Communicating Mathematically

One of my favorite activities I do in PBL 101 trainings for BIE is the ideal graduate.  The activity involves participants writing the knowledge, skills and dispositions students would have when they graduate. I add a twist to the activity by having people to think about one student that they love and one student they wish were absent. They must think of traits that both students would possess at graduation.

When I first did this activity for myself, it wasn't hard to come up with a list of items. What was difficult was narrowing my list down to something I could realistically work on students achieving in one school year. My list is 10 traits that have changed slightly over the years.

Although the list hasn't changed much, my strategies and classroom protocols change frequently. I think about what I do that prevents and support my ideal graduate. This is a very humbling experience because I have to admit what is not supporting my goal. For example, I have long wanted students to be a self-manager. A long classroom practice was keeping students materials in a bin in the room. I did it because they often would not keep up with items. However, this past summer I realized I was not giving them even an opportunity to self-manage. This year I have a bin but is only for students who feel they can't keep up with the notebook. I encourage students to keep the items and I periodically check to make sure they have them. So far, I have about 30 students out of about a 130 who use the bins.

Another trait I have made some major changes to this year is communication. I am modeling proper mathematical communication more and using a basic rubric more consistently to support my expectations. The rubric follows the same format at the concept rubric to help students understand. The rubric includes students written and oral communication of mathematical concepts. You can get a copy of one of my rubrics for a concept and communication by clicking here.

My changes are a great compliment to some of my past practices that support the building of students communication. One of my practices is a common one to classes--Ask 3 before me. I have a huge poster on my door that I reference a lot during the beginning of the school year and after winter break. I have discovered it is really important to call students on if they asked people before asking me. I often will go to the people they ask and see what they said. Rather than just letting the students say they didn't know. I challenge them to say what they do know and work with the students to improve their collaboration. 

Another strategy I use is one day dedicated to students only working with each other to solve a problem or a set of problems. This day is embedded in my 2-1 cycle. Students get at least 2 days to understand a concept before an assessment will be taken. Sometimes these assessments are placed in the gradebook. Every time the assessments are used for students to reflect on their learning progress. Typically, students are allowed to work together on the first assessment. I spend this time observing or reviewing other classes work. Below is a video I captured during one of the days students could work with each other. Notice the discussion occuring between the students.

How do you help students communicate mathematically? What is your ideal graduate?