The purpose of today's class is to focus on classroom discussion norms and do a practice discussion with a math riddle so students get comfortable for how math class will work (especially around discussing math ideas). I want to get student buy-in for discussion norms, so we start class by working in small groups and generating a list of student rights and responsibilities, specifically in regards to what happens during math discussions.
I break students into small groups and ask them to come up with a list of what they think are the most important rights and responsibilities in a whole class discussion setting. I ask them to come to consensus on the following two prompts:
Students get to work in their groups. Depending on the length of class time, students might have time to make posters, otherwise they can just write a list and be prepared to share out in the whole class discussion.
Next, groups share out their lists. I keep a master list at the front of the room and we talk about similarities and differences between their lists. Of course, I am listening for some key norms that I want to establish but I'm hoping students will come up with those on their own. The key ideas I want to be explicitly addressed are something like the following:
Together we decide on the main points and make a list. I'll later type up this list and distribute it to students. I would like to use it as a tool to come back to when norms are broken.
Next, I let students know my goals for math discussions. I want to be explicit with them that I am hoping our discussions will lead to exploration where they are trying to figure things out, making connections between ideas, and generating arguments about what they think.
I let them know that in order for these discussions to happen, I'll be asking them to do things like repeat what their classmate said, speak directly to each other, say more about what they're thinking, and asking them how they know what they know. I let them know that this work takes practice and that's what we'll be doing today.
I show them some sentence stems that might be useful for them as they start this kind of discussion. Helpful accountable math talk sentence stems can be found here: http://24-7teacher.blogspot.com/2012/07/accountable-math-talk-stems.html
With the norms in place and students prepped on what will happen during discussions, we practice with a fun math problem. Any math problem that really engages students or has multiple pathways to a solution will work here. I like to use a variation on the classic Fake Coin Puzzle problem. We read through the problem together and students get working on their own or in small groups. I let students know that today's goal is really to practice them sharing their thinking so it does not matter if they get to a solution. They have a limited amount of time (about 15 minutes) to work on the problem, so I don't expect them to get to an answer. I circulate around the room, paying special attention to students who start the problem but then get stuck. These are the students I want to share out at the start of our discussion.
I start the discussion of the Fake Coin Puzzle by having a student or small group come up that started a strategy but did not reach an answer. Here, I want to show students how discussions will go. I immediately ask another student to repeat what the first student said. I let students know this takes practice, but it's important that they pay close attention to what their classmates are saying. I might ask for a few different students to repeat, and then ask if anyone can "add on" to what the first presenter did. Whenever possible, I have students come to the board to show visuals of their work. I try not to verify or validate anyone's method but stay neutral and ask students to build on each other's thinking. Eventually, we get to a group that has a correct way to approach the problem, and here again I ask a few students to repeat how the students solved it.
We spend a few minutes at the end of class reflecting on what this method of discussion was like. I might ask students what was challenging about this type of discussion. I am hoping students will say that they really have to stay on their toes and follow the discussion because they might be asked at any time to rephrase or build on another student's work.