From “learning to variate” to “variate for learning”: Teachers learning through collaborative, iterative context-based mathematical problem posing

Abstract

Problem posing (PP) has been found to contribute to teachers’ mathematical pedagogical knowledge. However, little is known about what and how teachers learn when engaged in continuous iterative PP. We use the variation theory of learning to conceptualize what and how teachers learn during iterative PP, illustrating these processes via a case study. The main argument is that what teachers learn from engaging in iterative PP are different task variables we refer to as “dimensions of possible variation.” Awareness of these dimensions allows teachers to skillfully generate new problems or re-formulate previously posed ones to achieve desired pedagogical goals. We show how, during a collaborative design process with the PD coordinator, a teacher-designer became aware of some new-to-her dimensions and developed corresponding techniques for diversifying tasks. These awarenesses were still evident in an interview six months after the end of the PD. Recommendations for teacher educators are suggested.