Affects are intuitively accepted as having a role in the key stages that determine success in problem-solving (PS) and problem-posing (PP). Two disjoint groups of prospective mathematics teachers with similar background and competences have been exposed to PS and PP activities, respectively, and they had to describe their affective states during these activities. The students’ reports have been analyzed from the perspective of epistemic affects, motivation, and self-efficacy. While in the PS context, several students expressed reluctance to report emotional feelings or frustrations over failing to find a solution for the given problems, in the PP context, a phenomenon of adaptation to one’s own cognitive possibilities appeared and the posed problems created a state of comfort/ enjoyment in students. PP conveyed a sense of autonomy and control to a greater extent than PS. It seems that intrinsic motivation is influenced by factors that are different in PP vs PS tasks, with an effect on perceived self-efficacy. The PP activity instilled a robust sense of coping efficacy, which made the students perceive their work as successful, to a large extent. In PS, the initially perceived self-efficacy triggered motivation to persevere with the solving, while in PP, the initial motivation generated by a novel task evolved into students’ perceptions of self-efficacy and confidence in one’s own capabilities. The conclusions of this study can help prospective teachers to use emotions in teaching for understanding, anticipating, and dealing with students’ ideas about mathematics and mathematical thinking and, finally, for improving students’ self-esteem and self-confidence, with an effect in more successful results.

中文翻译：

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动机和自我效能感如何在解决问题和提出问题中相互作用？

情感在决定问题解决 (PS) 和问题提出 (PP) 成功与否的关键阶段中被直觉地接受。具有相似背景和能力的两组不相交的未来数学教师分别接触了 PS 和 PP 活动，他们必须描述他们在这些活动中的情感状态。从认知影响、动机和自我效能感的角度对学生的报告进行了分析。在 PS 语境中，一些学生表示不愿意报告由于未能找到给定问题的解决方案而产生的情绪感受或沮丧，而在 PP 语境中，出现了一种适应自己认知可能性的现象，所提出的问题创造了一种状态学生的舒适/享受。与PS相比，PP在更大程度上传达了自主感和控制感。似乎内在动机受 PP 与 PS 任务中不同因素的影响，对感知自我效能有影响。PP活动灌输了强烈的应对效能感，使学生在很大程度上认为自己的工作是成功的。在 PS 中，最初感知到的自我效能感引发了坚持解决的动机，而在 PP 中，由一项新任务产生的初始动机演变为学生对自我效能感的感知和对自己能力的信心。本研究的结论可以帮助未来教师在教学中运用情感去理解、预测和处理学生对数学和数学思维的想法，最后，