What does it mean to "Do Mathematics?"

Doing mathematics means that you are involved in the science of pattern and order (pg 13).  You are always exploring different ways to solve math problems.  You have to look at multiple angles of the problem to see if it is the correct way to solve it.  The old way of doing mathematics is “listen, copy, memorize, and drill” (pg14).  This is one way to do mathematics however the new way is more efficient and helps you learn why you get an answer not just, this is the formula, solve the problem.  The new way to do math is to have the students think of the problems and formulas and start from the beginning.  When you are doing this the students actually remember the process more and understands why something is the way it is.  This is doing mathematics because you are looking at the science of pattern and order.