We started the topic of Venn diagrams in Math 9 this week. In a class of international school students (and perhaps __any__ group of students) the range of knowledge on a given topic is all over the place given their different backgrounds and school histories.

The teacher-me of ten years ago would have done an overview of the concept of a Venn diagram. I would have started by asking questions about different parts of what was there in a Socratic fashion. It would have been full of questions that I had written down in my lesson plan designed to get students to think deeply about the content. Based on asking questions of a sample individual students, I would have gotten an idea of what the class knew. The students who knew the material already would either raise their hands and try to answer every question, or stay silent and answer every question on the worksheet in a matter of minutes. The students that didn't know the concepts, but wanted to, would likely stay quiet until either I approached them or until they could ask a friend for help. The students that were used to being defeated by math class would pass the time by doodling, pretending to be involved, or by distracting their friends.

This isn't the teacher I am today. I've written about the power of social capital in the room before, so this is nothing new, but I don't tend to do the 'topic overview' style lesson anymore. The one or two students that nod while we go through material aren't representative of the class. The strength of my experience in the classroom is being able to observe students working and know what to do next. I can't do this while standing at the front of the room and speaking.

My approach now is, whenever possible, to make an item of the topic a conversation starter. I gave them this image of a Venn Diagram, which appears in a collection of questions from old New York State Regents exams at http://www.jmap.org:

I gave them a series of questions that required them to figure out what they remembered, knew, or didn't know about the topic. Students made arguments for the definitions. Their disagreement drove the need for clearer definitions of what the intersections of the sets meant, for example. I was free to circulate and figure out who knew the concepts and who did not. Many of the issues that arose were resolved within the groups. Those that still had lasting confusion were my targets for conversations later on.

As I've added years to my experience, I've become more comfortable relying on this system to drive what happens in my classroom. Every time I get the urge to just go over a topic, I remind myself that there's a better way that involves students doing the heavy lifting first. There's a reason students are in a room together for the purpose of learning, and that reason is not (all) about efficiency. Humans are social creatures, and learning is one of those processes that is driven by that reality. There are moments when direct instruction is the way to go, but those moments are not as frequent or necessary as we might think at first.