Mathematics is a language all its own, right? So why aren't we teaching it as such? You know summertime; it's the time we teachers spend in workshops soaking in the theoretical views of the 'experienced'. I actually really enjoy workshops, specifically when I'm at that table that just explodes with ideas!
Back to the THEORY: If math is a unique language, then I should be teaching students to listen, write, read, and speak its language.
I realize that I spend so much time focusing on one component-writing the math. I need to teach fluency in math that focuses on all four of these areas.
I have observed several foreign language teachers come and go. The great teachers have their students fluent in these four areas. Students read, write, listen, and speak the language.
As I think back to high school, I was an excellent memorizer. I didn't really know how to read the notation or why solutions were written a specific way, but I could tell you what I needed to put where based on context clues. Then when I got to college, I had one of those professors. He spoke, read, wrote, and listened for the language of mathematics. He expected the same from us. I struggled like you wouldn't believe; however, after I graduated and entered the world of education for mathematics, I noticed the difference in my math language and others. Now, I am not an expert or near perfect, but I notice that my students have a higher level of math skills because I hold myself to high standards when using the language of mathematics.
GOAL: Even though I can read, write, listen, and speak the language of mathematics, I need to expect that from my students.
CONCLUSION: This is all just a theory based on self reflection and observation. We'll see how it unfolds over this next year.