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I don't think Algebra is necessary for the following reasons:

  1. It can be learned online or by reading the right books. 
  2. The way algebra is taught is terrible: they make you learn boring theorems and theory out of context, rather than making you discover algebra through your own research.

Unfortunately, education tries to kill artistic talent in kids (it failed with me) and algebra is one of the medicines used for that purpose.

Also the curriculum would greatly benefit from discussing applications and fun facts (such as 1+3, 1+3+5, 1+3+5+7 etc. is always a square), history or modern problems (such as the 4-color theorem, or the fact that every integer can be written as the sum of 4 squares, but not three), ultra-fast convergent series for Pi and its application in finding related magic numbers and cryptography or creation of good random generators (and discuss why Excel is bad at that)

If the only maths that I ever had was from high school classes, I would hate mathematics. Ironically, during the algebra and math classes, I never listened to the teacher, but instead did my own research which was much more advanced than classroom algebra. Not that I was smarter than other kids, but different, and fascinated by some stuff I read in well written mainstream math books, and technical books from other countries (Russia) putting an emphasis on different topics such as continued fractions or inequalities, in some exciting ways.

The root causes for the failure of algebra / math teaching are

  • The school system is very bureaucratic. It attracts teachers who can survive in this big bureaucracy (I could not): these teachers are very different from mainstream people, the school staff is not diversified enough and the system tends to eliminate the more creative people. Maybe that's why "math" is always associated with "geek" in US (although not in Europe) - but it does not have to be that way.
  • Even at the University level, very few students learn or discover applied maths and the fun facts / interesting topics mentioned above (continued fractions, sums of squares etc.) As a result, these topics - that could spark interest in algebra for high school kids - are not taught in high school. 
  • People who know how to get kids interested in maths are sometimes (always?) anti-bureaucratic, highly paid individuals (because they know how to apply analytics in many different contexts and are highly sought experts with both broad and deep math knowledge). Also, they might have very poor teaching skills, though they could improve on that. As a result, they would never accept a job as a math teacher, and they might even be turned down if they applied! But they could help curriculum developers in a consulting role.

Related article: How maths should be taught in high school

Anyway, here's the New York Times article:

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

Adam Hayes

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

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Comment by Ralph Winters on August 16, 2012 at 7:29pm

Vincent.  I think you place too much trust in the machines.  Even if you do not know the intricacies of GLM, you still need to utilize the fact that X**2 is typically greater than x*2 when developing or interpreting a statistical model, a skill that is basically covered in an algebra curriculum (inequalities).  I would hate for people to lose that.

Comment by Vincent Granville on August 16, 2012 at 2:14pm

I think Algebra will become something like Assembly Language back in 1970: something fantastic that everybody was learning at school 40 years ago, but that got replaced by compilers (AKA algorithms that translate assembly language into high level languages such as Python or Java). The need for Assembly programmers disappeared in 1980.

The same thing is happening to Algebra. Only a few experts need to know the deep mathematical details. In the future, you'll be able to do very advanced statistical analyses thanks to improved stats software - even if you have no idea what an eigenvalue is. Indeed, I'm one of the guys trying to develop such statistical software solutions. The GLM (General Linear Model - AKA traditional regression) is dying fast, it will be replaced by something else (I'm working on it!) that does not require deep mathematical knowledge.

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