# The TILE System

** Instructional Design Paradigm**

**Technology:** Hilbert *Mathematica* is a custom online version of *Mathematica* for student exploration, experimentation, and visualization (no downloads required).

**Content:** Base content written by Jerry Uhl, Bill Davis, and Horacia Porta written in *Mathematica* Notebooks and translated into Hilbert.

**Course Management:** The Learning Content Management System is simple, seamless, and specifically tailored to work with Hilbert *Mathematica*.

The TILE instructional design elements are tightly integrated, and each piece is designed to work in tandem to create a learning and teaching environment that gives students and instructors buildable models to explore and discuss. It is built to maximize students’ germane cognitive loads which consists of understanding mathematical models from the ground up, while at the same time reduces extraneous cognitive loads related to the minutiae of technology management as well as the initial burdens, barriers and restrictions of performing hand calculations before they even understand what they are actually calculating. This gives students the chance to learn mathematics inductively the way it was initially learned by the inventors of the mathematical models. Building mathematical models and understanding inductively gives students a scaffold in which to understand the deductive arguments of proof (which is how most mathematicians actually explore mathematics themselves).