This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

This article relates a case study on how a conversation with materials and diagrams -- the actual use of materials and diagrams to think, imagine, explain, collaborate, design and build -- featured a certain kind of interplay between material and digital components. The physical components present in this setting included a water wheel, which is a…

Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement the authors call "perceptuomotor integration." Just as expertise in playing a piano relies on the interanimation of finger movements and…

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the…