As elementary students begin to program using tangible blocks, they must coordinate their use of counting with the movements, directions, and numbers they use to move a character. In our study, we analyzed 13 first graders' first attempts at coordinating these elements when playing a programming game on the iPad that used tangible programming…

When to introduce negative integers to children is an important issue in school mathematics; delaying their introduction can lead to lasting misconceptions such as one cannot subtract a larger whole number from a smaller. Yet understanding negatives involves a complex extension of whole-number knowledge. It is not known whether this extension is…