## Mathematics Reasoning Visualizations

King's Centre for Visualization in Science (KCVS) is the outreach arm of CRYSTAL Alberta that creates and distributes the visualization prototypes that promote scientific and mathematics reasoning and deep understanding. Central to the work being done in CRYSTAL Alberta is modeling--mathematical modeling.

Quoting the KCVS website: "How do we use mathematics to enhance our understanding of the natural world or to make predictions about possible events? Mathematical modeling is ubiquitous in science. One of the projects of the King's Center for Visualization in Science is to shows students how mathematical models can be used to furnish useful insights into important problems. In some cases these models are done by and with colleagues at other institutions."

"A model is a simplified representation of reality. Maps, for example, are visual models of places. Similarly, equations can be mathematical models of processes. Different kinds of maps serve different purposes: road maps are useful for one kind of travel; topographic maps are useful for another. Different kinds of equations also serve different purposes. For example, a decreasing exponential function can be used to model radioactive decay, while an increasing exponential function can be used to model the initial stages of bacterial growth.

All models, whether they are visual or mathematical, leave out considerable detail. A model, by definition, does not completely mirror reality – if it did, it would be reality, not a model. For a model to be useful, it must leave out unimportant detail but keep important detail. The decision about what is important depends on the goal of the model.

In some cases, building a mathematical model can be as simple as fitting a curve – an equation – to available evidence. In more complex instances, a mathematical model may consist of multiple equations that are linked together to represent a series of connected processes. Our West Nile virus model is a system of six connected equations."