My current philosophy about creating a productive learning environment is that students should teach each other. More often than not, students feel more comfortable talking to their peers than their teachers. The role of a teacher should be that of a facilitator, a guide for when people are lost. Not all students will have the same knowledge, but their input will be valuable for the learning experience.
The most effective moments in the classroom is when students work together. Before students have to take a quiz, I give the students a practice quiz. Students work on the quiz together, then we go over the problems as a class. While students are working together, I can focus on personal instruction. Individual students will have questions about the practice quiz, and those are the opportunities when students will finally “get” the material. Those opportunities arise more often when they first work with other students, because they often ask the question as a group.
Classroom management is very important, regardless of what the students are doing. Even when they are working in groups, it’s important that each group can function on its own. Even then, students need affirmation that what they’re doing is correct. Now granted, I certainly cannot make every student pay attention to me. There will be students who will look right through me. That doesn’t mean I shouldn’t try. As that old saying goes: I can’t make a horse drink, but I can certainly lead him to water. When it comes to Mathematics, I am an excellent guide in doing just that.