I just acquired the art of problem solving prealgebra book.
I would like to ask, how does one use the AOPS books, are they meant to be supplementary to a full textbook? Or are they used for introducing new concepts that you would have leant in a textbook etc. I would like advice on how to get the most out of the Art of problem solving books, as a self learner that is.
Soon I am also hoping to use the AOPS Introduction to algebra book alongside a full textbook on algebra 1 once I am finished with prealgabra.
Also, would anyone be able to recommend a complementary full algebra 1 textbook to buy for my AOPS introduction to algebra book?
Thanks.
[Disclosure/context: I teach online classes for AoPS which use their books as the textbooks. However, the opinions expressed here are my own and I am not speaking for AoPS.]
The AoPS subject books (Prealgebra, Introduction to Algebra, etc) are meant to be stand-alone textbooks which you can learn from without using another textbook. That said, they are intended for dedicated students who will work hard and learn relatively quickly. They do not have many routine practice problems, and instead have mainly more challenging problems which force students to think hard and explore the concepts more deeply. A weaker student may prefer a more traditional textbook, to use either instead of or in conjunction with an AoPS book. AoPS books also tend to be less useful as definitive references than traditional textbooks: you will find fewer well-organized statements of important facts and identities and theorems in them (though I think this is more relevant to the more advanced books than it is to Prealgebra).
To get the most out of an AoPS book (or pretty much any other math book), do the problems. Seriously, do them. I can't stress this enough. Spend a good chunk of time trying all the problems at the beginning of each section, before you move on to read their solutions. Do the exercises at the end of each section, and the review and challenge problems at the end of each chapter. There are a lot of problems, and some of them are quite difficult, so you should not expect to be able to solve every single one of them. But you should take the time working on the problems and reviewing the material until you can solve most of them.
I would also recommend you get the Solutions Manual which has full, detailed solutions to all the problems, if you don't have it yet. That allows you to verify your solutions and also learn a lot more by reading solutions that might approach the problems in different ways than you did. (Just resist the temptation to peek at the solutions before solving or at least working hard on the problems on your own, since you'll learn a lot less if you don't work through them on your own.)
If you learn better from oral instruction than just reading a book, there are also videos on the AoPS site which are associated with each section of the book which you can watch to see Richard Rusczyk explaining the ideas.