Today's lesson was great!
I don't mean my plans were great--I mean it was great the way it went. So "went" would have been a better verb, both because it's not as passive as "was" is... but it's easier to just keep typing and explain that, rather than go back and fix it.
As I was saying, it went great. I am totally set up now for tomorrow's lesson to be a complete and utter failure. I've been sensing that for a couple of hours now.
We're working with integers (those would be the whole numbers (0, 1, 2, 3, ...) and their opposites (0, -1, -2, -3, ...). (Yeah, I put 0 in their twice. It only shows up once on the actual list. Don't judge me.) We're coming up with algorithms for adding and subtracting them. We spent today nailing down algorithms for adding. We'll spend tomorrow and the next day nailing down algorithms for subtracting them, so I can then point out the very easy shortcut that means they won't need those algorithms most of the time.
Why find algorithms for subtraction when just about everyone on the planet will subsequently tell them, "Just add the opposite" for the rest of their lives? Two reasons.
First, I remember learning to perform the four basic operations with integers. I remember feeling there were algorithms that would work for subtraction, but I was forbidden to try to discover them--and I wasn't going to spend my own time doing it! However, I was a strange kid, and that's not the main reason I teach them.
The big reason is most kids (or at least the ones I teach most years) have no idea how to figure something out. I'm talking generally, not just with math. It's sometimes frightening how "Show me the answer" they are about most anything that isn't a video game (although cheat sites are popular with them, I'm sure, so maybe they're that way about video games, too).
I'm not saying this to rag on them. I'm saying there's a need. I seriously saw kids working and figuring things out today that I never would have thought would even be willing to try.
Maybe it's the manipulatives, maybe it's my love for the subject matter, or maybe it's just that I was in a wacky mood yesterday and today and cracked a lot of jokes. Maybe it's what I feel has been a good introduction to the concrete-representational-abstract process in this unit (a rocky start switching to representational yesterday, but I got my act together and today was so smooth it... deserves a metaphor here. Whatever, it went well.
Tomorrow, we work with manipulatives to figure out why subtracting a negative seven means the number we get is seven greater than where we started. It could go really well. It really could.
But I'm not getting my hopes up. Or I am hoping--hoping for the best.
But I'm going to have plenty of back-up plan... for the worst.