做出了贡献。