Algebraic thinking came to me about 6th maybe 7th grade. I'm not sure if I was exposed to it earlier with anything other than an unknown variable a la 42 + ____= 63. It certainly didn't look like: 4x + 2= 3x + 9 in third grade. This is what our students get to work on with Ms. G who comes in once a week for Hands On Equations. I'm seeing and hearing mathematical thinking and organization that I hadn't seen in other units of study. Even if my students can't write a complete sentence because they are learning English, their creative thinking and expression comes out in this class. They are becoming the experts and sharing various ways to isolate x (they don't call it that). They are realizing instead of writing x + x + x + x (4x) they can chunk by using doubles (2x + 2x) or go all they way and multiply! They are building flexibilty in their thinking without even knowing it.
I hope they are building a love for math and mathematical thinking. Some things heard today: "When you take away the pawns from both sides it's like working with a mirror, you have to do the moves equally." "I can check to see if my 'x' is correct lots of ways. I can count each one; I can skip count them, I can multiply them." "I can try lots of numbers for the pawn but I make sure the sides are balanced and equal."
They work hard to line up and match the teacher version of the balance. I think this kind of matching may even help them when tracking on a standardized test. A lot went on in 30 minutes today!
