I have never been a ‘lecture’ teacher, but I did too much taking. I heard from so many people, that we need to give less information and let questions develop instead of looking for one answer. I call it the ‘Dan Meyer effect’ @ddmeyer. He suggested we taking a problem out of a textbook and deleting all of the unnecessary information, and the question that we were guiding them to answer. Second, I was inspired by Peter Liljedahl @pgliljedahl and Alex Overwijk @AlexOverwijk to start with a rich task and let students work at vertical surfaces (search Vertical Non-Permanent Surfaces). It is important that the task does not have information that results in a single answer.
Dan Meyer says you can always add (information), but you cannot subtract.
My best classroom magical moments were when I sent my students to vertical whiteboards and posed an introductory task with limited information. Once you add information to a task, you guide student down a road you have chosen for them. When I started being tight with the information, students (and I) learned way more about the task and the mathematics. I also learned more about how students learned. Not all students approach problems in the same way, and often there are better ways of approaching a task than the way I would have guided them.
This past year, I started many days by sending students to the whiteboards with partners and posed a task. The discussions about the task and where they went from the little information I gave them, amazed me on a daily basis. I learned more from them then they learned from me. We need to set up scenarios for our students that give them the autonomy to be successful without us guiding them down OUR path.
We need to be able to stand back, make observations and facilitate the learning, so that our students can solve problems on their own.
Teachers need to be facilitators of learning, not lecturers.