What algebra course materials would you recommend, especially for mildly to profoundly gifted students?

I just heard from a friend tonight that it's usually the third Algebra book that works. This tells me that you're not alone in finding it difficult to choose the right Algebra book!

What you've outlined sounds very interesting, but also quite time consuming for you to put together. If you don't have a lot of time for teaching, have you considered an online class? Art of Problem Solving offers online group classes, as do several other online schools.

When planning on my own, I try remember something Maria explained to me awhile ago: there is a difference between solving problems and doing exercises. It's a problem if you don't know how to do it, and you must spend time to figure it out. A student shouldn't have to do too many problems each day. An exercise is when you already know how to solve the problem, so it is essentially a review. Standard Math textbooks contain many exercises (which can be boring and time consuming), but few problems. However, it is the problems that really push the student. Art of Problem Solving has more problems, but this is not right every student.

It should go without saying that each student's strengths and weaknesses are different, and I have found this is especially true in Math. I have one child who needs and likes to do exercises, and one who prefers to work on problems. This has resulted in each one using different curricula. One difficulty we've had is that Math is hard to do alone. It has worked better for us when I do it with them, or they work with someone else. As far as repetition goes, I've heard varying reports regarding how much a very gifted child needs. Some say less than typical, meaning that doing endless exercises can be detrimental by producing boredom and negative feelings about Math.

Instead of working in a textbook in isolation, sometimes watching a video (such as Teaching Company, Thinkwell, or Dr. Callahan- a homeschool Dad & Math teacher) can be enough human contact. I won't call it interaction, because even though you're watching a person, there's clearly no dialog! For Thinkwell videos, I know many parents either watch the videos with the kids and go over the problems together, or simply teach using the lecture transcripts. This is what I have done with my extrovert. Dr. Callahan is similar to Thinkwell in that it is video lectures, but rather than using propriety materials he uses Jacob's Algebra and Geometry books. He also has very quick email response if you ever have a question.

It sounds like you've got a varied curriculum planned out, though. One that won't leave your child bored. Let us know how it works out!