Teachers are encouraged to connect mathematic instruction to the real-world by posing tasks that are situated in rich, relevant contexts, but research has found that many teachers integrate contextual problems (CPs) as motivators rather than as supports for conceptual development. To provide insight into how teachers’ conceptions about CPs shift as they teach through contextual problem solving, we interviewed six teachers before and after they taught from a unit designed from principles of realistic mathematics education, an instructional design theory which positions realistic contexts as learning supports. Our findings indicate that teachers initially viewed CPs primarily as affective or motivating enhancements, but after teaching the RME unit with university-based support, the teachers articulated integrated understandings of how CPs can function as supports for conceptual development. The teachers articulated how CPs provide initial access, sites for progressive representational formalization, and references to which students can fall back in order to interpret subsequent tasks. The authors identify connections between these ideas and the support provided by the university team and the teachers’ guides.

鼓励教师将数学教学与现实世界联系起来，将任务置于丰富、相关的背景中，但研究发现，许多教师将背景问题 (CP) 整合为激励因素，而不是概念发展的支持。为了深入了解教师在通过情境问题解决教学时对 CP 的概念如何转变，我们采访了六位教师，他们在一个根据现实数学教育原则设计的单元教学前后，将现实情境定位为学习支持的教学设计理论. 我们的研究结果表明，教师最初将 CP 主要视为情感或激励增强，但在基于大学的支持教授 RME 单元之后，教师们对 CP 如何作为概念发展的支持者进行了综合理解。教师阐明了 CP 如何提供初始访问、渐进式表征形式化的站点以及学生可以回退以解释后续任务的参考。作者确定了这些想法与大学团队和教师指南提供的支持之间的联系。