A Challenge!
If asked, how would you define mathematics? Consider yourself asked. Would you define it differently if the question had been asked by one of your students, another mathematics teacher in your building, your administrator, one of your previous college mathematics professors, or a person at a party who discovered that you are a mathematics teacher? If you would define it differently given a different audience, why?
This question of defining mathematics concerns my mind for several reasons:
 Those who teach mathematics tend not to have a consistent definition
 A teacher's definition often seems inconsistent with how they teach mathematics in the classroom
 To talk of integrated mathematics seems redundant by most published definitions of mathematics
 Too many students (K16) either tend not to have very clear definitions of what mathematics is or tend to define mathematics in a negative context
 Definitions suggested by both students and teachers tend to focus on computations and the use of numbers, and
 A workable definition of mathematics seems to lie at the heart of the development of a common understanding of what it means to be mathematically empowered (as discussed in the NCTM Standards).
For some years now, I regularly ask my students at WWU to define mathematics. Sometimes, I let them develop a definition in small groups. Unfortunately, many express that this is the first time that they have thought about a definition, let alone face the fear of being asked to write down a definition so someone else can see it.
For example, the following are some defintions gathered from students preparing to teach mathematics:
 Mathematics is the study of all the different ways to calculate and figure using numbers and variables. Math was created by old men locked up by themselves many years ago.
 Mathematics is the art of using numbers to find an answer.
 Mathematics is a bunch of numbers, symbols, problems, equations, solutions: confusion to some, intrigue to others.
 Mathematics is what I have chosen to study, stress about, sigh about, cry about, laugh about, and teach. Mathematics is an everchanging discipline.
As an exercise, you need to ask your students to define the term mathematics. Be prepared for their responses, as the classroom mirror does not lie. In turn, would you be willing to share some of the special definitions you receive by sending them to me. I will try to publish a collected set later this year. Be sure to identify the level of the student (and the class if appropriate).
While you are at it, why not stop and write down a definition yourself or ask your administrators to offer their definitions or ask students to even ask their parent(s) for a definition. You might even compare the results with a dictionary definition.
Source: Vade Mecum for Mathematics Teachers, November 1992
