Indeed, if there's one huge difference between industry and academia, it has always been the high value that industry has placed on teamwork. Today, more than ever, he basic manpower unit is the team.

It can take ten years or more for new ideas in science to be incorporated into the curriculum of schools. Given the rapid advances in science, new ways must be found to link researchers, educators, and learners.

As pointed out in the NSF workshop report, "Computational Science and Education: Workshop on the Role of HPCC Centers in Education," the focal point of change is the teacher. This proposal seeks support from NSF for a successful undergraduate faculty enhancement program whose goal is the development of a regional base of professors who can incorporate models and the accompanying computational tools, techniques, and technologies into their teaching. We have designed a coordinated education program that offers undergraduate faculty in science, mathematics, engineering, and education the opportunity to learn how to use and how to teach with models, and in particular their numerical implementation and solution, leading to understanding the fundamental role that computation now plays in modern science and engineering. Our goal is quite simply to enable twentieth-century science, mathematics, and engineering to be taught with twentieth-century methods before the end of the twentieth century.

We believe in models. Models shape our beliefs. This proposal describes some of the many models that we have used to explain what we do and why and how we do it. The very acronym we have chosen for this project, SCSI, is itself a model of how we see this project: in the same way that a SCSI connector allows a wide variety of interchangeable devices to be used by a variety of computers, we see the workshops, materials, and models developed and disseminated by this project to be interchangeable, and used in a variety ways by a variety of undergraduate
faculty.

The "launch ramp," or learning curve for numerical modeling, as pictured here, is
a model to help visualize our workshop design. We may start with a qualitative "hand-waving"
model for which the visualization is the model where simple theory and experimental data give rough insight into behavior: imagine your thumb being a female gnat and the other four fingers being the male gnats, then your hand with all the fingers wiggling is a good qualitative model of a small swarm. This insight may be refined by formulating the theory as mathematical models and then solving these models with a range of increasingly sophisticated tools, matching the Tools to the complexity of the problem. The progression to more quantitative models begins with running other people's models, then modifying these models, and ultimately creating new models, tuning the numerical solutions and visualizations along the way. Just as Sisyphus ended up rolling back down as he tried to push a rock up a mountain, we may find ourselves repeatedly coming back to reformulate the model mathematically, or to rethink the model at the hand-waving level, just to get a handle on what we are doing.

Our vertical scale in this model of computational science education indicates the degree of difficulty and the amount of computing usually associated with a numerical model that is expected to be more quantitative than qualitative. What affects the slope of the learning curve, moving from qualitative to quantitative modeling? The degree to which faculty have significant access to curriculum materials, the degree to which faculty understand interdisciplinary team skills, and their personal level of comfort with modeling and technology all play a role in their willingness and ability to integrate reform into the classroom. The Shodor Computational Science Institute is designed to facilitate this kind of models-based reform in mathematics and science classrooms at all levels, while constantly repeating the challenging question: how do we
know if it is right?

We see the use of models as supporting a sea change in undergraduate education, especially at liberal arts institutions: we need to address the apparent inability of our students to employ evidence based reasoning. Our students, and society at large, are unable to interpret data or fact patterns and convert them into information, or to compare sources of information in the formation of knowledge and understanding, or to assess the value of knowledge in the search for truth. The use of models returns the activity of science education to careful observation, observations that are accurately recorded and honestly reported.