In the high school math classes that I teach, my students spend a lot of class time working together in small groups. There are a lot of benefits to having students working in groups, so I've been pretty intentional about designing my classes so that group work is central.

There's a lot more to successful group work, however, than just having the kids scoot their desks closer together. When I first started using groups, I didn't have a lot of rules and I didn't really provide my students with much structure or guidance. I knew that I wanted them to a) work together to complete the assignment, b) figure out with each other (as much as possible) how to address any questions they had, and c) generally engage in mathematical conversations. I had a few basic rules for keeping them on task, but essentially I just put them into groups and said, "Go."

I quickly learned that they needed more guidance than that, and over time I've developed what I've started to think of as a Four Level approach to conducting group work. That is, I now have a little bit clearer picture of what I want my class as a whole, as well as individual small groups, to look like, and I have a set of rules and strategies for moving my groups toward that picture.

## Level 1 - The Behavioral Level

This level represents group work at its most basic level. Getting groups to operate at this level is almost 100% about behavioral issues and 0% about academic issues.

I teach a lot of what could be considered reluctant learners. Many of my students are not strong in math, many have a lot of fears and anxieties about math, and many just plain don't want to do anything that takes any mental effort. This means that many of my students are actively looking for ways to get out of doing their work, and some are actively looking for ways to disrupt the effective functioning of their group, and sometimes of the entire class. I can't allow that to happen, which means I have to be ready to address a lot of disruptive behaviors.

Here's what a group operating at Level 1 looks like:

**All students have their assignment paper on their desk and are at least pretending to work on it.**It may sound odd to say that I'm only requiring my students to*pretend*to work on their assignment, but this "rule" actually gives me a clear way to address a number of common student misbehaviors by providing a clear minimum behavioral expectation. That is, they have their paper on their desk, they are not sitting with their head down, and they're making at least minimal progress on completing the assignment. I address the pretending part in other ways.**If a student has a question about something, they will ask it.**Students at this level often don't ask questions about things they don't understand. Sometimes it's because they don't know how to ask, sometimes it's because they're embarrassed to reveal they don't know something, and sometimes it's because formulating and asking a question is too much work. At Level 2, students are able to actually ask questions of*each other*before they ask me, but at Level 1 I just want them to ask*somebody*.**Conversations are at reasonable volume levels.**The rule in my class is "Conversations should be audible but not discernible."**Conversations are within groups only.**This is a way of keeping off-task or disruptive conversations confined to a single group so that they don't spread to other groups and negatively affect the learning environment of the whole class.**Conversations are generally on task.**At this level, "generally on task" means around 50% on task, 50% chit-chat.

## Level 2 - The Basic Academic Level

This level represents a group that has largely mastered the behavioral challenges of Level 1 group work and are able to operate at what I think of as the basic academic level of group work. Getting groups to operate at this level is roughly 50% about behavioral issues and 50% about academic issues.

Here's what a group operating at Level 2 looks like:

**The students aren't just pretending to work, they're actually working.**Meaning, they're actually working*on the assignment*.**Students are willing and able to ask questions, and they will usually ask their group members before they ask me.**I actually establish a rule at the beginning of the semester that before anyone can ask me a question, they must first ask everyone in their group. Some students are actually eager to do this, since they don't want to talk to me anyway. Other students*only*want to talk to me, and it can be a long hard struggle to get them to have even the most basic conversational exchanges with a group member.**Conversations are at reasonable volume levels.****Conversations are within groups only.****Conversations are mostly on task.**Say 60-40 or better.

Groups at Level 2 still require continued monitoring and occasional prompts to stay on task, but they are generally willing to work together to complete the assignments.

## Level 3 - The Advanced Academic Level

This level represents a group that has largely mastered all of the basic behavioral and academic requirements of Levels 1 and 2. In addition, they actively engage in a few other behaviors. In particular:

**The students are willing, and occasionally even anxious, to help their group members with things they don't understand.**They're even willing to help other students/groups.**While there is sometimes an element of socializing and playfulness, the students'**Their conversations are around 80-90% on task.*primary*focus is is on the assignment.**The students engage in solid mathematical conversations with each other.**While they will ask me questions about things they don't understand, they will only ask after they have made one or more legitimate attempts to figure it out within their group.

## Level 4 - Doing Math

I don't have a very good description for Level 4 because I rarely (ok, never) have groups that operate at this level. And that's because I think to operate at this level, the students have to have mathematical tasks that allow (or require) them to engage in legitimate mathematical conversations, so-called "higher-level" tasks. Tasks that "require complex and non-algorithmic thinking" or that "require considerable cognitive effort."

Right now, most of the tasks that I give my students are pretty procedural. The students may have just learned about, say, the trigonometric ratios, and they're working on practice problems that will help to solidify the concepts of the trig ratios in their minds and learn how to apply them in different types of situations. That doesn't mean there's not high-level thinking going on; many of the problems require multiple steps, such as translating word problems into a diagram, translating a diagram into an equation, solving the equation and interpreting the answer, etc. But in order to reach Level 4, I think the mathematical tasks need to involve doing "real math."

Which means that if I expect to have groups that are able to operate at Level 4, I need to find, or come up with, some tasks that involve doing real math. Which I think is a pretty good thing to do.

Meanwhile, for the kids who are unable or unwilling to work at Level 1, I've developed a few strategies and tactics to help them. I'll talk about those in another post.

*Image by lavannya via Flickr.*

[FWIW, in the three classes I'm currently teaching (two Geometry and one AFM, all non-honors), I have a total of 22 groups. Of those, I have one that consistently works at Level 3, eight that consistently work at Level 2, and 13 that are at Level 1. I also have a total of 4 students (out of about 80) that struggle to remain at Level 1.]

Great piece

Wow, when you describe those groups, I know exactly what you are talking about! This year has been all about the group work for me too. I'm pretty lucky to have kids who come to me mostly ready for level two or high level one. But when I get them to level three, the feeling is amazing. I have to stop myself from interfering sometimes because they're just doing it! I have experienced the same problem with level four work. The problems have to come from me, they have to be relevant, and they have to be appealing. The times when I feel like they've been there have always been when we're doing math in support of a topic in physics (I have the same kids for both).

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Hi Matt,

It's cool when the groups work well, isn't it? I still feel frustrated sometimes at how many of my students struggle to operate at Level 1, but it's nice to have a sense of how I want the groups to operate, and what it takes to get them there.

Lance

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