It's always fun to watch the reaction when I describe how things are being run in my classroom this year. After describing the work that was done over the summer to carefully put together the worksheets, and how the worksheets are designed to lead the students through the material, and how I go from group to group listening to the conversations and helping guide the discussions as necessary, I still regularly get one of the following two questions: (1) "So you're not teaching them?"; (2) "So you just sit there all day and don't really do anything?"
I've learned to translate the actual meaning of these questions as, "So you're not lecturing?" The answer to this question, of course, is, "Yes, I'm not lecturing." However, for those of us who were taught almost exclusively by means of being lectured to, there is this sense that if there is no lecture, there is no teaching going on. And I used to be very much of the same opinion. Clearly I have changed my mind and have come to understand that while lecturing is one method of teaching, it does not guarantee that any learning is going on. I have seen ample evidence of this over the years. Specifically in math, I have seen both of the following on a far-too-regular basis:
(1) Students (and parents) who complain that questions on a test were "different" than those that were assigned for homework, meaning they expected the questions on the test to be identical to those that were assigned for homework, except with different numbers. This, of course means that the students didn't actually learn the concepts...they just memorized the steps involved with the problems that were assigned. This is how many of us got through many of our classes in high school: just memorize what the teacher gives you, and give it back to them on the test. Then, forget it almost immediately and start memorizing the new stuff. This of course leads to...
(2) Students who forget the material they were taught last week/month/year. Ask almost any math teacher how they spend the first six weeks of the school year, and you will get pretty much the same response: reviewing. And if they are feeling particularly honest, they will admit that what is really going on is reteaching, since the kids don't remember very much from their previous math courses, despite earning an A or a B in the course. The refrain "I've always gotten As and Bs" is far too common, and most of the time it's honest. However, the grade does not reflect how well the student has learned the material...only how good their short-term memory is.
In short, in my experience, lecturing is good for short-term memorizing, but not for long-term learning. So how do we actually learn things to the point that we really understand them? The answer to this is easy if you stop and think about it: learning and understanding rely on struggling with the material yourself, reasoning it through for yourself, discussing the topic with others who are struggling with it as well, discussing the questions you have with an expert, and then practicing a few exercises. Think back: if you really understood a concept in math or science, there was no need to do a lot of practice. In fact, if you understood the material really well, the practice got annoying. On the other hand, if you didn't really understand a topic, then the late exercises from the homework were just as difficult as, if not more so than, the early ones, emphasizing the fact that you hadn't really learned the material, and no amount of extra practice was going to change that.
So, as I sit at the tables in my classroom with my students, listening to them as they discuss their successes and struggles with the assignments, responding to the questions they have (usually with a question in return to help them finish the discovery they began), no, I'm not lecturing. But they are most certainly learning. And since I'm the one who put together the worksheets that are guiding their discovery, and since I'm the "expert" to whom they are bringing their questions, then ultimately I must be the one teaching them. But in addition to teaching them some math, I'm also teaching them how to learn. Sounds good to me.