...In math, not every student needs advanced mathematics. I would even be willing to go so far as to argue that one's mathematics could stop before Algebra 2, depending on one's goals. For many students, a better understanding of topics like percentages and ratios would be more useful than topics like proofs of the quadratic equation. However, in our technological era, there are many thought-processes to be learned from more basic Algebra that would be useful. For example, the concept of variables is vital for understanding spreadsheets. Also, Algebra opens up a whole new way of thinking. Taught correctly, it challenges the student to think about the general principles behind mathematics and understand them in a much deeper way than possible without the abstract concepts that Algebra teaches.
I think spelling is vital. It is part of speaking English properly. As human beings, we need to communicate. One might as well say that Chinese is the same if the characters are formed wrongly. I'm open to spelling reform, but the idea that we depend on computers to tell us how to spell is ridiculous. I recall reading a paper not too long ago in which the student talked about how something was "ridged" rather than "rigid" and I had no clue what she actually meant. Spelling is vital to clear communication. I will agree that the way we teach spelling is ridiculous. Seriously, we memorize a list, barf it out on a spelling quiz, and that's it? Even many of the teachers who use this method admit that kids forget within a week how to spell the words. Oddly, this doesn't make them question their methods. Here's an idea: have students regularly use their new words. Make spelling part of vocabulary lessons and have students actually write!
As for handwriting: I type a lot. I have really awful handwriting. But, there is real power in handwriting. When we ask students to write things down, they internalize them. Not much time has to be spent in handwriting, but it's interesting to note that boys in particular find it easier to begin writing if they use cursive. They don't develop fine motor skills as quickly as girls, and this puts them at a disadvantage in language arts. If we use cursive, boys don't have as much of a disadvantage as if we do not.
Also: I'll just note that if I want to remember something, I write it down. Once I write it, it's in me. If you tell me to meet you at 3:00 I'll forget. I could even type it and I'll forget. But, I could write it on a random scrap of paper, and it's in me. I'll remember. As I've learned Chinese on my own, I do make flashcards for my vocabulary, and they are typed, but I learn the majority of my words by writing them down in a sloppy, disorganized notebook. If I write them once, most words stick.
What needs to change is how certain subjects are taught because the way we do it now is useless. I mentioned spelling. Another is English. Although English should include literature, I really question why it doesn't have a lot more nonfiction. Seriously, what do most people read in their professional lives? I remember taking some history courses in college and we read some nonfiction works (not textbooks) to learn the subject: a biography of Hitler, a memoir written by a soldier in the First World War, a book written by Hitler's architect (Albert Speers), and a variety of others. More importantly, why are we having students write fiction? Very few will actually become authors, but many will have to write nonfiction papers.
As for math: part of the reason people think Algebra is useless is that we have focussed too long on algorithms instead of understandings. Who cares if I can do long division or factor a polynomial if I have no clue why it works or what it's good for. I had a discussion today with some math teachers about the Pythagorean Theorem. One of the teachers had no clue what it was good for, though she knew how to use it. When I started drawing squares around the triangle at the center of this theorem I seriously rocked her world. She had never seen anything like it, and had never even thought to wonder why each term in the equation was squared.
Math education needs to emphasize alternate methods of solving problems....