I've been taking it pretty slow with them (2 days on combining like terms; two days on one-step equations) and was really worried about how bigger equations would go. I was shocked on Monday when they totally ROCKED two-steppers. All of the exit slips were in the green bin and aside from a couple of negatives, answers were correct. Today I gave them a quiz on one- and two-steps which I'm hoping will prove to be good scores.
After the quiz the kids picked up a sheet for their INB with other types of two-step equations. We'd really only done the ax + b = c type in class (or x/a + b = c) and I wanted to get them thinking about something like ax + bx = c (combining like terms first) and 1/2(x + a) = c (clearing out the fraction instead of distributing). I was walking around while the kids were working and saw that quite a few of them were getting the hang of it.
We still had 10 minutes or so left in class, so I grabbed a marker and headed to my whiteboards. I wrote up 5 or so problems (like the ones on the worksheet) and tossed out markers to kids who wanted to work them. Once they finished it I replaced their equation with another one, just a bit harder. Then another. Then another.
Here's what we ended up with:
Keep in mind, these kids have never seen equations like this before... and yet going from step to step was a natural progression for them. I didn't help a bit. We ran out of time for the equation on the very left side... the girl working on it took a picture so she can finish it up tomorrow just in case it gets erased. The smaller one squeezed in the middle is from a girl who moved here from Cambodia and speaks little English (although her language is improving drastically). She obviously took some sort of Algebra and knows how to solve equations, which I'm sure is making her adaption easier.
So I learned a lot today. I can't underestimate these kids and what they're capable of. I need to challenge them and keep them learning (btw, the kids at the board were LOVING this). But I also need to keep in mind the other kids not involved, whether they didn't want to work at the board or were still working at their desk on the worksheet or were embarrassed to say they didn't know how.
The task ahead of me is clear. Without making students feel dumb or inferior, I need to start differentiating assignments. I want to make sure that everyone gets the knowledge they need to succeed, but I also want to push the kids who are willing and able. Multiple assignments, here I come! Now I just have to find a good balance.
Just overheard some student teachers chatting outside my room. The girl who's with a math teacher across the hall said this:
"I've taken every single math class available at (insert school name here) but I came here and I don't know how to explain Geometry to them. I don't know how to *teach* proofs. I don't know to *teach*."
I know it takes time, but that's a little scary.