Sunday, October 16, 2016

Differentiation in Math Class: Centers

My fourth grade class is all over the map, mathematically speaking. Some are really ready to learn fourth-grade content, while others need extra support in order to do so. Still others need time to revisit concepts from earlier grades, and a final group is ready to be pushed to fifth and sixth grade math. This is a common situation in many classrooms, and it can leave a teacher scratching her head, wondering what to do each day.

One of the ways I approach this situation is to plan some days that are based around centers. I use the term “centers” loosely. Mostly what I mean is that different students are doing different things at different times, and students usually rotate from one activity, game, or group to another. Here is a portrait of how I planned such a day last week. (Thanks to @jennalaib for inspiring me to write this blog post.)

I had several groups of students to consider in planning my math class last Friday. The majority of my plan was based on the work they had done two days earlier, when my student teacher taught a lesson on prime and composite numbers.
  • Of our 24 students, she and I determined that five of them were pretty solid on determining if a number was prime or composite.
  • Sixteen others either needed more practice (they had worked slowly on Day 1, so we weren’t sure yet how facile they were at finding factors), OR we knew they needed more support from a teacher.
  • For three of our students, determining if a number was prime or composite wasn’t a good use of their time. Of these three, one has Down’s syndrome and is learning to add and subtract numbers under 20. The other two need practice with multiplying and making arrays. The visual models of multiplication are very important for them to continue to make sense of multiplication. They can work on finding factors by making arrays, and we can talk about whether a number has many or few factors, but our focus for them is more on what multiplication means than how many factors a number has.

Based on this information, I made a center plan for our 60-minute math class. We would begin with a 10 minute number talk, then students would have slightly more than 20 minutes in each of two centers. This left a few minutes to clean up and transition after each center.

I created the following plan for each group of students:
  • I started with the 16 students who needed more work on prime and composite, since that was my biggest group and my main goal for the day. I broke them into two heterogeneous groups of 8, so that each group had only 2-3 kids who would really need more intensive help from a teacher. Each of those groups would meet with my student teacher for one 20-minute “center” to continue identifying prime and composite numbers.

    Their second center would be to meet with me for a discussion about finding factors. This was meant to be a whole-class conversation, according to our curriculum, but participation has been somewhat limited during whole-class conversations in my class so far this year. (I think this will get better as we get deeper into the year.) Plus, I wanted to be able to support different students to access my questions in different ways (questions like, “Is 3 a factor of 51? Is 6 a factor of 86?”). I thought this would be easier in small groups than in a whole class format.
  • My student who is working on counting and adding small numbers also had two centers. The first was to work one-on-one with my co-teacher (the special educator). I asked them to solve some addition and subtraction problems about making jewelry with beads and for my co-teacher to take some notes for me so I could know what strategies she was using and if these problems (with totals under 30) were the right level of difficulty for her.

    Her second center involved learning an Investigations game from the first grade curriculum called Five in a Row. This game has many versions that vary in difficulty, so I wanted her to learn the most basic version so she could play it all year, progressing from the easier version to harder ones involving adding 3 numbers or subtracting. I partnered her with a peer to learn this game on the computer. I rotate kids through working with her, usually for 20-30 minutes at a time so they don’t miss too much of their own math work. This is good pro-social time for her as well as good math practice.
  • The two boys who are working on understanding multiplication better did something similar. They also played an online game, this one from the third grade Investigations curriculum (Multiplication Compare). I had taught it to them the day before. For their second center, they worked with my co-teacher and she taught them to play How Close to 100? She took detailed notes on how they did. Her notes, indicating that the game was too hard for one of the boys, led me to create a modified version of the game for him to try this coming week.
  • Finally, the 5 students who were solid on finding prime and composite numbers had a choice of 3 multiplication / factoring games to play: a fourth grade Investigations game called MultipleTurnover; the Product Game; and Factor Find from Origo. They stayed with the game for both their centers.

So how did it all go? Mostly, it went great. Here are the highlights:
  • The room had a busy hum throughout the workshop and everyone, with the exception of one student, was working nearly the whole time.
  • My student teacher got to work with a few students who needed more practice with prime / composite and they made good progress. She took notes for me on their work in a Google doc.
  • My co-teacher took detailed notes about the three students she worked with, which helped me think about the next steps for all of them. She could focus deeply on each of them because she had them in such small groups.
  • Because the two groups of 8 were heterogeneous, both my student teacher and I were able to give students the right amount of attention. If we had had 4 or 5 students who were struggling with the content in either of those groups, it would have been overwhelming to attend to their needs. This way, we each got to check in with those who needed our attention.
  • Because these groups were heterogeneous, the level of engagement was high. My small-group conversations about factors were really rich, and I was fascinated at how quickly students took up my questions and ran with them, taking the work in whatever direction made sense to them with only a few small nudges from me. Students really pushed each other’s thinking in these conversations.

What could have been better?
  • The student who played Five in a Row had a hard time understanding the game. It would have been better if an adult had taught it to her with the peer, rather than asking the peer to introduce it on her own. After some time with an adult, the two of them could have carried on playing independently.
  •  The two boys who played Multiplication Compare played it for some time, but by the end of the 22 minutes had started playing a different (non-math) online game. (The temptations of the Internet!) Invariably during a center-based math class, students must work independently, and some are more able to do so than others.
  • The five students who got to choose a game had no time with an adult. I didn’t get to see what strategies they were using or ask them questions about their thinking. For one day, this was fine, but I have to be careful that students who have mastered the content don’t end up working independently most of the time. The next time we do centers, I’ll be sure to spend time with each of them.
  • This kind of teaching is a lot of prep. Luckily, a lot of these math games are online through our curriculum. Otherwise, I would have been pulling together tons of cards, dice, directions, etc. It’s important that my students have a repertoire of games with which they are familiar so that I can give them choices during centers and I have less prep. I have plastic boxes set up with the materials for all the non-computer games that I can quickly grab in the morning, and I have created tiny urls for the online games so they can access them easily. While some center material is new each day or two, other things are recycled and re-used, which cuts down on prep.

I don’t have three adults in the classroom every day, so on some days more kids would have to work independently. But the days when there are three of us are great days to do centers with purposefully planned small groups.

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