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

I'm looking for recommendations from the mathy people here-- it's been so long since I took any precalc (and there's been significant reorganization in how secondary math is taught) that my own experience is little use to me.

Needs to:

a) move at a reasonably good clip, low repetition, low spiraling levels (so probably a college text is better than one intended for high school)

b) have MANY applications-types questions, and relatively few of the basic drill variety

c) ideally, a good older edition which I can get for cheap. I'm looking, in a perfect world, to spend less than $60 on this.

d) video tutorials or something like that on an instructional CD, meh-- maybe. A solutions guide or online companion site, probably better.

My DD is very driven to practice skills with applications/challenge questions, and not driven by much else, honestly. She's not what I'd call a "mathy" kid (math for its own sake), but she's not slow to catch on, either. Any text probably needs to be well-written enough that I can follow it, because she is definitely not an autodidact with math.


Ideas?

I've looked at Blitzer-- that seems to be the one that I'd go with at the moment, but I'm looking for advice from people who know a lot more about math textbooks than I do.

TIA!!

"Advanced Mathematics: Precalculus with Discrete Mathematics and Data Analysis" by Richard G. Brown is part of the Dolciani series of math textbooks. Val reviewed it favorably on Amazon http://www.amazon.com/McDougal-Littell-Advanced-Math-Student/dp/0618250379/ref=cm_rdp_product . It has both computational exercises and more difficult exercises which ask you to prove things.

I am in love with AOPS. IMO, best pre-college math textbooks I've ever encountered. (I and DC are very 'mathy'.) We've used only 'prealgebra' and 'introduction to counting and probability' textbooks (both excellent) until now, though. AOPS has 'precalculus' textbook and associated course, but unfortunately, no alcumus (online problem engine) for precalculus (yet). Each book has excerpts and short diagnostic pre- and post- tests online; for precalculus, it is here:

http://www.artofproblemsolving.com/Store/viewitem.php?item=precalc

So judging from what I've seen of other AOPS books:

a) move at a reasonably good clip, low repetition, low spiraling levels so probably a college text is better than one intended for high school) - YES (though it is technically for pre-college)

b) have MANY applications-types questions, and relatively few of the basic drill variety - I am not sure about 'application-type questions' - you can check the samples online for yourself, but these are not basic drills (though DS gets bored about mid-way the end of chapter problem sets). YMMV. Actually, if you use this, I'd like to know what you think - whether these are drill-or-no-drill problems.

c) ideally, a good older edition which I can get for cheap. I'm looking, in a perfect world, to spend less than $60 on this. - YES: $47 book + $12 solution manual (or $53 if bought together).

d) video tutorials or something like that on an instructional CD, meh-- maybe. A solutions guide or online companion site, probably better. - There is a solutions manual. There are (great - in DC's opinion) video lectures on SOME topics online, though I'm not sure if there are any specifically for precalculus.

(As a side note, books are also available on amazon - may be faster shipping.)

Of the traditional texts, I like the Lial book for self study. It has clear explanations, lots of problems of all types (you don't have to do them all), lots of review problems (again, you don't have to do them all), chapter tests, and cumulative review problems for those who need it. And the solutions manual is excellent. You can get used copies very cheaply online.

If you have a math student who would do well with a discovery approach and extra challenge, you might want to take a look at the Art of Problem Solving series (as arlen1 suggested). They have a book that is called Precalculus, but a student who has finished a traditional Algebra II course might be better placed in their Intermediate Algebra book. They have placement tests to help you decide.

If I were in a time zone where the class times were during DS's waking hours, I'd have him in an AOPS online class quick as winking, fwiw. I ? third the recommendation for the books, even if the classes aren't of interest. Given a sufficiently challenging text, I disagree that it'd be a waste of time, though she certainly could just go on to calculus, or indeed to something else, e.g. more statistics.

My now 13yo ds went through an inexpensive sequence of iPad books - Trig., Precalc and Calc. published by a company called School Yourself (schoolyourself.org). I find their use of text combined with short animations very good, although I can't personally judge effectiveness as I already know the subjects well. I think they worked well for ds in explaining concepts, but they were very limited in the number of exercises for the reader. We have thus supplemented with "Calculus Workbook for Dummies," available for $11 from Amazon.

Another possibility is a good analytic geometry course.

Yes, I actually wanted to note this too - AOPS's (introduction to ?) 'number theory', 'counting and probability', etc. could be options for your DD (of course, depending on her interest and other considerations) - there is no set 1-straight-line sequence of courses. I've seen more detailed recommendations on possible paths on AOPS somewhere but can not find it right now (though there is always Richard Rusczyk's 'Calculus Trap' short article).

As to the questions of placement ('Am I ready?' and 'Do I need this?'), I find pre- and post- tests (found online) for AOPS books and courses very useful.

Re. 'very driven to practice skills with applications/challenge questions, and not driven by much else, honestly' - yes, the backbone of AOPS *is* a lot of application/challenge problems (as opposed just to regurgitating knowledge/skill) - but probably few, if any, 'real world' problems - say, applications in physics or chemistry.

I think the books are well written. In 'prealgebra', the first chapter is 'arithmetic', and it is started actually from something like 1+1, but then goes on to (the student) proving various arithmetic properties (e. g., distributive laws, etc.), defining division via solution to 'ax=b' and reciprocals, and (the student) proving more arithmetic properties. Of course, some subtle details may be skipped here and there, but compare this to the standard practice in US of introducing proofs for the first time only in a geometry course, which is (normally) taken very late.

BTW, if you find 'gaps', you can fill them going to specific topic in alcumus (it is free), try the problems - the provided solutions would include specific theory/practice references (and possibly video lectures).

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.

HK, I hope you won't mind some unsolicited advice:

AP Calculus in 12th grade has become quasi-standard for the best students. I would have qualms about an educational program that sent someone to college at an earlier age than usual but with a lighter math background than many of her classmates, especially if she wants to major in math.