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Why should most students even bother with algebra? Their parents almost certainly don't use it. It's more-or-less a hazing ritual. And it's entirely reasonable to not want to put up with being hazed.
Sure, I've got to understand algebra because I program computers. But not very many people do anything like that.
Imagine that instead I were opening a cupcake shop. High school algebra is full of problems like this one: My fixed costs for my cupcake shop are $100,000 per year. My cost of ingredients for a cupcake is $0.30, and I think I can sell 100 cupcakes per day. What do I have to charge per cupcake to have a positive net?
So, the algebra way to do this is to write out an equation, 100000 = 365*100*(c-0.30). Then solve for c. And if I were in this situation and I had been paying attention in high school algebra, I could transform this to c = 100000/(365*100) + 0.30. But if I hadn't, here's what I would do: I would say that a cupcake costs around $3, plug $3 into that equation, and immediately see that I'll be a bit short. So maybe now I have to try $3.25, which will work. Boom, problem solved, no algebra.
Bret Victor calls this process "scrubbing".
And, of course, there's basically never a situation where you need a quadratic equation. I guess figuring out areas/volumes, but the scrubbing approach will work just fine there.
Realistically, if I were planning my cupcake shop, I would use a spreadsheet, which unfortunately nobody learns in high school. That's too bad, because lots more people use spreadsheets than algebra.
When writing out equations using an asterisk as a multiplication symbol prepend it with a backslash like this:
"3 \* 4". Markdown treats anything between two separate asterisks as italics and backslash is the escape character.
Thanks.
It seems like part of the problem is that people don't really know or agree what mathematical education is for. If we knew for what reasons or purposes we were teaching everyone math, that might help us figure out what math they should learn.
It seems to me like various purposes for math education include:
More generally, people don't even agree what education is for. It could be:
Generally, all these goals are considered good, but sometimes they are in conflict, if you try to optimize for one of them too much. For example the first rule, in extreme, would require learning only details related to one's future job, nothing more; but students could learn more details, and have more practice when they finish the school. The second rule, in extreme, would require teaching everyone everything. The third rule requires a value judgement what makes a person good citizen, and in extreme, it would require focusing on those skills and ignoring everything else.
In many discussions about education, one of these ideas is assumed implicitly, and then there is a suggestion how to get closer to this goal... usually at the expense of the remaining goals, which is why other people protest against the suggestion.
I'm not so sure about that. They way computers are integrating into society it seems likely that the status of people who can't at least do basic programing will soon be similar to the status of illiterate people ~100 years ago.