Mathematics (specifically arithmetic) is possibly the most important form of communication that you will ever learn.
Math is a language all by itself.
It has a syntax (way in which information must be ordered), specific abstract symbols that have defined meanings, and when used appropriately it can communicate complex ideas and information. Math helps us to communicate value, cost, income, time, measurement, and many other areas critical to our everyday lives.
By learning math we learn how to communicate with others around us.
Understanding arithmetic can open a whole new world related to business, geometry, science and physics. Both time and money are only understood by having a basic knowledge of arithmetic. For example, if I wanted to explain to someone the concept of addition I could use physical (concrete) objects to do so, but if I wanted to make it a language I need to be able to explain it with symbols (abstract).
Therefore learning math is about being able to communicate to someone else without the use of concrete representations. Of course, the best way to help students understand that they have something to communicate is to show them concretely. Then ask them, "How could you communicate that without objects?"
This is when the language of mathematics comes to life. I encourage you to check out the MasterPieces and MasterFractions and see how you can help students move from concrete to abstract with understanding! Until next time...