DeltaTick: Applying Calculus to the Real World through Behavioral
Simulation
For my dissertation, I am developing a
computational modeling environment, DeltaTick, that helps students connect the behavior
of real-world systems to the mathematical and symbolic ideas that are
traditionally used to explore them. Specifically, it does this by enabling
students to define the elements, features, and behaviors of a system of
interest, and then to execute those behaviors over time to examine the
mathematical patterns that result. I am currently actively developing DeltaTick.
For a theoretical background and motivation for the design of DeltaTick,
see:
Wilkerson-Jerde, M. H. & Wilensky, U. (2008). Complementarity in Equational
and Agent-Based Models: A Pedagogical Perspective. In
M. Jacobson (Org.), Complexity, Learning, and Research: Under the Microscope,
New Kinds of Microscopes, and Seeing Differently. AERA 2009, San Diego, CA,
April 13-17.
Connecting and Connections in Expert Mathematical Practice
The first major research project I started at Northwestern is an
in-depth study of expert mathematicians' reasoning when making sense of new
and unfamiliar mathematical ideas as presented in disciplinary tools
(namely, a mathematical proof). I use think-aloud protocols and network
representations to investigate what mathematical resources are utilized by
experts during the process of mathematical understanding to build a "densely
connected" knowledge around the idea presented.
A brief review of this work is:
Wilkerson, M. & Wilensky, U. (2008). How Do Mathematicians Learn Mathematics?
To appear in Proceedings of the Joint Meeting of PME 32 and PME-NA XXX,
July 17-21.
Visualization of Agent-Based Computational Models
With Abigail Jacobs, Pratim Sengupta, and Zack Moy, I am investigating the
role of visualization and space - and particularly the affordances and
constraints
of dimension and perspective - in learners' sensemaking around agent-based
models.
Sengupta, P., Wilkerson, M. & Wilensky, U. (2007). On the relationship between
spatial knowledge and learning electricity: Comparative case studies of students
using 2D and 3D emergent, computational learning environments. Paper presented
at the AERA 2007, Chicago, IL, April 9-13.
Ubiquitous Presenter (at UCSD)
Before I joined the Learning Sciences Program, I worked as the main developer/designer of
the Ubiquitous Presenter
Tablet PC application
with Beth Simon and William Griswold at the University of California, San
Diego. Ubiquitous Presenter is a web-based extension of the University of
Washington's Classroom Presenter application, and enables professors using
Classroom Presenter to share synchronously, store,
and receive live student feedback on slides that they annotate during classroom
lectures.
A brief background on Ubiquitous Presenter is available in:
Wilkerson, M., Griswold, W. G. & Simon, B. (2005). Ubiquitous presenter:
Increasing student access and control in a digital lecturing environment.
In SIGCSE '05: Proceedings of the 36th SIGCSE technical symposium
on Computer Science Education.
A complete list of papers and presentations is available in my CV or
here.