As I changed my ways of teaching to include more student participation, problem solving, math thinking, group work, and use of manipulatives and models, a voice inside my head kept talking to me.
What you are doing is not real math, I could hear the voice say. It is frivolous to ask students to make charts and diagrams, more like art than math. Asking them to talk about their own ways of figuring things out is a tangent—you know the most efficient ways to do the calculations, so just teach them those and forget about their folk math. And getting them to work in groups to figure things out is a complete waste of time; it takes too long, and there is no way for you to tell what they are really learning in those groups. Probably they are not learning anything, and you have no control!
These new things will not help students pass the exam, the voice went on, and you know how important the exam is. You know what is on the test; drill on those things, and forget about the rest. You will just confuse the students more when you expect them to understand math rather than memorize, it continued. Just give up these new ideas, and it will be easier on everyone.
Working in these new ways just causes problems, I heard the voice say again. You know that your students have huge holes in their math backgrounds. When you stray off the beaten path in math class, you fall into one of those holes, and when you try to fill it in, you fall into another hole, and you can never get out. Furthermore, every student seems to have a different set of holes! The only way to get through the material is to stick to the path, and help the students figure out how to stay on the path to the end of the course. You know you're creating more holes by doing it this way, but it's the only way.
I dealt with the voice in various ways: I talked back to it, I found support in other teachers (both at home and away), I talked to my students, I made change slowly so I could see what was going on, and I stuck with it. I still hear that voice from time to time, but it is weaker, and I know how to make it quiet now—I point to the positive results I get when I ignore it!