Developing prospective teachers’ conceptions with well-designed tasks: explaining successes and analyzing conceptual difficulties

Several researchers have documented prospective teachers’ (PTs’) conceptions of various mathematical topics. However, less is known about how PTs’ conceptions develop. To address this gap, I designed two tasks with the goals of addressing the PTs’ initial conceptions of multidigit whole numbers and helping them develop more sophisticated ones. I examined how PTs’ conceptions changed while working on these tasks in two settings (a teaching experiment with 6 PTs and a mathematics methods course with 33 PTs) and modified the tasks on the basis of the results. 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. Instructional implications are discussed. © 2014, Springer Science+Business Media Dordrecht.