Motivators or conceptual foundation? Investigating the development of teachers’ conceptions of contextual problems

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.