The purpose of this study was to explore how prospective teachers’ (PTs’) conceptions of various mathematical topics develop.Consistent with prior findings, this study showed that PTs entered with limited conceptions. This study showed further that
(a) well-designed tasks (addressing the PTs’ incoming conceptions as well as focusing on the desired conceptions) can help PTs develop content knowledge,
(b) conceptual difficulties may persist even with well-designed tasks, and
(c) artifacts of children’s mathematical thinking can be used to develop mathematical content knowledge.