2/15/07

I made a deal with my students last Friday, but I don't know how well it is going to work out. Their opinion was that math is beginning to follow too much of the same format all the time. For some time now, our regular routine has been to do a warm-up, sometimes go over homework, and launch a problem for them to work on. If it was a relatively short problem, we would summarize it in class; otherwise, the summary was postponed to the next day.

But they were like zombies out there. So last Friday, I had them get up and do some jumping jacks. They know how I love to sing, so we sang a funny song as we did jumping jacks. This little break livened them up. That's when they began to tell me how bored they were by our usual routine. The deal I made was that, if they worked hard on the problem of the day, I would find a way to change things and make math more interesting.

Well, they did work really hard on the problem that day, so I walked in on Monday with the beginnings of a plan. We have just started a new book, and I don't want to stray too much from the way the investigations are written. So I decided to start with something small. Instead of having students write their answers to the ACE problems on the board, or going through the problems with them, we played a game. The game took longer than I had expected, however, because there were a few students who "forgot" to do their homework over the weekend.

Anyway, I passed out a dry erase board, eraser, and marker to each student. We read through the questions (ACE 3, 8, and 10, starting on page 10 of Comparing and Scaling) one by one, and answered them as a game. Students had to write down the answer to the question on their dry erase board. Then, when I asked, they were to hold up their boards. We discussed how to find the answer, what the answer is, and what connection it made to the problem we did.

This "game" really motivated my low students. Michael (whom I've spoken about before) really bought into this -- he loved it! And the best part is that he did really, really well. He hadn't completed the homework, but was able to do the work and was happy to do it.

To recap, Michael is one of our Special Ed students. We currently have a deal with him that if he works in class, he is not responsible for completing the homework. Lately, though, he has been completing parts of his homework and has started to participate more in class. As the class played the new game, he got really excited and said that he loved this way of doing math.

The drawback of the game was that it took such a long time. I think that it might go faster the next time we play. Hopefully, it will also go faster when most students have done their homework and aren't just doing the problem for the first time.

Today we started work on Problem 2.1 of Comparing and Scaling -- the Orange Juice Problem. I began by asking students whether any of them knew what orange juice concentrate was. In the past, it has been a stumbling block for those students who didn't know what concentrate was. I was happy to see that my students knew what it was, and were able to give me examples of how they have used it or when they have seen concentrate being used. We read the problem together and then they set to work. I assigned groups of four students to this problem, and gave each group a sheet of chart paper to do their work on.

Each person in each group was to get a marker of a different color, and write their name in their color. This is a way for me to see who is doing the work, but it also motivates students to work, because they know they must be responsible for something. For the first day of work, I asked students to find the mixtures that were the most and the least "orangey," and tell me how and why they did what they did.

I was very impressed, because all of my groups found the correct "most orangey" and "least orangey" mixture on their first try. I don't think this has happened for me before. Most of the time there's one or two groups that look at a part-to-part relationship with the wrong twist, and make mistakes on the most or least orangey mixture. It was an exciting moment to walk around the room and hear some of their conversations. One of the groups included two of our Special Ed resource students, one low-level student, and one very high-level student -- who happens to be very lazy. I was amazed that this match-up turned out to be great! My high-level student, Jacob, sat and listened to the ideas of the lower level students, but instead of being lazy and doing nothing, or just saying they were wrong, he started a great conversation with them. He asked them what the information they were finding meant -- was it a part-to-part relationship, or was it part-to-whole?

This group had a great discussion and ultimately they were able to correctly solve the problem. I really believe that all four of them will be able to explain it when we look at the problem tomorrow.

I was slightly disappointed, however, that the ways my students used to solve the problem were not very original. Every group solved this problem using percents. I love it when groups use pictures to help them solve something. I am trying to decide whether I should push groups to have a picture to accompany their work. Two of my three groups solved the problem by looking at the percent of concentrate out of the whole juice mixture. The other group found the percent of concentrate and the percent of water to make their comparisons. Each group has only their work and their written explanation as to what they did. Is it that important to have pictures with it? Is it worth the extra time that it will take the groups to complete their pictures? I have learned that, when students do not think in pictures or cannot "see" a problem at first, it makes it much harder for them to do that problem a second time. Maybe I will ask the groups who have finished to begin working on a picture to explain their work. Even if they have not finished, it will be a good way to start a discussion.

Tomorrow, students will be explaining their work. I am trying to figure out how I can ask different questions or point out different information in each of the group's posters, since they all solved the problem in basically the same way. Should I focus on one type of question or one piece of information for each presentation?

In one of the summer workshops I attended, I remember that the woman leading it talked about prioritizing the posters that students create. She went around and mentally made notes about how each group solved the problem, and then presented them in the order that she wanted students to see them. After she had a few groups present their work, she asked whether other groups had taken similar approaches.

So, should I have one group present its method of determining part-to-whole, another group present part-to-part, and then ask the remaining group which of those two methods was most like their own, which they then have to explain? Or should I just have all three present and try to focus on a different aspect for each of them? Our presentation focuses only on which mix creates the most orangey mixture and which mix creates the least orangey mixture. We are not going to look at parts C, D, or E during the presentations. Students will be completing a worksheet that has those parts and some additional information on it.

As I look ahead to the rest of the week, I can see that I need to get through 2.1 tomorrow. Problem 2.2 (the Pizza Problem) might also take a day and a half to two days. I am going to work on extended response questions for 2.2. There are three problems in this investigation, and I need to make sure that I am on track for a quiz next Wednesday. It's so hard to predict how far you will get with these books each day. Sometimes the problems that you think will take a long time only take part of a class period, so we are able to do the summary, as well. Other times the problems take longer than you expect, and you can't get to the summary. I know that the summary is the most important part. Without it, students don't pull the information together or make sense of the connections.

How can I plan it out so that there's time for my summary, no matter what? Can some of the summaries be briefer than others? I guess I will just have to figure that out as I go along. Click here to learn more about CMP2's instructional model of launch, explore, summarize.