Honestly, there's a better solution to this issue. The question should be tackled from a different angle: how is algebra (and all the maths) taught???
My wife is a math teacher. She loves the actual teaching part--WHEN SHE'S ALLOWED TO DO IT THE WAY IT SHOULD BE DONE. But with state- and federally-mandated testing of a huge variety of topics, teachers are forced to cram as much information as they can down students' throats. They *must* "teach to the test" in order to keep their schools alive.
Teachers don't get the opportunity to give the students THEIR opportunity to understand the concepts behind the algorithms. They are so time-crunched with the amount of material they need to cover that there isn't time to insure kids understand the "why," so they are obligated to get them to rote-memorize the "what and how" so they can pass their test.
Allow teachers to use the methods they're trained at, are expert in. Allow teachers to put responsibility on the students and parents (another topic entirely, but a very salient one!) for the students' learning. Allow teachers to use research-based teaching methods, rather than just rote memorization "because that's the way it's always been done." Let teachers effing TEACH. THEN this whole question will likely go away, because kids will be able to LEARN algebra--to UNDERSTAND it.