At my school those of us teaching the same course teach the same thing on the same day. That's the way it has been done so that's how it continues to be done. I am stepping out of the box with my grade 10 applied class this semester, spiralling through the curriculum while the teacher of the other MFM2P class teaches it in a more traditional way. Anyway, not to rock the boat too much, I am teaching calculus by units and in the usual "this is what we are covering today" way. I do many investigations with my classes (I have 2 sections of Calculus & Vectors). I try to make sure that my students understand the why, always. But I still felt like I could be doing better, even within the framework that we are using.
Last year had added a "teamwork" portion to one of the lessons from last week - it was a more challenging problem that they worked on in groups on the big whiteboards. And, although this was not the first time I had done this, it struck me that this is what I am missing from the rest of my lessons.
These "teamwork" questions are harder questions, ones that make students think a little more, stretch them. They are the questions that when assigned for homework either get skipped or students copy a solution without understanding it. But they are the kinds of questions that students should be doing. The ones they must do. And now they are - every day! After we have gone over whatever concept we need to, the whiteboards and markers come out and the conversation gets lively. It is fantastic! Whiteboards are magical things in a math classroom. They give students permission to make mistakes and to try different ideas (and to draw pictures). They let students stand up, crowd around and point at what is good, at where there is a flaw in logic at something they don't understand and talk about the math!
The added benefit to doing these "teamwork" questions is that it is (hopefully) helping prepare students for the unit tasks they write, usually the day after the unit test. I have been asked for years how students can better prepare for tasks and I think I have finally found the answer. Clearly I am a slow learner (!) but I'm very happy that I have finally figured this out and have found my groove in calculus.