Books & Chapters

Conference Papers

General Area

There are many expanding areas in human computer interactions that push the boundaries of the relationships between people and software. The promise of better understanding data through interactive presentations drives many researchers to study information visualization, representation, and interaction. One direction is to utilize people's tacit understanding of space to aid in their understanding other domains. In geometry, there was much initial interest in exploiting visualization to aid in research (for instance at The Geometry Center). Although there is still interest in this direction, more energy has recently been spent exploring the educational, or introductory, benefits of visualization and interaction in geometry.

Specific Area

My interests have to do with investigating interactive spatial representations of abstract knowledge for use with introductory learning tools. Complex relationships can be suggested among visual components in the spatial domain as noted in Tufte's books about illustrations. With the dimension of interaction, the spatial properties of visuals can encode subtle causal relationships as demonstrated in many of the examples that are considered part of the dynamic geometry movement.

Research Summary

My work has focused on tools for exploring and understanding patterns. These patterns are spatially represented and encoded in geometric structures such as tilings, polyhedra, lattices (also referred to as nets), and polytopes. Although geometry is the context, the focus is on the patterns and their regularity. The spatial regularity of the structures lends itself to algorithmic descriptions that can be represented computationally with automata and Turing machines. The interfaces for the tools integrate the multiple representations with the goal of introducing the abstract complexities associated with the structures. A number of interactions that I designed for specific structures were extended to general exploration techniques. Two of the more notable techniques are stacking-unstacking (a continuous technique for exploring spatial regularities in structures) and focus+scoping (a technique for locally exploring complex structure). Generally, these interactive techniques and the representations incorporated in the tools provide a rich platform from which many user studies have and will be performed to help understand the importance of elements and designs for visually rich investigation tools.

Courses

I believe teaching a course is a complex task that admits many successful strategies. A strategy's level of success will depend on the particular situation and environment in which it is employed. This dependence, if not carefully considered, can make concrete discussions comparing teaching styles seem perplexing and contradictory. Ultimately, I believe that learning is a function of time spent engaged with course material, which means that successful teaching strategies somehow capture students' interest and encourage them to focus their attention on essential course material. In courses I have taught, I have focused on two aspects: motivation and skills. To help students connect with a topic, I try to demonstrate a strong motivation for learning it, which often communicates central perspectives of the discipline. To help students focus their efforts, I try to highlight and label important skills that can act as a concise means of viewing the courses in terms of concrete, achievable milestones. A focus on these aspects has helped me employ different approaches to course material; a focus on motivation helps a top-down approach, and a focus on skills helps a bottom-up approach. A top-down approach tends to present the course as a transformative experience that offers the potential to change the student's perspective. A bottom-up approach tends to present the course as an information package that contains many skills to be acquired. I believe that balancing these approaches is useful in helping students achieve a deep and detailed understanding of the course.

Assignments

Computer science seems to offer a perfect context for exploring complex, abstract concepts in a concrete manner. Often, abstractions are required to study and understand concrete computer examples. I see assignments as an excellent way for students to gain experience with course skills and have opportunities for directed reflection on subtleties of the material. It is a challenging task to construct well balanced assignments that provide basic experience, yet encourage and promote sophisticated and course related thoughts. When I construct assignments, my goal is to provide strong motivation while covering the required skills. I try to impress upon my students the importance of assignments with Confucius' quote, ''I hear I forget, I see I remember, I do I understand''.

Lectures

My on-going interest in teaching parallels my research interest of constructing and studying computer learning environments as well as my personal interest in performing. As a designer of learning environments, I try to conceptually streamline tools so users do not become distracted or confused by details that may not contribute to my goals for the tool. This streamlining can sometimes mean sacrificing pet interests that are not essential. My past years as an improv actor in dinner theatre, I have been honing my on-the-fly presentation skills to listen to and steer my audiences so that their interactions and interjections enhance and become part of a coherent play. I believe that both of these interests contribute to the way I view teaching as a carefully pruned activity, as well as, a flexible and inclusive activity.