“Listen to your students.” That was the crux of the message that I heard from Dr. Les Steffe during his 2-day visit at the AIMS Center. The context was mathematical, though I am sure the message can be applied more broadly. Dr. Steffe has spent the last 50 years as a Math Education Researcher at the University of Georgia. What makes him extra special is that he is always involved in the child-side of the research. He personally goes out into classrooms and teaches the students and coaches his graduate students in the process. This is not common practice.
So, what does it mean to listen to your students mathematically? It means that you know your students’ abilities and their means of operating with various materials. It means that you can think like the student might think and predict their activity. Then, upon some experience and content knowledge of your own, you can make strategic decisions about what to do next with the student. The goal is to provoke more sophisticated ways in which the student operates. As a teacher, we don’t want to tell a student what to do or how to think. We want to engage in mathematical activity and conversation with the student.
What kinds of experiences and content knowledge would help us as teachers to listen to our students? This is where the volume of research on the mathematics of children comes in. We know from the research that it is not just about the task(s) placed before the student. Students will access a task differently depending on what mental structures they have built. Students may use their environment, their fingers or other tools to make sense of a task. Students may use their fingers as replacements for items to be counted, as substitutes for the items to be counted or as a way of tracking their counts. All of these are significant clues as to what the student understands. I look forward to exploring some of these with you in future blog posts.