The plan is for her to take AP Statistics next year via her high school-- which we already know means that I'll be teaching her the material, since there pretty much ISN'T any real interactive instruction from them.
That "Khan Academy" model, by the way, really doesn't work for my DD. She hates canned instruction. This is why distance coursework isn't on the table, basically, unless it's a pretty high quality program with a good reputation for live instructional sessions.
We're hoping that she could test out of MTH 111/112 as a college freshman (or earn college credit) and go directly into the calculus sequence, but as others no doubt are aware, much of the "traditional" Algebra II... isn't-- at least not anymore. Ergo, I don't think that my DD's Algebra II foundation is all that secure in terms of just skipping precalc.
Our goal-- precalc via independent study or a college course the summer after she graduates (this summer she is working 8-5 M-F, so not so possible).
I can help, but I'm not well equipped to actively teach this material the way that I am statistics-- I'm an analytical chemist, not a physical chemist. Statistics, I know as well as mathematicians who teach it. Calculus and fancy algebra, not-so-much. So any text would need to be solid enough that I can use it to rejuvenate anything that I don't remember, too. My foundation obviously is radically different than DD's since it was many many years ago, and there is no doubt that it's been 20 years or more since I have thought about some of it.
The college program that she is interested in has the option to do a 3y Math BS, but the catch is that she must start with the calculus sequence as an incoming freshman. This is appealing since it: a) gets her into upper division coursework more rapidly within the major, and b) leaves her some breathing room to explore other interests and probably a double (?) major, even if it's in something in the humanities, where course scheduling becomes a nightmare with a STEM major and leads to incompatibilities.
So that, in a nutshell, is why we're looking and a bit more detail on the nature of WHAT I'm after. It has to be something that I can use well enough to teach her or work alongside her, and it has to be written in a sufficiently engaging style that she can read and enjoy it, and the problems have to be complex enough and interesting/quirky enough that she'll willingly do them.
SHOWING derivations is probably preferable to either extreme-- just giving them out like postulate candies, or asking students to derive all from 'first principles.' DD is neither type of student; she's quite mathematically strong, but not "mathy" the way some kids are.
