My professor asked my to check out this NPR link, <http://www.npr.org/2011/02/09/133601966/language-essential-for-understanding-large-numbers>
And then added, “Again and again we hear that mathematics is universal and language-free, but is this really true?”
Here is my response:
I teach the language of math. Within my lessons I also teach number sense. Last week I taught 3rd-5th graders the basics of the Trivium through poetry, which means that our logic, our words for the logic, and the way we put those word together are all separate events. The classic reference words for the three are logic, grammar, and rhetoric and they are distinct. That is an important notion because students need to realize that a number is as different from a digit as a mouse is from a picture of a mouse, and as different, again, as the mouse scampering across the floor (but not my floor). While E.A. Poe and A. Einstein may have processed their thoughts differently, being able to separate symbols from the objects they represent is profoundly important.
Matthew Peterson explains to us in a Ted video how he has been able to teach mathematics while circumventing words. I think that is great. Working with adult ESOL students, I recognize how I do not need to teach the students how to think. They have the notions organized in their heads. We are focusing on connecting English language. The language we teach must be about the concepts and relationships between concepts beyond their definition. Of course students must be able to demonstrate their understanding via language, but we do not want them to be talking about a picture of a mouse when they display a picture of a mouse. We want them to be referencing the actual scampering mouse.
I believe there is a trans-cultural language of math that we cannot do without, but meaningful language must be based on a logic that is real with or without the words, and I see no reason mathematical reasoning cannot come without words.
Here is the Ted link: <http://m.youtube.com/#/watch?v=7odhYT8yzUM&desktop_uri=%2Fwatch%3Fv%3D7odhYT8yzUM>