## Expressing Mathematically – Part 2

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.

## Parts of a Circle

A circle is a  two-dimensional geometric object whose points are all the same distance from the center. The circle has  four basic components.  We will begin by identifying the components of a circle visually and verbally.  The words are labels used to name the components depicted in red and are used to translate the geometric illustrations into verbal descriptions.  Different words would be used if your native language is not English.Mathematical equations express relationships.  There are mathematical equations that define the relationships between these components of a circle in various ways.  These equations are used to find the lengths of the circumference, radius, and diameter of a circle as well as its area.   We’ll look into these relationships beginning in the next blog.

Do you know of any other math terms that describe some part of a circle?

## Expressing Mathematically

In many ways, mathematics is a language with its own alphabet, words, grammar and syntax.  Mathematics expresses itself in multiple ways. Lets see how.In my home office, I have a coaster illustrating a Siamese cat (A).  I can specify the shape of this coaster verbally, using the proper word (B).  A different word would come to your mind if your native language is not English.  I can also specify the shape of the coaster visually, by drawing a circle of the given radius (C).  By envisioning such a circle on a 2-dimensional coördinate system (D), I can identify specific points on the edge of the coaster numerically (via ordered pairs of numbers).  Finally, I can specify the shape of the coaster in the form of an equation (E).

In math, we must translate a given scenario into one of these translation so that we can successfully generate the requested solution.  We will explore how we specifically do this in future blogs.  This is a source of frustration for math students who have not yet mastered these fundamental, and often overlooked, skills.  It can impede their progress to understanding more complex mathematical concepts.

Do you believe that there are forms of expressing math that does not fall under one of the five categories shown above?