I think my very first post on this thread I noted that algebra is an abstraction of mathematics. It is one of the first, if not the first, such "abstract" thinking exercises one finds in one's schooling. It is not about 2+2 being 4, it is about what we can say about numbers in general and their relationships with one another and how they obey certain rules.
I think ideally everyone should be able to learn basic algebra, but perhaps requiring it for graduation is not something the students and schools are prepared for. I know everyone didn't need algebra to graduate when I did in the 80s.
SD
In the 70's we had to have at least one semester of algebra. I didn't do well in high school math. I was interested in other topics. But, I went to college as a non trad, started at 30, and excelled in math, 4 semesters of calc, diffEQ, etc. I was pleasantly surprised. What an esteem booster to have graduated from college, single mom of 3, and maintain 3.4 gpa in engineering. Several posters earlier on this thread talked about teaching methods deteriorating. I agree. My HS geometry teacher gave us a test, told us not to cheat, and walked out of the class for the rest of the period. That was typical. What did she think 15 year olds were going to do?
This made me think about some words I hadn't considered in a long time: associative, commutative, and distributive properties. Those are probably the first abstracts I remember being taught.
-PJ
When I graduated back in the Stone Age, everybody that had any ambition to go on to college took algebra and geometry. Students who were really serious, of course, went on to trig/pre-calc, and calculus. However, the high school also offered "Business Math" for students who had no college or skilled-trade ambitions. Perhaps a multi-tiered secondary educational system is the correct solution. A large number of kids would be left behind, but c'est la vie. Better yet would be a voucher system that allowed a marketplace of private schools compete with a variety of approaches to secondary education.