In one of my earliest blogs (“Expressing Mathematically”), I introduced the idea that mathematical concepts and skills can be expressed in different ways. Our senses identify natural and artificial objects **{world model}** that convey math concepts. We use language to identify and communicate our understanding of the sensed math concept written and spoken ways **{language model}**. We also use geometric curves, shapes and volumes to represent these objects **{visual model}** in a 2D or 3D mathematical world. We can also plot our visual models on a coördinate plane or volume **{graphical model}** to generate numerical data about the geometry. Finally, we can express mathematical concepts and skills using symbols, numbers, variables and equations **{numerical model}**. Keep in mind that all these models are different aspects of what we generally refer to as **mathematics**. I will use these terms often throughout future blog to explore math concepts and skills through these unique perspectives.

## Expressing Mathematically – Part 2

**Tagged**equations, graphical model, graphs, language model, models, Numbers, numerical model, perspectives, variables, visual model, world model