Taking Risks with Student Independence: Being Okay to Let Go

So this year my middle school is using the Connected Math Project 3 curriculum.  It has three phases: Launch, Explore, and Summary.  The lauch, lauches the lesson. Duh. Then students explore the activity and answer questions. Then, we summarize at the end.

Out of the many questions that are attached to each CMP lesson we’ve decided to pick 1-2 or to come up with our own rich question that students can explore for a significant time and so that we can have rich discussions afterwards.

But we also wanted to do something that would make students interdependent and wean them off of calling us over every time to understand what the question is about or asking for an entry point into the problem.

So the math team decided to structure the explore section with a specific protocol that we’ve called our discussion protocol. It consists of timed steps (usually step A-D or as many as needed). It’s easier for me to explain what we do with a specific lesson. This is Problem 2.2 in the CMP3 book Prime Time. The big mathematical idea is finding the lowest common multiple and recognizing that the LCM of relatively prime numbers is the product of the two numbers.

We launched the problem by having the students watch a short video on cicadas from the connected math website which essentially explains what cicadas are and that they come above ground either after 13 years or 17 years. At the end of the video they are asked, after how many years will the cicadas return if the 13 and 17 year cicadas return together if they came together this year?

Explore/Discussion Protocol
This is where our protocol actually begins. We’ve assigned 4 roles to each group.

Student Roles

  • Facilitator: The facilitator is the person who will read all the instructions for each step. This is the only person we give the actual task paper too. Students in my classes call this the facilitator’s paper.
  • Manager: The manager needs to make sure everyone in the group is on task and that the group is completing the steps before the timer goes off.
  • Speaker: The speaker will share the discussions that happen in the group with the entire class or be the group representative in other groups (semi-jigsaw).
  • Recorder: The recorder is the person who writes down the group’s ideas on the paper.

The students have really been taking the roles of facilitator and managers seriously. The facilitator’s paper is quickly becoming a sacred paper in the groups.  The managers also love the power–we’re still working on the speaker and recorder as those are less sought out roles.  

Teacher Role

We’re monitoring and observing students. We’re also thinking about which groups we want to do a group share out so we can highlight misconceptions, multiple approaches, multiple answers, etc. We’re also conferring with students. At times we’re also sitting with groups, especially if they need more of a guidance.

The “Steps”

Each step that contains a question begins with, “Read and make sense of question (insert question # here). (90 seconds)” For this step we expect students to make sense of the question together. At first I thought 90 seconds is too short, but it’s been working well.

Then students have 5 – 7 minutes to think about the question and to take notes. They can conference with others, but the expectation is that they are forming their own thoughts. At this step, we’re also doing a quick check to make sure that the question was actually understood by the students. We initially planned 2 questions, but then just stuck with question #1 only.

Question #1 – If they appear together this year, after how many years will the 13 and 17-year cicadas appear together again?

Question #2

a) Imagine there are 5 and 10 year cicadas.  When will 5-year and 10-year cicadas appear together again?

b) Imagine there are 2 and 3 year cicadas.  When will 2-year and 3-year cicadas appear together again?

c) Imagine there are 4 and 10 year cicadas.  When will 4-year and 10-year cicadas appear together again? 

We usually have one step that is a group check in. The students share their findings and strategies. Then at the end each member is expected to either:

  • make a comment
  • give a complement
  • or pose a question

I haven’t implemented this yet, but I’m thinking of giving students a graphic organizer where the recorder will record these comments, complements, and questions which would be collected at the end. Only because I want more accountability for this phase. 

The last step is usually preparation for a class or small group share out. Some things we have done:

  • Students create posters with an explanation of their strategies.
  • Students create posters with 4 quadrants in which one is a “comments” section. Here we ask them to write down what they struggled with, if there were any disagreements in the group, what they liked/disliked, etc.
  • Reflecting on the work done in the group by completing statements like: “For me, the most important idea that was discussed in my group was …. because….”

Further Developments to Consider

The sharing/summarizing after we’ve done all of this is what we’re struggling with.  I’m not sure what is the most effective way to share out what the groups have been taking about in their small groups and facilitating a student led discussion as opposed to being a back and forth between teacher and students, which is what is happening more or less right now. There are some things that we have been doing, which I will post later on. 🙂 

We’re also continuing to work on the pacing and timing and we understand that the time will always be the enemy, but that’s why we’ve chosen to focus on key questions.  

Here is another lesson that we did recently on finding the greatest common factor. Students had colored tiles as manipulatives to work through the problem.  Click on the following link to see the facilitator’s paper that we handed out:

Problem 2.3 Student discussion protocol

Wow that was a long post.