Group learning: using students to help each other

Twice this past week, I had students break into small groups to work through problems. This strategy worked very well, and I plan to use it periodically in the future.
On Tuesday, we had a class period devoted to reviewing for the upcoming test. The previous week, I'd also taught a review, and it seemed like a drag for both me and the students. Part of this was the fact that the review was scheduled for 2 periods, but I think the bigger problem was that I was just having students work on problems one at a time and then take turns showing them on the board. My students love board work, but doing problem after problem for 90 minutes, especially when none of the material was new, got boring. So, for this week's review, I broke the class into small groups (strategically mixing up ability levels and behavior types) to work on the problems. Even though it meant that there was a little more chatter than there otherwise would have been, I think the group work was a great idea. All the groups were being productive, and the students stayed more engaged than they would have if I had just done the board routine. Another cool thing about having students work in groups is that I was able to get the chatty students to focus just by my physical presence in a way that doesn't seem to work as well in lecture. I moved between groups pretty frequenty, and if I just looked over or stood next to a group that I noticed was getting off topic, they often noticed and kept working. This was a particularly important discovery for me, since I've admittedly been having a hard time calling out kids who talk about non-math topics (side note: I still need to get tougher about that; group work isn't an escape hatch).
Today, I broke students into groups again. It didn't go quite as well; students were singing and keeping beats, and I didn't crack down on them hard enough. Nevertheless, I think today's group work was still beneficial. Last period yesterday, I had covered a topic that students were struggling with (graphing 2-variable inequalities), and I was given 2 periods today to cover a topic that I thought could be addressed in just one lesson, so my second-years gave me the OK to take first period to do some more work on graphing 2-variable inequalities. I had the students do some graphing warm-up problems, then went through a 2-variable inequality problem with them, and then broke them into groups. To me, the coolest thing that came out of it was seeing how students were able to help each other. One girl was struggling, and no matter how I tried to explain it to her, didn't seem to get it. Another girl in her group gave her lots of help, and she seemed to be understanding more by the end of the lesson. Side note: a really cool thing happened with the same student during second period. I asked her if she could try a problem on the board, and she said she didn't think she could do it, and I said, "I'll help you do it on the board. We'll work on it together." She immediately perked up and said, "OK!" She went to the board, did the problem out, and got it right! And pretty much all I did was stand there and tell her she was on the right track once or twice when she asked me. All she needed was to feel like she wasn't completely on her own. Neat.
The next time I do groupwork, I'm going to lay out some rules before I divide the students up. Talk to only the other students in your group, and talk only about math. Stay in your seat unless Ms. Long Skirt Blue Jacket gives you permission to get up. I'm also considering have students later hand in the problems they did during group work just to make sure everyone stays on task.

Summer School, day 5

Today was my 5th day of teaching at Holly Springs Summer School, and I felt good enough about the day to compel me to write a blog about it.
Last Monday (a week ago), I showed up at summer school having just flown in the night before and observed my classroom. I hopped right into teaching the next day. After most of my lessons last week, I walked away feeling that the lesson had gone decently well, but would have one thing that I should have done a better job of; this could take the form of a moment when I didn't adequately alleviate student confusion, or, most commonly, a time when I didn't manage the class as well as I should have. Despite these mistakes, I felt generally positive at the end of every day about how things had gone. I also felt that I was making amends to my mistakes in the next lessons. Also, I enjoyed myself a lot, and am feeling better with regard to the self-doubts I had about becoming a teacher.
Today was a great teaching day for me. I felt like I finally integrated all of the things I learned from my errors last week into one lesson that just went smoothly. I was teaching a concept that I was concerned would be confusing to my students; as I learned last week, some of the topics that I thought were straightforward presented formidable challenges to many of my students. Today felt like a really good balance of breaking concepts down into a form that students could understand while at the same time successfully challenging some of my students to reach the next level of understanding.
This day could have shaped up to be a disaster. I was teaching 4th period, but due to a mistake I made in interpreting the class syllabus that hadn't printed correctly, I wrote a lesson plan for the wrong thing. Whoops. As I realized after getting to school, the lesson that I had written for 4th period was just another component of the 3rd period lesson that my co-teacher was teaching. No wonder it seemed like not much material! I told him about the problem and gave him the work that I'd done so that he could integrate it into his own lesson, which he did seemlessly. To complicate matters further, the school computers were effectively not working today. So, I had to sit down for one period while I wasn't teaching and scribble out a new lesson plan for 4th period. And I did it! I was able to organize my teaching, come up with relevant examples, write up a homework assignment, and make some overhead transparencies in a short period of time. This is very comforting to me; I'm progressing in how quickly I can write lesson plans without sacrificing the quality of my lessons, which will be an important skill once the real school year starts.
Something that my mentor teacher and I discussed last week was the importance of being positive. It's amazing how much of a difference positive comments make in student excitement levels; this effect can come from something as small as saying, "Great job, you almost have it. Who can tell me how to change this answer a little bit?" and saying, "Well, that's not quite the answer. Who can tell me how to fix it?" I did a good job today with encouragement; I continually reminded my class that we were doing difficult work and that they were doing really well with it.
Something I struggled with last week was the balance of having students do work on the board, demonstrating for students how to solve a problem, and having students answer questions for me while I worked a problem out on the board. It's not a good thing if I spend too much time in front of the board because no one wants to listen to a teacher just lecturing at them, but on the other hand, having too much board work leads to disruption. Every time a student gets out of her (or his, in the case of my single male student) seat to go to the board, she takes some time to get her notes together, and even though I try to have students explain what they're doing as they write, they inevitably end up writing for a while before they talk to the class. This can create too much down time, and other students will start talking about non math-related topics. One thing that I'm working on, and practiced to some extent today, is picking a student to go up while others are still working on the problem. Today, I felt that I had a good balance between me showing things on the board and students showing things on the board. I think that striking this balance had a lot to do with why classroom management also went well for me today. I'm getting better about time management, and was able to close the lesson with a couple of minutes to spare; I struggled with this a lot last week.
I can say a lot of positive things about how today went, but I think that the part of the lesson that makes me happiest at the end of the day was watching one of my students, Frannie (*this name, like all the other names of students and teachers in this blog, is a pseudonym) master a difficult concept. I introduced a concept toward the end of my lesson that I had been on the fence about including at all, since it was more complicated than the other work we'd done that day. I broke the problem into smaller steps and had the students help me with each step. I wouldn't say that all of them followed 100%, which is OK since it was meant as a challenge anyway, but Frannie did a great job of telling me what to do at each step even when the rest of the class was stumped. Frannie is not normally one of the quicker students in my class, so seeing how well she did today made me especially happy. During "lunch period," (when the students generally do homework for the 25 minutes before lunch), I called Frannie over to the desk and gave her a piece of candy, telling her how well she did today, and had my own reward of seeing her face break into a huge grin. She immediately ran over to her friends in the class and showed them the candy bar I'd given to her, and while bragging isn't such a good thing, I loved seeing how proud she was.
I hope that I have more teaching days like today. I'm also realistically thinking about how my summer school classroom is different from the kind of class I'll have in the fall: I have only 12 students (11 female), my students are well-behaved and excited about math, there are between 2 and 4 teachers in the room at any given time even though only one is teaching, and I started teaching only after my co-teachers had already established some sound classroom management. Truthfully, I don't even deserve a lot of the credit for the way the lesson went. However, I can think of today's lesson and everything that went well about it as something to strive for during the regular school year.

Cold-calling from index cards

Today, I took two 45 minute periods to review for tomorrow's Algebra I test. I conducted the review session primarily by giving students a worksheet of problems on each of the topics we've covered, giving them a minute to work on a problem, and then calling on a student to go to the board and show the class how to solve the problem. Normally, I pick students to go to the board by asking for volunteers. Today, I tried something different. I made an index card for each student and announced at the beginning of the review session that I would choose people to do board work by shuffling the cards and randomly pulling out one card.
I ended up really disliking this method for my class. I have a class of 12 excited students who, on a normal basis, frequently ask ahead of time if they can go up to the board to do the next problem, and although they sometimes get distracted and try to talk to each other when they're supposed to be solving math problems, all of them will work on the problems assigned in class. The bottom line is that I am never at a loss to find eager volunteers to go to the board and solve a problem. For this reason, I was somewhat hesitant to even try the cold-calling card method for a lesson, but I tried it anyway.
As luck would have it, I ended up pulling the same person's name out of the deck multiple times, while there were 4 kids whose names were not getting pulled out at all. The kids whose names weren't getting pulled were not happy with this situation. They kept on asking me if they could do the next problem on the board, even though they knew that I was using the cards to pick people; several other students made the same request. By the end of the period, I felt like the 4 kids whose names I hadn't pulled were getting shortchanged, so I just abandoned the stack and called on each of them. When I talked to my second-year mentor teachers after the lesson, they said that I didn't really need to just randomly pull a card out, and I could stack the deck. Unless I have students who will personally resent me for calling on them when they don't volunteer, I would rather just call on random people than pretend to randomly draw names.
Another aspect I didn't like about the cold-calling method was the lack of personal attention. As I discussed with my second-year mentor teachers after the lesson, my students get very excited when they raise their hands and I pick them. The personal attention makes them feel special and proud, and cold-calling took away from this interaction.
I have not completely given up on the idea of using cold-calling in some future classroom if I have reluctant and/or unfocused students. One positive outcome I observed from employing the cold-calling method was how the students all fell silent and focused their attention on me every time I announced that I was about to draw a card for the next volunteer. In the case of my class, this was positive anticipation, since everyone was hoping I would draw their names. I think that in a less motivated class, where the anticipation would be more negative, the suspense would nonetheless draw students' attention and keep them focused, because no one knows what name will come up next.