Increasing Rigor with Accountable Math Talk: Starters for Students

Last time, I shared the need to increase the amount of time teaching conceptually, as compared to teaching only procedural knowledge. As a teacher of mathematics, my work and my coaching are strengthened by visiting several classrooms and observing teaching strategies.  In order to support and build teacher capacity, I often compare practices of teachers with high student value added results and those that are not so high. One take-away I am focusing on is based on the Standards for Mathematical Practices (SMP) #2 Reason abstractly and quantitatively and #3 Construct viable arguments and critique the reasoning of others.  Self-reflection and evaluation are two themes that are no longer limited to teachers and adults.  With our increased focus on rigor and standards mastery, it is imperative that students are able to evaluate their solutions for reasonableness, as well as critique the mathematical thinking of others. 

So, what is common in classrooms with high achieving students? One practice that has "stuck out like a sore thumb" for me over the last few weeks is allowing students opportunities to engage in mathematical dialogue.  The National Board for Professional Teaching Standards states that "Accomplished teachers deliberately structure opportunities for students to use and develop appropriate mathematical discourse as they reason and solve problems.  These teachers give student opportunities to talk with one another, work together in solving problems, and use both written and oral discourse to describe and discuss their mathematical thinking and understanding." In classrooms where students are struggling with math, I ask that teachers reflect on the day and/or week, by asking:  1. Have my students had time to engage in "math talk" during my class?  2. Have I intentionally planned for "math talk" today or this week? and 3. How do I know that each student has engaged in "math talk" this day/week?

One lesson I learned as a classroom teacher was that arranging students in groups (close proximity) did not automatically mean that they would have meaningful learning dialogue. I can remember giving students a group assignment and saying, "be sure to talk with your group members and give feedback."  But, now I am sure that students were thinking to themselves, "what does she mean or what should I be saying or asking?" While preparing for National Board Certification, I learned that this communication skill must also be modeled and taught.  In my research to offer assistance with this in my schools, I took several of the "starter phrases" and put them together in card form so each pair of students can have readily available examples of how to have "math talk" when they are defending their work to come to a consensus. Here are 3 examples of the 16 cards that are held together nicely with a small ring binder. Click here if you would like to download the entire set. 

I also encourage teachers to go a step further and generate reflective data on students' mathematical discourse.  In other words, how often students respond with the correct or incorrect answer, and from what level of Blooms Taxonomy or DOK do these questions come. What valuable data to have for reflecting on lessons, using in parent conferences, or preparing for special services. This can be done with a chart on a clip board or using one of my favorite tech tools, the Stick Pick app, which conveniently serves as a random student picker as well as a tracker of total student responses, % correct, and Bloom's level. Click here to view the Stick Pick Blog for more information. 

Below is a snapshot of data from Stick Pick. Feel free to comment. I would love to know how you ensure and track student accountable talk in the classroom.