Have you ever pondered that question?
Think about it... what is Math?
Is it formulas, rules, algorithms, computations, concepts, memorization, numbers...?
Recently I decided to so some digging and learn what it is that we do when we are studying math. Here is what I have learned.
Math is the study of:
1. Numbers - 0, 1, 2, 3... these are representative symbols of the next part.
2. Values - this is the quantity, the amount of things, such as five apples. The quantity is different than the number, even though they both go together. I have found this to be a rather significant concept for students to grasp.
3. Shapes - each of the values are represented by shapes. These shapes can be geometrical or non-geometrical.
4. Space - each shape takes up a specific amount of space. This space may be physical or abstract, but in early mathematics it is generally very physical.
5. Interrelationships - now are aware of those four things then we need to look at how do they all interrelate? How do we combine, compare, or contrast these things together?
6. Specialized Notations - these are the specialized symbos (+, -, /, x, =, etc...) that are specific to mathematics only. We need these in order to communicate clearly the interrelationships.
That is what I have found to be the study of math. Now once we realize what those things are, then we can look at computation, concepts, application, memorization as it relates to mastering mathematics.
I encourage you to think about this yourself. Consider sharing it with your students and engage them at a deeper level of conversation.