I got to teach math to the "advanced" math group on Tuesday and they did great - they were so into it and we got to do much more advanced stuff than we'd have been able to do with the whole class. It seemed like they were excited about being "out in the hall with Ms. Gallagher" for once - I usually take the low-performing kids out with me to work one on one and this was the first time I'd taken out these guys. We worked on complex word problems involving time zones and travel times to various countries, stopping through other countries, and cost of travel for a group of travellers flying first class vs economy etc. There was a lot of "find the unknown" and they really had to reason it out together. In my Penn math class we've been talking so much about how important TALK is in math for kids, that they need to explain their own reasoning and listen to eachother's reasoning and I really believe that. They disagreed or agreed with eachother and talked it out and explained why and then listened to each other and adjusted their own reasoning. It was great to see the stuff we've been learning in action, and I feel like everyone got a lot out of the collaboration.
Today, however, I did math with our low-performing kids, and it was really a challenge. Eth in particular had a very tough day. I had a hard time keeping him on task in math, and an even harder time in our guided reading group later in the day. Today's lesson was about true and false number sentences, and we played a game where they were in teams and had to decide whether the number sentence was true or false and hold up a T or an F or a ? (if it wasn't possible to say one or the other). I gave a point to the first team with the correct answer. They did well with this - with team involvement - everyone participated. But I'm not sure that it really fits with the way that I think math should be taught. I don't want it to be a competition like that. I want them to explain WHY - not just give the right answer. I want to talk it out and to make sure that everyone understands. They did pretty well on the problems that they did on their own after we worked the concepts out together, so maybe they did understand it, but I didn't really walk away from the lesson feeling good on it.
I also tried to teach them that if you do something (like add 8) to each side of a true equation, its still true, and that this is a good way to figure out complicated problems if you see that there's something the same about them on both sides. This was WAY over their heads. They kind of got it, but when I tried giving them problems with the same thing on both sides, they all worked the problem all the way out rather than cancelling out the "same" things on both sides like we'd talked about. Maybe they just didn't recognize they are there? This is part of the Everyday Math curriculum, and it will help them a LOT in algebra if they start thinking about equations and number sentences like this now. We will have to work on it again next time.
I would like to do some more of this "if you do the same thing to both sides of a true number sentence, then those two things cancel each other out and the sentence is still true" with my advanced math friends. I think that I could do somewhat of a constructivist lesson with them, so they can figure out why it always works and why it's important and can make things easier for them when they're working on true and false number sentences.
I'm going to teach another lesson next week to a small group about the use of parenthesis and order of operations. I'm trying to think of ways to make it interesting, exciting, and meaningful, but it seems that my teaching tactics need to be determined by my audience, and I'm not sure who will be in my group.
