I'm introducing concepts of Algebra to my students. That is to say, if a student asked, "Mr.Rowinsky, what are we doing today in class?" I would likely answer, "Algebra."
We're playing with the idea of equations. Balance. Left Side. Right Side. Equal sign in the middle. Some great discussion about this new mathematical animal takes place in the classroom. It's a challenge. It sometimes involves working backwards. It sometimes involves taking tiles and trying to match it with an algebraic abstraction. But mostly it's just abstract. There are moments of "I don't get it" and moments of "Oh ya, that makes sense!" It's frustrating in so many ways to some students. Likely more ways than I can imagine, and definitely more ways than I can teach. But this is the challenge.
A certain student has no difficulty solving x - 7 = 18. They will even momentarily suspend the trivial nature of the equation1 and indulge in my suggestion that adding 7 to both sides might be helpful. x - 7 + 7 = 18 + 7 and yes, as you already knew x = 25.
However, when the question is flipped, 18 = x - 7, some interesting things happen.
"Do I have to subtract 7 because it's reversed.
"How do I do this, it's all backwards?"
"I subtracted 18 from both sides but it didn't work."
These are not the loudest voices in the class. Just a certain few. The few that I'm trying to highlight here because I believe I know why they are having difficulty with this equation. (Outside of the fact that
Students have been convinced to believe the this symbol "=" actually means, "Put answer here".
That is math to them. Find the answer! And if they don't know the answer, they are not good at math. Or, they can grab a calculator and that solves everything.
I am now collecting some like terms. Again, sometimes tiles are used. Some seemingly concrete ideas to explain the abstract. And, they are following and having fun with it.
If I ask, what is 3x + 2x, they say 5x.
How about 7a - 3a, they say 4a.
And b + 8b - b...tough one, but yes, 8b works.
But again, a certain student might step back a bit and then ask me, "But what's the answer?"
They are frustrated that there is no equal sign, and that they still don't know the value of x, or, a, or b?
"How is this helping me?" they'll ask.
They want an equal sign. And they want a blank space for an answer.
They don't want to simplify.
They don't want to evaluate.
They don't want to factor.
They don't want to represent this equation with tiles.
They want an equal sign and they want the answer!
And by they, I mean certain students. And that is my challenge.
Oh, I'm up for it, but it's challenging nonetheless.
I'd love to hear what works for you. Please share what you've seen, and what you've heard in your classes when you first introduce Algebra.
1. [This alone is a point to consider. A triumph in my eyes.]↩