Development of teachers’ conceptions through learning and teaching: The meaning and potential of multiple-solution tasks

This study analyzes development of teachers’ mathematical and pedagogical conceptions in systematic (through learning) and craft (through teaching) modes and the relationships between them. We focus on teachers’ conceptions of the meaning and potential of multiple-solution connecting tasks in school mathematics. We found that in systematic mode teachers increase primarily their shared conceptions and that the development of mathematical conceptions precedes that of pedagogical conceptions. Only in craft mode do they develop new understandings while their mathematical and pedagogical conceptions become integrated and advance each other mutually.