When you are first introduced to math you think along the lines of the number line. The younger children think about the numbers and where they would fit on the number line. Also, using manipulatives to try and figure out number sense, which number is bigger than which.
The older you get the better understand you have of math. Next students start thinking about math as being addition and subtraction. Thinking about number sense and trying to figure out the addition and subtraction facts. Next, comes thinking about multiplication and division. Once you start thinking about these concepts you really start getting an understanding of mathematics.
Mathematics is a subject that consists so many other subjects, calculus, geometry, trigonometry, algebra, etc. Math is a very important subject because it is the foundation of so many other concepts and ideas. With mathematics you have to show your thinking and explain your reasoning and thinking. This is a great writing tool and many students learn by showing their thinking. As a teacher, you can see so much more in mathematics when the students show and explain their thinking. You can see when and where the students went wrong and you can figure out how to help the students get to the end result.
There are many different concepts and ideas that come to mind when I think about mathematics in general. Dealing with the number system is by far the most interesting. There is so much that you can do with them. for example, Multiplication, Addition, Subtraction, Division, We wouldn't have any type of mathematics without having these numbers.