By Matt Kitchen, posted April 25, 2016 –

One of the best ways to get students to learn at a deeper level is to get them talking about what they are learning and their learning process. If planned and executed correctly, mathematical discourse will allow your students to solve more difficult problems with greater ease, raise both the confidence level of your students and the level of engagement in your classroom, and allow for quick informal assessments.

My pursuit of mathematical discourse (before I had any clue what that really meant) began with the idea of "group work." None of my education classes in college really touched on the subject, so I thought back to what I experienced in math class, which was basically group or partner work. Following what I remembered from my years of middle school and high school, I attempted partner work by letting my students start their homework or work on some practice problems with their partners. What resulted were random students turning their desks to make groups and holding conversations about the weekend. The cacophony became deafening. I realized that they weren't actually working on math together; they were working on math individually but talking while they did so.

Needless to say I did this for part of my first school year, and then the next year I assigned no group work. Seriously, zero. A year or so later, I discussed my fear of group work with a math mentor, and he suggested it was all about the task I provided, or in my case, the lack thereof. The idea was simply to change my frame of reference for group work, which meant that I had to change my frame of reference for teaching (which I touched on in my previous blog post).

By only providing my students with direct instruction and then practice problems, there really was no reason for students to work in groups other than to check answers, which I could easily provide. If I gave students a problem-solving task, then the necessity of a group working together to bounce ideas off one another would become more natural.

As I began incorporating some rich tasks for the first time, I quickly realized that I could actually have students successfully work in groups. The only problem was that the logistics of classroom control became much more difficult, and I began having flashbacks to my first year of teaching (and losing control of my classroom). I knew I was going to have to address this issue, so I went on a search for how to successfully operate with groups in math class. I found this video on the Teaching Channel. 

I highly recommend this video to anyone who is unsure about how to configure groups or who could use help improving his or her math group situation. It shows some practical ways that two different teachers structured group work. As with teaching, I love to see multiple approaches to the same problem because it helps me choose the way that will work best for my personality, strengths, and techniques. One teacher used an approach of assigning specific tasks to each member of the group. The second teacher used "group gears." I loved it from the first moment I saw it. I brought this idea into my class and worked to improve it over the next two to three years of instruction.

There are three group gears that I employ in my classroom:

• First gear: Independent problem solving
• Second gear: Quick checking
• Third gear: Group problem solving

By incorporating this strategy, I was able to give my students clear expectations about what they should be doing and how they should behave in each situation. It did take a good amount of rehearsal over the first few weeks, but it was time well spent.

In first gear, students have the chance to try things themselves. Not every problem necessitates that they work through it with a partner. I need to see if they can step up to the plate by themselves. I will usually issue a problem or task and then tell my students that they are starting in first gear for the first two to five minutes (depending on the problem). After they finish trying the problem or task, I want to give them a chance to talk about it, so I will tell them that I am shifting them into second gear. This gear rarely lasts longer than two minutes. If students are sitting in a group of four, it usually only involves the person sitting next to him or her (pairs) as they each share their answer and how they reached it. From here, if it is a difficult problem, then I might shift them into third gear and have them work on solving the problem with their partners for a set amount of time.

There are times when we jump straight into third gear, but the gears are usually used in pairs. If it is a quick problem, then I will go first gear, then second gear. If it is a more challenging problem, then I will go first gear to third gear. I try to make sure that I give the students time to think on their own first, so that they all have something to bring to the conversation when it is third gear, group discussion and solving time.

The last piece of the puzzle is a word or sound used to get the students’ attention. When I say, "Focus," my students know they need to get quiet. I know teachers who use a bell or a hand signal. Practice it with your students from the very first day of school. It allows me to move in and out of the gears with ease and bring the class to group discussion time.

This simple strategy has allowed me to easily teach using inquiry methods. Students are more likely to try a new type of problem or task if they know they can bounce ideas off a group, and you often get more buy-in if they are allowed to think on their own for a few minutes first. Even if they get frustrated working on their own, they know that they will be allowed to think through things with a group in a short amount of time, which allows them to persevere that much more.

Are your students discussing math in your class? If you don't have a strategy that works, then try mine or seek out another. But don't go through another year without getting your students actively involved in mathematical discourse. Exercise patience, allow for mistakes (yours and your students), and keep trying. Don't accept a status quo of partner work on some practice problems. Give your students a problem-solving purpose in your class and make sure they know that their partners are there for a reason.

Matt Kitchen, matt@makemathmore.com, is a math teacher in Ohio. He creates lessons for his real-life math lesson company www.MakeMathMore.com and tweets @mattkitchen.