What we do?
We have developed a method for writing mathematical arguments, that makes it easier for teachers to teach, and easier for students to understand. We started out at university level, but soon realized that there was a need earlier and moved to high school mathematics, and realized that there was a need even earlier, in middle school. Mathematics is a language, a way to write what we are doing shorter, and use what others have written before to make our own calculations even shorter. In all those abbreviations, we often loose our listeners. That is why we need to help them them see what we see, by explaining each step and by using a logical structure that helps others understand the solution. When students solve their assignments in the same way, and are forced to justify what they do, they quickly realize which things they have not understood.
Why we do it?
We do it because we can see that it helps students and they tell us that it does. Grades are increasing, and drop-offs are reduced. Because when you understand math, it becomes interesting.