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.)
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.
This is what is so great about this place. Love that.
