Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS.

中文翻译：

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初等教师数学解题的教学知识

对数学教师知识的研究一般更侧重于数学概念而不是数学过程。本文针对后者，重点关注数学问题解决 (PS)。它报告了一项研究，该研究调查了未来小学数学教师 (PT) 的 PS 教学知识。参与者是西班牙一所大学的 149 名 PT。他们的教师教育计划即将结束。数据来源包括学习PS知识问卷和教学PS知识问卷。研究结果表明，PTs 结合了不同水平的 PS 学与教知识。他们中的许多人展示了许多特征的适当知识，用于 (1) PS 学习，包括学生作为问题解决者，PS 作为一项有价值的任务，与 PS 相关的非认知因素，以及 (2) PS 教学包括 PS 教学方法、PS 中的话语、PS 卡住状态时的干预、PS 评估和 PS 资源。然而，他们的知识也存在矛盾和局限性，对教师教育产生影响。这些适当和不适当知识的结合导致了一些与教学行为相关的冲突，并会限制学生对 PS 的学习。