Symmetry is a great addition to the algebra pedagogy. I teach both the axiomatic and visual methods to my HS classes. I allow the students to choose the method that is easiest for them during a test. Most of them choose the visual method because it requires less symbolic logic and it takes less time to obtain a solution.

I am now retired and formerly taught mathematics in HS and Middle school. I am very impressed with Algebra Through Symmetry and regret that it was not available during my teaching years. Many of the students that I taught had extreme difficulty with the traditional axiomatic method. Based upon outside classroom contact with current students, they learn algebra quickly and easily by using the visual method.

If you find that your students just don't "get" algebra by classical methods, this approach may lead them to a fundamental understanding.

I use this approach in my continuing education program in high school. The standard way failed for these students. The symmetry approach baffles them somewhat, but they also find it fun (relatively) to try this. I consider this paper too short for a regular class, but great for shorter classes that can only cover some standards in depth, such as California.