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

We've looked at those options, and they don't exist for her locally, believe it or not. Well, not meaningfully, anyway. They're actually high school courses administratively under the aegis of the local CC. On the genuinely college-level front, she can enroll as a non-matriculated student, (assuming that she can get a seat in a popular/high-demand course, which has been problematic), but the costs are actually MORE than if she were a regular college student, since our local district (and also her school's district) don't participate in the actually-on-college-campuses-DE program statewide, which also isn't great from a financial standpoint. It's cheaper to send her where we're looking than to let her take three classes at the local Uni as a non-Matriculated student. The size of the local uni is also a concern, as class sizes are in the 150-300 range.

Honestly, high school level coursework isn't what she needs. We're hoping that she can put up with it one more year-- during which time, yes, she'll be taking dual enrollment classes (but here in OR, those are not taught ON college campuses, but by high school teachers), but also four classes which are a total waste of her time, but necessary if she is to stay enrolled with them.

We're all very very weary of playing the game imposed by the K-12 system with it's notions of what constitutes academic challenge and depth. Even the DE-qualifying coursework that she's taken (and she's already had 4 of those in high school-- we just didn't pick up the credits because they don't advertise the program) were no better than anything else. It's appalling-- we've delayed DD graduating from high school by about a year, but doing more than that seems actively harmful at this point. It's not giving her a chance to actively explore much of anything, and it piles on the busywork instead and pretends that makes thing "more challenging." All it really does is starve DD for what she actually needs, and punish her for any divergent thinking via her latent perfectionism. They just fired the sole teacher who actually taught at the genuine DE level. Not that I'm feeling bitter or anything. :-/ I know for a fact that DD's curriculum is actually slightly MORE demanding than what her local brick-and-mortar peers are seeing, so it's all K-12 schools, not just hers... I mean, the lack of direct instruction is particular, but the level is slightly better, so it's six of one... half a dozen of t'other.

All that high school has done (even AP + honors, which are the DE options) is make her say "Wow, bummer THIS class sucks so much. The subject has such potential, too..." She's always so excited that the next year might be "real," and elated when she reads her new textbooks... then let down when it's the same old low-level assessments and discussion about how to memorize material. It really hasn't solved anything-- it's made the multipotentiality problem the same or worse. Enrichment is no longer enough, and we're approaching the breaking point again (I can tell, knowing my DD). Talking to an enthusiastic and welcoming Math department chair was the first glimmer of academic HOPE that I've seen my DD have since 9th grade. I felt faintly horrified that she's ordinarily so dejected about school and so inured to to idea that she learns NOTHING.

Seriously, guys-- we HAVE thought about this. A lot, even. We're also very familiar with the system, having been college faculty (in STEM).

It's why I tried to explain initially WHY I needed advice on particular materials and what type of learner my DD is, rather than asking if it is a good plan to start with. I realize that the unsolicited advice is well-intended, but we really wouldn't be doing things the way that we are if we had good alternatives.

Has occurred to me! I think all four of us would learn a lot, and not all of it would be to do with mathematics ;-)

OK. After the Brown book I suggest a relatively short book

http://www.amazon.com/Analysis-Elementary-Functions-Robert-Sorgenfrey/dp/0395340578
Analysis of Elementary Functions
Robert H. Sorgenfrey and Edwin F. Beckenbach

that provides a bridge from trigonometry to calculus, and/or "Modern Introductory Analysis" by Dolciani et al (there are several editions).

This reminds me that I meant to say: I don't know where "proper" analysis, the sort I learned in the first year at university, gets taught in the US high school/university sequence, but I think your DD might really appreciate learning it alongside calculus, or even before, HowlerKarma. School calculus (and this certainly applies to the AP calculus syllabus, which I have looked at) tends to nod at continuity and the definition of derivatives as limits, and then expect you to get on with it by rote. Tom K"orner's notes here
https://www.dpmms.cam.ac.uk/~twk/C5.pdf
are a good guide to the stuff I'm talking about, and his "Further Reading" section at the end recommends some books.

Excellent-- THANK YOU. I didn't have the terminology, but this is something we've been concerned with in all of DD's math coursework thus far. There has been an elimination of much of the deductive reasoning work that used to be so much a part and parcel of geometry and everything after. It's all just pushing stuff through the grinder now. They SHOW them proofs-- a bit-- but then the most they are asked to do is fill.in.the.blanks.with.the.right.postulate.

(Makes me crazy, that. Also-- leads to a lot more of those wildly out of level questions at least with my DD.)

She wants to know where the quadratic equation COMES from. KWIM?

The reason that I'm a little reluctant to have her tackle AoPS at this level, though, is that it may be too much for her all at once, given her previous conditioning. (Gee, thanks mediocrity-focused public school maths... ugh.)

Great recommendations here, everyone!! It is sincerely appreciated.

DD has already dug into her AP Stats textbook for next year. (Apparently this is more fun than the ten overdue AP Literature assignements for THIS year... LOL).

It's Bock, Velleman, and de Veaux's "Stats: Modelling the World."

I can't speak to the math (yet) but the writing style is very engaging and amusing, so it's right up my DD's alley. I'll update as I have a chance to look through it further.

Please do: I shall probably be in the market for a good stats book some time soon.

Mind you, the match between what's in A level stats here and what's in AP stats there seems very loose, and it doesn't even seem to be that one asks more than the other - but my understanding of stats isn't good enough to see what's underlying the different choices that have been made in designing these syllabuses. If you're interested enough to look, the contents of units S1-S4, starting on page 79 here, are what I'm comparing with.

So, joining this discussion pretty late.

Here's what struck me as I read through this thread:

• Your daughter's school is teaching watered-down mathematics
• Her Algebra 2 knowledge isn't as strong as it could be
• She wants to major in maths via an accelerated 3-year program
• You're concerned that you might have trouble teaching Advanced Math/Precalculus

Here are my thoughts.

Based on what you've written, I'm concerned about your DD's readiness for an accelerated degree program in mathematics. Not because of her abilities, but because of your summary about what she's been taught.

My son was in a watered-down public school geometry class last year. It, too, used the fill-in-the-blanks approach to geometric proofs. We were lucky that they let him study independently using the Brown geometry textbook. I read through the school's geometry and algebra 1 textbooks and was appalled at how they had stripped both subject down to the easiest of the easy A-section problems in the Brown series (A section: easy but with increasing difficulty, B: medium and ditto; C: tough). Each section had dozens of problems that all asked the same thing. They "changed" the problems by doing things like rotating the triangle 90 degrees. Oh, BTW, these textbooks were official state-of-California-approved books.

Does this sound like your DD's coursework? If so, IMO, she probably needs a solid foundation in Advanced Math/Precalculus. If not, feel free to ignore this message.

Here's my suggestion: drop AP Statistics and tell the school that she's going to take an in-depth Advanced Math course as a homeschooler. Find a way to make this work if you can. If not, stick to your summer plan but be aware that she'll be sacrificing her earnings. My son's school was flexible on this point; maybe your DD's will be too. Tell them something along the lines of "The college said she should." Maybe get that person you knew as a student to write a letter. Something like that.

I haven't seen the Lial book, but as Bostonian noted, I know the Brown series very well. I recommend them highly. Each section has a discussion of the topic at hand and multiple examples. They derive things like the quadratic formula rather than simply presenting them. Sometimes they derive one or two equations and then leave derivations of other ones to the student as problems in the B or C sections.
The Advanced Math book has a lot of problems that relate to physics, chemistry, astronomy, and a variety of other subjects.

Importantly for your DD (I think), the Brown Advanced Math book goes through some of the material in Algebra 2, but in more depth. But because of the way the book is organized, it's easy to identify the problems that your DD already knows how to solve, and you can assign the stuff she doesn't know.

IMO, if you think that AOPS will be too much for her, it isn't clear to me how she'll be able to cope with true college-level stuff. My HG+/PG nephew (started college about 10 years ago) had a real shock in that regard, and he was quite well-prepared, having taken calculus in 12th grade and having done well in it.

Additionally, I see your point about colleges wanting students to take their calc. courses. My understanding of the situation is that this is because they AP courses leave them ill-prepared for the next class up. Back to my nephew: he was agog at what Intro Calc covered in college in 3 weeks compared to what he did in an entire year in 12th grade. People here have posted similarly over the years, and the math faculty at the CC where I taught for a while said the same. I think this is why many colleges won't turn a 4 or 5 on an AP exam into a ticket to higher-level math courses. Certainly, my nephew tried it and ran back to the Introductory course after 1 or 2 classes, only to be worked very hard in the lower-level course. You see, they are assuming that all or most of their students kids had this stuff last year.

So this leads me back to the Brown book. If you buy a copy (only ~$15 shipped for a used one on Amazon), you'll see that the last chapters of the book deal with limits (Ch. 19) and derivatives (Ch. 20). Again, I don't know your DD and am only writing based on what you've told us here. BUT, IMO, it's probably a very good idea for her to have exposure to calculus before she hits it in the first weeks of college. Remember, her whole world will have turned upside down at that point, and it's a lot easier to deal with a little bit of "been there done that" than its opposite.

As for you not feeling comfortable teaching her: you might be surprised at how logical it all is. I've taught myself a lot of math over the last couple of years, and it does come back. But failing that, hire a local student.

Buy a solutions manual. A teacher's edition is a nice extra, because it gives you lesson plans an homework suggestions.

Do a search by ISBN and always contact a seller before buying to MAKE SURE they're selling the teacher's edition that matches the edition of the student book you bought. If you really want it and have no other choice, you can get a copy from the publisher by calling them and telling them you're a homeschooler. Be very careful to get matching editions. You can get all the ISBN's on the publisher's website.

Phew.

Thank you SO much for the insights on the Brown textbook-- you knew EXACTLY what I wanted to know and why! I really love teacher's editions for another reason, too; they often have enrichment/explanation notes which are detailed or too technical for inclusion in the student editions. DD has also learned this and actively ASKS me to get teacher's editions of texts when I can.

DD's foundation is probably better than I give her credit for, honestly, because she simply doesn't learn any way but "thoroughly" when she learns math.

However, Pearson's idea of competent math instruction leaves a huge gap on the way toward MY notion of thorough. LOL.

DD has already stumbled onto the idea of limits and functions on her own...

and has expressed exasperation at the 'slow/painful' process of using algebra to "approximate" (her term) solutions to classical mechanics problems in Physics this year.

So maybe I'm selling her short on the AoPS approach. I dunno. It just seems like she is seldom willing to spend any time cranking through the mechanics unless the problems themselves are pretty interesting to her.

Physics has been golden that way. She definitely remembers all the trig she learned, though-- she has breezed through optics.


That's why I think that keeping AP Stats is a good move strategically-- for her. She will have next summer, and honestly, employment probably isn't on the radar anyway for other reasons.

It's also possible that we'll be able to stuff in precalc next year. You never know.

It is taught only to math majors, in a course such as Math 25 or 55 (Harvard) http://www.math.harvard.edu/pamphlets/freshmenguide.html taken by very well-prepared freshmen or by sophomores with less preparation.

Are you answering your own question here


If she wants the right answer to the physics problems, then calculus is what she needs.

I know you said she doesn't learn online well, but maybe you could do this and use itto teach her as she learns calculus.

https://www.edx.org/course/mit/8-01x/classical-mechanics/853