Two things I’d say. It rather makes me despair to see people talk about algebra as though it was advanced mathematics. Algebra is hardly even a branch of mathematics; it’s just a notational tool to allow you to move beyond arithmetic. It’s not quite true to say that it’s impossible to do any maths more advanced than arithmetic without algebra; the ancient Greeks managed without, for example. But it’s certainly completely central to the way maths is done today. Unless you think that high school should be satisfied with achieving no more than basic literacy and numeracy, passing a one-year course in basic algebra is not an outrageously high standard to hold for high-school graduation. Depending what you think a high-school diploma should stand for, it might even be an outrageously low standard. Judging by the article, this girl who couldn’t graduate because she didn’t pass algebra actually didn’t have basic numeracy skills, which means both that she shouldn’t be qualifying high school and that the school system has competely failed her.
The other point I’d make about the ‘I’ve never needed to use maths since I left school’ argument is that we all forget a large proprtion of what we learned in school unless we use it frequently. I did maths to quite an advanced level at school; I did two maths A-levels, which, for non-UK readers, meant I got as far as complex numbers, basic calculus, polar functions, basic mechanics, some statistics including things like Poisson distributions.
I can’t actually do any of that maths anymore. But having done it does mean that I’m not intimidated by equations; that I know what a standard deviation is, and a tangent and a function, and what binary numbers are, and what calculus is useful for so on. It’s not enough to enable me to do anything much, but understanding the concepts makes it easier to read popular science books, for example, or to make some kind of judgement about how useful a statistic is.
I also think that as a result, I’m much more comfortable than I would otherwise have been doing the kind of maths that *does* come up in everyday life. It’s good that schools teach a bit more than the students will really need, because hopefully that means the important suff will have a chance to really get properly absorbed.