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