Teaching Mathematics: Towards a Sound Alternative

"This book was an important part of my own research journey. It’s by a man named Brent Davis and it’s a write up of his PhD thesis. What he got interested in was trying to say something about the listening of the teacher. I just found that such an appealing idea. From when I first read it in 1999, the idea of the importance of listening has been a recurrent theme of interest for me, both in my teaching and in my research. In the book, Davis distinguishes an evaluative form of listening — where as a teacher what I’m basically doing is saying this response is right or wrong – and contrasts that to a non-evaluative form of listening. He then further differentiates that, but I don’t think that’s so significant. What seems to be powerful — from when I started looking into this idea and doing video recordings in classrooms trying to analyse the listening that was taking place — is that it really did seem possible to distinguish between what happened when a teacher evaluated a student comment (basically saying “Yes I agree” or “No I don’t“ or some variation of that) and the dialogue that ensued, compared to when a teacher made a more non-evaluative response, for example, inviting someone else to comment, or writing the answer on the board and asking if anyone had a different answer. In the video recordings I took, the classroom somehow became alive as soon as the teacher stopped evaluating. A space was created for other voices to be heard. If you imagine a whole class discussion going on, very often the pattern of dialogue will go “Teacher-student-teacher-student.” What I got interested in was when it might go “Teacher-student-student” or “Teacher-student-student-student-teacher” and so on. In the small sample of classroom data I took, the only times the ping-pong pattern was disrupted was when the teacher was responding and listening in a non-evaluative way. In my Master’s dissertation I looked at one particular teacher and tried to analyze the listening in her classroom. Over the year in which I was taking videos, there was a real shift. The result was that the role of the teacher became much less important. There was this amazing lesson that I saw, where the teacher just wrote 1/2 plus 1/3 up on the board. In a sense that’s a closed activity, in most traditional classrooms it would just be learned by rote. But because this teacher had established a classroom environment where the children were expecting to have their say and question what each other thought, this extraordinary discussion ensued about how you might figure out the answer. It led to some really deep mathematics being discussed about fractions, and the children doing some really interesting work on different sums that might come to the same total. It feels to me like the difference here is in the classroom environment that is created as a result of the teacher taking different approaches to listening."