Epsilonica has this post: Lockhart, Jenkins and compulsory maths about how he wishes he had been taught math.
I don't think that everyone needs to love math any more than everyone needs to be an artist or a musician. On the other hand, here are three reasons I think everyone should master some key mathematical skills and concepts:
- We are constantly bombarded by information and much of it requires some analysis. Sometimes, we need a solid grasp of logic, and at other times, we need to understand some basic statistics or probability. Math helps us make sense of many situations.
- Math is a great problem-solving tool. The more math you know, the more ways you can see that it can be helpful as a way to model real-world situations.
- Math is beautiful.
Points 2 & 3's implications: These are a bit trickier. You need teachers who really have used math and teachers who are passionate about math's beauty. Neither of these is a slam dunk. In my experience, most math teachers are academics who have lived their entire lives in schools. Some of them really love math, but most have never really used math to solve real problems in the real world to make a living. Not every teacher needs to have earned a living with math, but I think most schools would benefit from a broader mix of backgrounds. Some academics, some turbo geeks, and some practical mathematicians should be in every math department from high school on down to at least middle school.
I will complain about elementary school math, arbitrary timelines for learning algebra, and the inflated importance of calculus courses some other time. Those are big topics unto themselves.