My First Observation

October 2023 

I still remember the very first classroom observation feedback I received from my principal. It was my fifth year of teaching and my first in that district. Yes, that means I had no observations my first four years as a teacher. One of the key pieces of feedback that I received was the number of times I randomly called on a student compared to a student with their hand raised, as well as the number of times I called on girls versus boys. From that point on, I was conscious of making the effort of calling on and hearing from a wider variety of students. 

Obviously, effective discourse is more than just calling on a wide range of students. And, having a discourse-rich, student-centered classroom involves more than helping our students learn to listen to each other, which I talked about last month. We must also be aware of which students are being asked what kinds of questions. Are we asking deeper thinking questions to just some students, or are we putting structures in place to allow all students time to develop a response? We must be continually aware of the positionality of our students.  

We must position our students in ways that promote our beliefs that they are capable of learning mathematics. Students must recognize that we believe they can understand the concepts rather than merely memorize rote procedures. The positioning of students as capable is not just for some, it is for all students. Our role as educators is to ensure that all students have the opportunity to share their reasoning—and their brilliance. 

In professional development sessions I’ve attended, the importance of teachers positioning all students is strongly emphasized, however, I don’t recall discussions focused on how students position each other. Just as educators help students learn how to listen, we, in turn, can help students consider how they can position each other. Educators can address the societal stereotypes and inequities as they arise in class to aid students in recognizing that all their classmates bring important contributions to learning mathematics. We can also help our students develop their identity so that they continue to gain confidence in sharing their reasoning.

We must develop norms for classroom participation in order to aid in positioning all students as mathematically competent. Mistakes and incomplete understandings must be valued and utilized to help students learn the mathematics. As our recent position statement, Transforming Practices and Policies so Multilingual Learners Thrive in Mathematics, notes, educators must center multiple modes of communication in learning mathematics. Structures must be put in place to allow every student to share their thinking, whether verbally or in some other format.

As we consistently work to increase the amount of discourse in our mathematics classrooms, I encourage all of us to pay careful attention to the positioning of our students. All our students deserve to be heard and have their brilliance shared. Let’s commit to giving them the space and voice to do so!

Kevin Dykema
NCTM President
@kdykema