Here is a conversation I had with my 2 year old recently:
2: “I really want a car of my own when I’m a little bit bigger.”
Me: Why do you want a car?
2: “I want to drive in the back seat.”
Me: In the back seat? Why do you want to drive in the back and not the front?
2: “I want to be just like you and dad, mom.”
My confusion was was cleared up when I realized that she is in a rear facing car seat, so to her I am in the back and she is in the front. I bring this up because I think it has a lot to do with why I love having mathematical discussions in class as well as really push students to justify any written work that is turned in. My first assumption when my daughter told me she wanted to drive in the back was different than what she actually meant. Its a matter of perspective.
Many of my students know a lot more of the math than they are able to communicate in accepted mathematical language. The discussions allow me to figure out if there is a concept gap, a language gap, or some other kind of gap. Of course in order to succeed in math, a standard vocabulary and frame of reference might be needed, but why we choose to write and do math the way we do is not obvious to all students.One of my main goals for this year has been around helping students figure out how to express the math they do know, even when they think they don’t know anything. The key to doing that is to figure out what they actually mean and then help them frame that in mathematically accepted language.
I feel like I’ve had a lot of success with the discussion side of this piece. Students are talking about math in much deeper ways than they started with. I’ve also seen them make connections with the material in problems leading to more correct answers. I still need to figure out how to make the spoken word to written word jump smoother. The amount of times they ask me to repeat back what they said so they can write it is astounding. But, we are getting there. Writing about and discussing math is vital. I hope my students come out of class knowing that math is not an answer on a piece of paper.