Backwards by Design

I want(would like) my students to have a core comprehension of the overall subject matter in the lesson. I don't want them to memorize processes or equations. I would like them to be able to understand where the equations come from and use their reasoning and logic skills to come to an answer. In the previous I feel that the vast majority of students are not learning math, they are being told math, and that to me the reason Americans have such a disdain for mathematics. Forcing students to work one way for no other reason than, "I said so" isn't teaching, it's telling. There are an infinite amount of ways to get from one destination to another, so why block all ways but one? Why mark off points on a problem when the student didn't do it exactly your way? Why not commend the student for finding another way? Why not show the rest of the class this newly found path?

With that said, accomplishing comprehension without telling students exactly what to do is going to be a difficult process and creating lessons backwards by design is going to be key. Knowing where the students need to end up and how they can get there will be tedious and take a long time, but I feel it can be done.

For lack of a better example, learning is like a road; I need to set up obstacles and road blocks along the path to get students to comprehend the lesson in a way that they understand. Teaching math in this manner creates meaning for the students since they come up with everything themselves. The students will see where the equations came from. They will see reasons the "because-I-said-so" teachers told them to do what they did and truly understand the material better than they.