Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical tasks available to teachers. Additionally, we encourage teachers to pose OTs by transforming textbook mathematical problems. In this paper, we analyze teachers’ skills and affective conceptions related to posing OTs and using them in teaching. Forty-four teachers with different teaching experience (years of experience—YoE) and different levels of expertise participated in a 4-h workshop that introduced them to OTs and their categorization. They were also given a homework assignment: pose OTs and solve them to demonstrate their openness. This assignment was accompanied by a 5-point Likert scale questionnaire that examined teachers’ affective conceptions about engaging and teaching with OTs. We drew distinctions between different types of OTs (TOTs) posed by the teachers and the problem posing strategies they used. We found that the types of tasks and strategies that teachers use are a function of teachers’ experience in terms of both the level of mathematics taught and years of teaching. In the affective dimension, we found interesting connections between conceptions regarding the difficulty of posing OTs, conceptions regarding the suitability of OTs for teaching and learning, teachers’ readiness to implement OTs in their classes, and their predictions regarding teachers’ and students’ problem-solving behaviors.

中文翻译：

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提出开放数学任务的开放数学问题：教师做什么和感受什么？

教育文献表明，解决开放式数学任务 (OT) 是一项强大的以创造力为导向的活动。然而，在学校学生每天使用这些任务是极其有限的。为推动中学 OT 的实施，我们管理了一个大型研发项目 Math-Key，该项目为教师提供开放的数学任务。此外，我们鼓励教师通过转换教科书数学问题来提出 OT。在本文中，我们分析了教师在摆出 OTs 并在教学中使用它们的技能和情感概念。44 名具有不同教学经验（多年经验——YoE）和不同专业水平的教师参加了一个 4 小时的研讨会，向他们介绍了 OT 及其分类。他们还被分配了家庭作业：提出 OT 并解决它们以证明它们的开放性。该作业还附有 5 点李克特量表问卷，该问卷调查了教师对 OT 参与和教学的情感概念。我们区分了教师提出的不同类型的 OT (TOT) 和他们使用的问题提出策略。我们发现，教师使用的任务类型和策略是教师在数学教学水平和教学年限方面经验的函数。在情感维度上，我们发现了关于提出 OT 的难度的概念、关于 OT 对教学和学习的适用性的概念、教师在课堂中实施 OT 的准备情况以及他们对教师和学生问题的预测之间的有趣联系——解决行为。