Order and sameness versus disarray and diversity

New Year’s Resolution: Have students work harder than the teacher! (Part 2: Structured versus Unstructured)

Last #mathmonday, we explored setting up your classroom culture. Once students understand the expectations for being a mathematician, next up is creating lessons that REQUIRE students to engage in the mathematics.

Think back to when you wrote lesson plans in your undergrad program. I remember writing the problems or tasks that I was going to use to set the stage of the lesson, maybe the activity or lesson idea, and then the assignment I was going to have the students complete for independent practice. I typically wrote the lesson from the perspective of what I was going to complete as a teacher. What I learned from Jerry Cummins was that I needed to write a lesson plan from the perspective of the student. Instead of just thinking about what mathematical tasks or problems I was going to use, I needed to think about how I was going to require all students to engage in the tasks.

The challenge is: how do you get ALL students to engage in a task? Once students understand the rights and responsibilities of a mathematics student, teachers have to create opportunities for students to practice their new skills. If one of the student responsibilities is to help others, teachers need to create opportunities that require students to help each other, listen to each other, and learn from each other.

Last week, we talked about the first of four big ideas that promote positive learning environments where students take ownership of their learning and learn to love mathematics. Now, let’s dive into the second big idea: structured versus unstructured.

(2) Structured versus unstructured

If you do not have 100 percent of your students engaging in meaningful mathematical discussions every day, it is time to add more structure. Routines, procedures, and roles are crucial to sustaining meaningful discourse.

  • Routines: Students are creatures of habit. When I attend a class or conference session, I tend to sit in the same spot every time. Students are the same way! When students begin a mathematics lesson or walk into Geometry, do they know what to expect? Consistency matters. To build consistent expectation, I started writing a short agenda for the day so that when students entered class, they knew what mathematical tools or resources they would need, what the expected learning was for the day, and what success would look like at the end of class.
  • Procedures: Personally, I am a visual learner. My own children will ask me about a mathematics problem, and I swear I only hear, blah, blah, blah. I actually have to see the problem to be able to understand the problem. When coaching, I have noticed that many directions and procedures in the classroom are solely verbal. Do you ever have students ask, “What are we supposed to be doing?” I recommend both verbal and written instructions. And when doing a new activity, routine, or procedure in the classroom, model the expectation. Fishbowls are great structures to use to model classroom expectations. I have also role modeled with one or two students the expectations of the activity before beginning something new.
  • Roles: If there are students who consistently choose not to engage, you can assign roles in student teams. I recommend student teams of four (good number for partner work and larger group discussions) and each person in the group is assigned a role. My favorite roles were: team captain, materials manager, task master, and on-call. The team captain is responsible for keeping the team together—the team cheerleader so to speak. The materials manager always made sure that everyone had the materials they needed for the day and collected them at the end of the day. They also made sure that all of the tools where in place before the team left at the end of class. The task master was the time keeper for the group most days. Some days they also were able to roam the room to talk to other task masters to see if their team was on track. My colleague, Kim Edelson, came up with the on-call role and this student was responsible for whatever I needed them to do on a given day or they might be “on-call” for someone who was absent from the team. I rotated the roles every month (or sooner if needed). What I found with using the roles that there was equal participation. Every student member of the group was afforded equal shares of responsibility and input throughout the lesson.

I noticed that the more structured I began each school year, the less structured I could be throughout the rest of the year. When I planned my lesson from the student’s perspective and provided multiple opportunities for students to productively engage in the classroom community, more students were successful and enjoyed mathematics. The more students knew what it meant to be a mathematician and the expectations of being a learner, the more they were learning.

Once the routines, procedures and roles are established, we have to continuously monitor the engagement in the mathematical discourse. Look for my post next #mathmonday as we explore “there is no ‘I’ in team!”


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