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…

The goal of this article is to develop a new perspective on transfer of learning integrating cognition, emotion, and bodily experience. It is based on a case study with a 10-year-old girl as she explored the use of a motion detector, allowing for the simultaneous graphing of the position versus time of 2 moving points. The paper elaborates on the…

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…

This paper explores children's efforts to make sense of graphs by analyzing two students' use of a computer-based motion detector. The analysis focuses on the students' growing understanding of the motion detector which enables them to plan their movements in order to create graphs and interpret them in terms of kinesthetic actions. Students…

Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

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…

The broad goal of this report is to describe a form of knowing and a way of participating in mathematics learning that contribute to and further alternative views of transfer of learning. We selected an episode with an undergraduate student engaged in a number of different tasks involving a physical tool called "water wheel". The embodied…

Presents a case study of how one 11th-grader learned the meaning of the velocity sign. Her learning was not just an acknowledgment of a rule but also a broad questioning and revision of her thinking about graphs and motion. (16 references) (Author/MKR)

This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In…