Student
Visualization
Visualization
refers to the formation of stable and coherent mental pictures of abstract
constructions and processes, especially constructions encountered in mathematics
and the sciences, such as the notion of a Riemann integral, or the meaning
of angular momentum.
This ability to visualize new constructions and processes requires practice
and experience. The best students enter their courses with refined and exercised
habits of visualization, and these students usually progress smoothly and
quickly. But many students are forced to spend much of their time "discovering"
the right pictures. And with the accelerated pace of many introductory courses,
this often frustrates them the first time through. Computers as heuristic
tools can provide real support both for visualization and participation. The
role of interaction here is subtly different from that considered in the support
of participation.
Here, it is a matter of helping students who may not know what questions to
ask form meaningful ideas about key constructions and processes. This is often
accomplished through a rich variety of examples, simulations, and pictures
at many different levels, and by allowing the student to select and vary those
examples as need be to "see" the concepts they exemplify. The current Library
holdings represent a first approximation to this goal. The collection is not
intended to be a heterogeneous "database" of mathematical materials.
Examples of Visualization:
Marden's Theorem Every triangle has inscribes an ellipse that passes through its midpoints
Derivatives Derivatives of functions, implicit differentiation strategy explained