ABSTRACT In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students’ answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master’s Degree in Mathematics. In order to study the possible development of the IK of these students, we explored their interpretations of secondary students’ productions and compared those given before, during, and after a collective discussion about these productions. Our findings reveal considerable differences in PTs’ knowledge and interpretations provided during the three activities, confirming that these and similar activities can be useful in training mathematics teachers in order to develop their IK.

中文翻译：

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数学教师对学生错误和非标准推理的解释性知识

摘要 在这项工作中，我们检查了数学教师在解释学生答案时调动的数学知识，我们将其表示为解释性知识 (IK)。特别是，我们分析了未来数学教师 (PT) 的 IK，他们是数学硕士学位的数学教育课程的学生。为了研究这些学生 IK 的可能发展，我们探索了他们对中学生作品的解释，并比较了在集体讨论这些作品之前、期间和之后给出的解释。我们的研究结果揭示了在三项活动中提供的 PT 知识和解释的显着差异，证实这些活动和类似活动可用于培训数学教师以发展他们的 IK。