I like math. I do. But at the time that I learned calculus, I was fixated on passing the class (with a host of other more-pressing life concerns weighing on me) and not on "understanding the deeper mathematics." I then went on to other things, most of which required advanced skills only in statistical methods and differential equations. The math required by my spouse's graduate physics coursework was downright
terrifying. Then again, I have math phobia, and it all started in high school, but culminated in a spectacularly bad calculus experience. Too long a story.
I have certainly taken graduate mathematics coursework and done well with it-- ironically, in spite of my apparent struggles with calculus as an undergraduate, I have been "the mathy one" at every single professional placement since then. I'm not particularly "slow" as a math student, but I'm an applications and modeling person by nature.
Anyway. I'm not so sure that Bostonian is completely understanding my point that my DD, while not having any particular overwhelming DRIVE for math competition and the like (again, there are other factors here that are in play), is also not a typical but bright math student. That kind of textbook seems to work tolerably well for her
as a support, given her learning style. She has a disconcerting tendency to interrupt straightforward instruction with questions that require a lot deeper understanding to answer (they otherwise generate; "WTH?? Why are you so off topic?"). I've even fallen prey to that myself in subjects like psychology, history, and econ with her, where I simply didn't know WHY she was asking, or how it connected with what she was supposed to be learning... so I've learned to respond carefully with a wary... "Why do you ask?" This is why I say that she both is-- and is not-- an autodidact. She learns FROM other people, mostly, but not in the ways that they necessarily intend.
Being something of a polymath myself, in most subjects this is fun, but with calculus material, I confess that I'm intimidated. I WANT her to have good answers to her questions, and to be able to probe her understanding Socratically, because she seems to need that in order to construct her own understanding-- it's about scaffolding for her.
Ergo-- it seems as though the AoPS text might be precisely what I need to understand the theoretical underpinnings well enough to teach my DD the precalculus concepts solidly in a way that suits HER needs. The other option is to look for a tutor that
has graduate-level understanding. I'm probably far more concerned about my own background here than is truly warranted, but this is my math phobia surrounding that word "calculus" talking. LOL.
Before anyone jumps to conclusions about her math acceleration not matching her LOG, please recall that she is one of those rare kids who seems to NOT be either "mathy" or "science-ey" or "verbal" but
all of those things (and more) in equal measure. She simply doesn't have enough hours in the day to pursue
everything that she's into, which makes her incredibly sad.
We've not encouraged her to throw away any of those interests, because we can't (yet) judge which of them are most likely to bear fruit. Well, okay-- the Pokemon obsession had to go.
She thinks math/music/?. Several years ago, she thought perhaps physics, but she really doesn't enjoy classical mechanics (hmmmm... maybe because it was algebra-based... who knows). She likes math very much, she's very strikingly good at it, and she likes knowing it inside and out-- well enough to bring a variety of approaches to bear in teaching. She's quite gifted as a teacher. (She is one of only 16-18 kids chosen to act as a peer tutor in a system of ~30K, for whatever that is worth... and I think that DOES say something about her abilities to understand the math, not just her soft/people skills, because she's regularly in high demand and has been asked back over and over again. She regularly solves problems that stump the teacher-- often using her own methods to do so.) All of that to say that we don't KNOW that she'll stick with math. It just closes the fewest doors on likely interests for now, and lets her get into a collegiate environment and give her a chance to explore interests with electives from across the campus for a year or two while she builds math background.
