Gifted Issues Discussion homepage Forums Recommended Resources Precalculus text for independent study?

I don't want to derail this thread, but I'd love to hear/discuss (maybe in a new thread) your thoughts about this, 22B. DS9 has taken precalculus, but is a very different character, I think, from HowlerKarma's DD, and I don't see him starting university before 17 or 18 probably. So how to make this work well has been exercising us.

I am sort of shocked that anyone would assume that my 13yo is not up to the task of a major in applied mathematics on the basis of "only" starting as a regular freshman-- in calculus.

As to those of you with young children who are very accelerated now and you think that you can delay college until 18 - good luck with that! That appetitie for learning doesn't fade away. In our experience it gets stronger every year. I had plans of gap years, fifth years of high school, etc. My son did not.

My DD is, in fact, way ahead of most of her peers across the board-- in any area where she has had exposure, I mean. We supply her with college level textbooks and she eats them up. Current obsessions include the historical development of psychology and sociology, musical instrument acoustics, neurology, and poetry forms. Oh, and literature, which is sort of a given with her. She has been pretty hungry for deeper learning experiences for 4-6 years now, and we've indulged it via afterschooling-- in areas where she isn't likely to encounter the subject later in a mandatory course somewhere. She is being raised by two experienced college advisors, after all.

She actually UNDERSTANDS the AP Physics B course that she's taking, and completely retains what she learns, which, if you check out the discussions that Val and I have had about that class, is kind of astonishing in any high school student-- regardless of age. Again, it's because of the limitations of her school environment that we opted to have her take physics but not chemistry (well, and also because quite frankly, we didn't think that the chemistry teacher was actually qualifed to teach our DD that material-- more on that in a moment), plus we wanted her to have an actual laboratory experience.

She can be highly autodidactic, but it's very spotty and idiosyncratic. Not exactly a good way to establish a foundation for further study.

The professors that DD talked with did go through the three-or-four year plan with her on paper as to math coursework. They know that she aspires to a grad program-- there was some discussion of doing a 5y M.S. program there.

I understand the cautions being expressed in Bostonian and CFK's posts, but for my own DD, she will tolerate one run through "learning" calculus, and it had better be a good one, because remediative instruction is something that she tolerates very ill... and that's a gross understatement. She's a mastery learner, and high school is NOT set up for kids like her. High school now is just a continuation of K-8. It's more spiraling, more 'skimming' the surface, and more test-prep. Sad, but true.

She will earn college credit next year for both English Composition and for Intro to Statistics. We've deliberately NOT had her earn credit via AP examinations because that isn't why she's taking AP courses. She needs NO help graduating from college any earlier. But she definitely needed more challenging material. She will-- probably-- place out of lower-division coursework in many, many areas as a college freshman. We just don't want her to accumulate CREDITS while doing it. It's an asynchrony/maturity issue, and our logic is exactly like 22B's here-- we want to narrow that gap any way we can.

Hiring a tutor is a reasonable idea-- might have DD put out some feelers this summer in her internship and see if she can connect with an math/stats grad student locally who'd be willing. The reason why I'm willing to teach her stats but not precalc/calc is the same one that Colinsmum alluded to-- my background supports stats. I know it inside and out. I know precalc/calc about as well as a good student who has taken the courses and done very well at mastering the material in them. That's not always good enough with DD-- this is the other problem that we (increasingly) had with the math instruction at the high school level-- knowing what's IN the book/course is one thing, but knowing the subject inside and out is actually needed for kids that interact with the subject in ways which are beyond the scope of the class, but evidently necessary for them to scaffold the material.

THIS is why my DD has such trouble being an autodidact for some subjects. She needs the interaction with an actual subject expert that understands far MORE than what is in the book. I can do that with stats, but not with calculus. She has trouble with any teacher who isn't a subject expert because of the way she learns.

I'm very frustrated by this situation; her school won't actually teach the kids math in a meaningful way, and her dad doesn't have the time/inclination. His background is MORE than up to the task. Mine isn't. But he refuses to sacrifice his free time to do it.

Yes as to what Bostonian wrote. My son started taking grad courses his first semester as a freshman because he was so far ahead of the game going into college. He will complete his BS in three years but will have over 15 grad courses on his transcript by that time (if all goes as scheduled). Grad school competition can be fierce. There are far fewer spots than for undergrad. And even fewer that are funded.

Edited to add:

Suggestion for HK or anyone else in the same situation: go thru the college course schedule and plan out the three years. See exactly how many course she can fit in to that schedule (keeping in mind that not all schools offer all courses every semester). See if your child is where he/she needs to be at the end of that time in order to get where he/she wants to go after.

I may try the technique of using AOPS for me to learn it well enough to teach it to DD using the Lial text (or something else that seems to suit her).

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.

Frankly, we'd rather that she spend 5y on an undergrad degree so that we don't pay quite so much for 'exploration' (which is necessary for her).