The Utility of Dynamic Manipulation for Learning Mathematics in the Data-Rich Environment of Fathom Dynamic Data Software

Abstract

This paper explores the evolution of dynamic manipulation affordances as they emerged during the design, development, and deployment of Fathom, a computer learning environment for mathematics and statistics widely used in the United States at the secondary school and college levels. Dynamic manipulation is direct; you click and drag a data point in a scatter plot to change the coordinates of that point. Dynamic manipulation is continuous; while you are dragging a data point, everything that depends on the point¡¦s coordinates is updating. Dynamic manipulation environments are immersive; you are involved with the data and its representations, playing with and surrounded by it, with minimal intrusion from the technology.

In a data environment different kinds of dynamic manipulation takes place. Dragging data typically has as its purpose the determination of the effect that changing the data has on derivatives of the data such as graphical representations and computed quantities. Manipulation of parameters to a model may be for the purpose of making the model better fit the data or to explore the full family of models described by the parameter. Finally, dynamic manipulation of display objects such as real number axes serves to change aspects of the display to better suit the investigation in progress; e.g. to zoom in on a particular range of data to better see its structure or fit to a model

How does dynamic manipulation affect learning of mathematics? Conjectures drawn from observations of teachers and from software design trials are made and justified. Where possible, proposals for research are described.