Problem solving is a key priority in school mathematics. Central to the valuable role played by problem solving is the quality of the problems posed. While we recognize the features of good problems and how to support learners in solving problems, less is known about the ways in which prospective teachers’ (PTs) conceptions of what constitutes a ‘good’ problem develop within the confines of an Initial Teacher Education program. This study explored the effect of engagement in a mathematics education course on the problem-posing skills of 415 prospective primary teachers. A 3-week instructional unit consisting of a series of lectures and tutorials on problem solving and problem posing was implemented. A questionnaire examining participants’ understandings of and ability to pose problems was administered prior to and following instruction. Results reveal that participation brought improvements in conceptions of what constituted a good problem and in the ability to pose good problems (targeted at grades 1–4). Initial problems generally were arithmetic, required one step to solve and had only one correct solution. Following the instructional unit, attention was paid to designing problems that had the potential of multiple strategy use, multiple possible correct solutions, multiple modes of representation and the incorporation of extraneous information. Despite these improvements, the complexities of problem posing and the challenges that persist for PTs in posing good problems are evidenced. Recommendations are made for the enhancement of problem-posing experiences, most notably developing skills in identifying mathematically worthwhile problems from a selection of problems or in reformulating given problems to make them better, that support PTs in developing the knowledge and understandings required to pose mathematically worthwhile problems.

中文翻译：

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提出数学上有价值的问题：发展准教师的提出问题的技能

解决问题是学校数学的重点。解决问题所发挥的宝贵作用的核心是所提出问题的质量。虽然我们认识到好的问题的特征以及如何支持学习者解决问题，但对于在初始教师教育计划范围内如何构成“好”问题的准教师（PT）概念的认识却鲜为人知。这项研究探讨了参加数学教育课程对415名准小学教师提出问题的能力的影响。实施了一个为期3周的教学单元，其中包括一系列有关解决问题和摆姿势的讲座和教程。在指导之前和之后，都会进行问卷调查，以检查参与者对问题的理解和能力。结果表明，参与带来了对构成好问题的概念和提出好问题的能力的改善（针对1-4年级）。最初的问题通常是算术问题，需要一步解决，只有一个正确的解决方案。在指导单元之后，注意力集中在设计可能会采用多种策略，多种可能的正确解决方案，多种表示方式以及并入无关信息的问题上。尽管取得了这些改进，但事实证明，提出问题的复杂性以及PT在提出好的问题方面仍然面临的挑战。提出了改善问题提出经验的建议，