I was over at www.ted.com, watching a video about symmetry and group theory, and then I watched Arthur Benjamin’s video on how he would change mathematics education. He asserts that our mathematical hierarchy starts with the four processes and builds to the pinnacle of calculus. He claims this is an outdated pinnacle and we should be building towards statistics instead. Statistics is more useful and would help the entire population to make better decisions in their lives.
What should the purpose of math be? In many ways it is the same question as what is the purpose of education? Is it so we can grow up and get a good job, make good living decisions and pay our taxes? Or, as Charlotte Mason suggests, is it to have our feet firmly fixed in as many rooms as possible, to think and to fully live in a world full of ideas? Would it be possible to build to statistics and calculus, the useful and the inspirational? Hmmm. What about geometry? Can I just study that in depth? Perhaps, there is so much to study and learn, we all may just need different paths, and there is no one right sequence to follow.