This post came from a request from my Facebook group: Creating Innovative Thinkers with Jessica Kaminski. How do we encourage students to engage in mathematical discourse especially when there's language issues involved? This is such a great question!
The Common Core Mathematical Practices state that students should be able to communicate their thinking with others through writing and speaking. This requires students to use mathematical language, use metacognition, and function upon the norms of societal conversation.
Mathematical discourse is defined as asking questions, making conjectures, and evaluating the mathematical arguments of others (Kilic, Cross, Ersoz, Mewborn, Swanagan, Kim, 2010). Each of these aspects of discourse work together to get students to communicate their thinking as the Common Core Mathematical Practices state.
When I read this, I get excited, because this is what math class should be like! Students should be talking, asking questions and challenging each other. Then, reality sets in, and I realize I have 5 ELL students, 2 speech delayed students and several other students who just don't know where to begin. So what do we do?
I'm going to be honest. I've been in a lot of schools where they use very scripted routines to get students talking. Partner A and Partner B. This person talks, this person restates, and then this person talks. In my opinion, this doesn't work. It's not natural. It's a procedure, and conversation isn't procedural. I prefer a much more organic approach, and I've seen it work over and over!
My first suggestion is to begin with the basics. Teach your students how to contribute to a conversation. In my Day Zero: The First Math Lessons (available here), I address this in Lesson 4. Students need to know what to expect when having a conversation. What does it look like? What does it sound like? How do I know that I'm engaged in the conversation?
Begin here and be explicit in your expectations. You can see some of mine in this chart available to download in the Member's Area Freebie section.
Consider asking some fun get-to-know-you questions that encourage students to practice their conversation skills. Begin with the basics, and then tack on the ability to take turns. One strategy that I have used is to give each student a specific number of popsicle sticks. My talkative students get 2-3, while my quieter students may get 4-5. I post a fun question and ask the students to place a popsicle stick in the middle of the table each time they speak. Once they are out of sticks, they have to be good listeners. If they still have sticks leftover, they have to contribute to the conversation.
Each time I have used this, I have changed it up. I usually have a seating chart on a clip board and observe groups. I place tally marks each time students talk and make comments to them. Next time we try it again, I change the number of popsicle sticks. We KEEP doing this until students understand how they contribute to the classroom dynamic.
Now what do you do when they don't know how to comment on each other? They are looking at each other and taking turns talking, but their comments aren't meaningful. They may not even relate to one another's comments. This is the time to teach students some purposeful prompts to get them talking.
I begin by introducing 2-3 of these prompts at a time. As students are talking about the fun topics or math concepts using their popsicle sticks, I now challenge them to respond using one of these prompts. I write them on the board and give them copies of the prompts. Once students are using them regularly, I introduce two more. All the prompts are listed somewhere in the classroom. Now, when students aren't sure how to respond, I point them to the anchor chart and ask if they can use of these to help them.
My last suggestion would be to provide students with many opportunities to develop vocabulary. Zoltan Dienes discusses a lot about how students develop math concepts. He encourages students to play with materials before introducing formal vocabulary. Consider having students play games and look for patterns. Then, assign them the vocabulary word after they have developed their own meaning first.
It's vital to have these developed words on a word wall. Students can help create this classroom word wall by writing the word and drawing a picture that explains the meaning on an index card. This picture can be placed in the room somewhere, and students should also record in their own math journals. Part of the success of this is that it's made WITH the students. I know there are a ton of premade cards, but the creation of the word wall by students incorporates their meanings that they created while exploring.
As students are talking, encourage them to look at this word wall. Ask them to use the language present. They should also use materials and visuals to explain their thinking. This is a huge help to students who may not have English as a first language or have language delays. You are providing them with options.
Want to really put your students to the test? Consider hosting a Socratic seminar! Post a problem or a beautiful piece of art and ask some open-ended questions about the piece. Place students in a circle so they can see each other. Then, step back and allow students to talk without your intervention. This is an excellent activity that requires practice, but when students learn the process, it's beautiful to behold! I was fortunate to work in a school where we did this from Kindergarten-8th grade. Our students could agree and disagree over so many concepts, but were able to hold a group conversation!
After students have practiced a few times, encourage students to be reflective. Did they contribute to their group? Did they ask thoughtful questions? In my Member's Area, you can check out the self-evaluation and the group evaluation forms. I use these every now and then to get students to think about what they are doing. It can also be used for a participation grade.
I hope this helps you get started with mathematical discourse in your classroom! It is such an asset to instruction, but one that must be taught, practiced and evaluated. Click here to download your FREE prompts and begin using them today!
Information taken from Techniques for Small-Group Discourse (2010).