Yes, you CAN teach the advanced subjects in your homeschool if you want to, but you don’t necessarily HAVE to! You can choose to work ahead, learn the subject, study it in advance, and have your children learn it, but you don’t have to do that. There’s a huge difference between teaching and learning. What you’re trying to do is to get your children to learn. Whether you’re the one who teaches it or not is not nearly as significant as whether or not they might learn it.
If parents don’t know how to teach piano, they hire somebody to do it. The child will go to piano lessons, take lessons from someone else, and practice on their own. Parents wouldn’t know what they’re supposed to do for studying piano, but parents should oversee that they practice what they are supposed to.
My family studied calculus and physics in the same way in our home. I bought a self-teaching curriculum from Apologia for physics and a self-teaching curriculum from Saxon for calculus. The kids would get their instructions either from the book or the CDs, getting the instructions from someone else and learning independently. My only job was to make sure they did the work and to oversee their daily work being done. With calculus, you can’t hear the results and there’s no piano recital at the end of the year, so I would use the answer keys and give the tests. Of course, it’s hard to correct a test like physics and calculus because I didn’t know what the words and symbols meant; I had to look at the answer key and at the answers that my children gave me to make sure that they were exactly alike. If there was a discrepancy and my children were absolutely certain that their answer was correct, I was thankful that it was a homeschool curriculum because they would then be able to call the 800 number.
We also learned Latin in our homeschool. My children and I did not know Latin beforehand and we used the Latin Road to English Grammar. The first year we studied Latin, I studied ahead, stayed two weeks ahead of them and actually did learn the language! The second year we did Latin, I wasn’t as excited about it and learned along with my children. By the third year, I didn’t want to do it at all. The children still wanted to, so they continued with their Latin studies independently just like physics and calculus.
Even though I didn’t know Latin, physics, and calculus, my children both went to college well-prepared in ALL of those subjects. One of my sons is an engineer and takes physics, calculus, and advanced math for fun in college and still earns straight A’s. My other son really likes the languages so he was well-prepared with our Latin studies.
Remember that self-teaching is the goal; not you teaching it to them, but your child teaching it to themselves. For more information on homeschooling high school, check out http://www.TheHomeScholar.com or pick up one of my Kindle books, such as Planning High School Courses: Charting the Course Toward High School Graduation.