The purpose of this paper is to identify changes in teacher’s pedagogical content knowledge (PCK) as a result of their participation in two learning studies in mathematics.,A group of four mathematics teachers and the researcher of this paper explored two objects of learning related to division with decimal numbers and the straight-line equation in a learning study (LS) project over the course of one year. The data used consist of eight video-recorded lessons, four written student tests, eight student interviews and 14 recorded team meetings. The analysis was based on the variation theory principle about learning (Marton, 2015) and on ontological assumptions within the phenomenographic approach (Marton, 1981).,It was found that teachers’ PCK was changed and refined through the LS process in terms of differences in ways of understanding and discussing critical aspects related to each object of learning. In the paper, the terms “presumed critical aspects” and “explored critical aspects” are used to illustrate this difference. Furthermore, the concepts are viewed in relation to three subdomains of PCK: knowledge of content and curriculum (KCC), knowledge of content and students (KCS) and knowledge of content and teaching (KCT).,Bringing out the difference between “presumed critical aspect” and “explored critical aspects” advances the view that critical aspects are dynamic and emergent in practice – in the interaction between teaching and student learning. The research exposes “explored critical aspects” as a specific form of PCK in which KCC, KCS and KCT are intertwined.

中文翻译：

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通过学习研究学会发现差异

本文的目的是确定教师的教学内容知识 (PCK) 由于他们参与了两项数学学习研究而发生的变化。,一组四名数学教师和本文的研究人员探讨了与数学相关的两个学习对象。在为期一年的学习研究 (LS) 项目中使用十进制数和直线方程进行除法。使用的数据包括 8 节视频课程、4 次学生笔试、8 次学生访谈和 14 次录制的团队会议。该分析基于关于学习的变异理论原理（Marton，2015）和现象学方法中的本体论假设（Marton，1981）。研究发现，在理解和讨论与每个学习对象相关的关键方面的方式上存在差异时，教师的 PCK 通过 LS 过程得到了改变和完善。在本文中，术语“假定的关键方面”和“探索的关键方面”用于说明这种差异。此外，这些概念与 PCK 的三个子领域相关：内容和课程知识 (KCC)、内容和学生知识 (KCS) 以及内容和教学知识 (KCT)。方面”和“探索的关键方面”提出了这样一种观点，即关键方面在实践中是动态的和新兴的——在教学和学生学习之间的相互作用中。该研究将“探索的关键方面”暴露为 PCK 的一种特定形式，其中 KCC、