We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…

This study explored how a teaching experiment, which taught double counting with a constructive task assignment according to an ongoing assessment, helped students with mathematics difficulties develop their multiplicative reasoning skills. The participants were two fifth graders with math learning disabilities and one at risk. A micro-genetic…