Gifted Issues Discussion homepage Forums Recommended Resources Precalc-Trig resources

Okay-- so I don't know WHY, exactly, Precalc now includes some topics that weren't addressed previously until calculus (you know, when you NEEDED them) and at this point it really doesn't matter that much.

My DD's Precalc class has no instruction. It uses a crappy textbook (Glencoe's Advanced Mathematical Concepts: Precalculus with Applications).

I have provided her with Lial and Hornsby's Precalculus, which is definitely a more thorough and better-written text.

The problem is that she is truly floundering with material that she has NEVER seen before, and for which the course itself seems to think that she should memorize a particular algorithm (apparently)-- but then barely demonstrates it at all, and provides no practice.

Only assessments.

The assessment level clearly (I've looked at them, recall)-- requires MASTERY of the material, including some that hasn't been presented at all.

The teacher is AWOL, basically-- no help there.

Khan was somewhat helpful here, but the way that the course has presented Parametric functions and polar coordinate systems is so-- so-- well, it's so stupidly backwards and over-simplified that DD is having a LOT of trouble figuring out WHY they are using particular approaches.

Honestly, geometry preparation (now) isn't sufficient to adequately lay a foundation for trig at this level. But it's not like we can go back and completely remediate THAT at this point, even if we wanted to. So we're going to be patching things as she goes.

HELP.

I need some additional resources for:

Trig identities
Parametric Equations
(DD knows vectors inside and out after Physics)
Conics and analytic geometry
Polar Coordinates
Complex Numbers


Probably I'm also going to need this for:

combinatorics
exponentials (well, maybe not-- I think this stuff is intuitive to her)


Anyone know of anything where DD can actually get some practice with feedback? She's not learning it thoroughly enough just from reading and watching video. She's getting super discouraged, and the more so because this grade is going onto a college transcript, being a dual-enrollment class.

Is there a Schaum's outline with this kind of thing in it??

There are Schaum's outlines for trigonometry and precalculus.

You may want to look at Brown's Advanced Math. It derives a lot of the identities, and has a lot in the way of explanation.

Schoolyourself.org is a work in progress that will eventually cover all these topics. It is interactive web instruction that I think takes an intriguing approach. Unfortunately, they don't have all the topics you need up yet, but others may be interested in the math topics they do have: algebra, geometry, etc.

You could try ALEKS (http://www.aleks.com/), it is an online computer program that will gives immediate feedback, and instruction. It is used in colleges & universities as supplemental material. I can't tell if the pre-calculus program included all of the above topics. One of the good things about ALEKS is that it test the student for what he or she knows, doesn't endlessly repeat material the student already knows, and it gives immediate feedback. I also know extensive work has gone to make sure this program meets (and exceeds) content standards. On the other hand while it does fine teaching the basic material, it doesn't really teach the advanced critical thinking. Every time I mention ALEKS I feel I should disclose that I personally know the original designers of this system.

I was just looking at the AoPS books for my son, and perhaps their pre-calculus book would have details of this material. But I can't recommend them as all I've seen so far in the web site. These books seems to be more directed at gifted students.

I am a bit astonished that a pre-calculus class includes all these topics. Things sure have changed since I went to H.S. and university. I did my Senior Project in University on Polar Coordinates and I don't think I had seem much more than a glance at them before that year.

Thanks-- found a used copy in a neighboring state for just about $5. It should be here next week.

Similarly, a Schaum's outline for Precalc, which I hope will be helpful. Naturally, the sections on polar coordinates and conics aren't preview pages on Amazon, so I have no real way of knowing at the moment. Grr.



The mismatch between the instructional and resource material and the level of the assessments is nothing short of astonishing to me, in all seriousness.

First quiz in this unit made me go--

Which was better than DD's response, which was more along the lines of

I am a bit astonished that a pre-calculus class includes all these topics.


You and me both.

I recall seeing complex numbers in high school, all right-- but not really WORKING with them in polar coordinate systems until Physics, P-Chem, and DiffEQ. Certainly I first encountered polar coordinate systems in college material relating to analytic geometry. Not in this class, which is effectively the same material as is (theoretically) covered in MTH 112.

Not being there yet, I am just going to suggest a few things not yet mentioned in here - feel free to gently point out the errors etc so I can remember for when our turn comes

Have you tried the Life of Fred Pre-Calc/Calc and Trig/Geometry books?
Is there not an online EPGY course for this perhaps?

This is where I think trying to plan an education for our children who we piece bits and pieces together from different sources due to lack of anything that truly fits their needs gets really challenging. My first thought when I read the list of topics was that my math classes in high school covered almost *all* of them before my AP Calculus class in high school. That doesn't mean I had a better or more thorough math curriculum - it just means they were on our list of things that needed to be covered before you got to Calculus. Curriculum simply varies so much from learning institution to learning institution, even in "classic" things that would seemingly be a straightforward progression such as math.

I don't know if it's something your dd would want to use as an approach to filling in the gaps, but if she's not opposed to working with a tutor, that's an option. I think you're in a college town, right Howler? If you can find a college math major who enjoys tutoring that might be one way to go which would allow you to quickly cover what's missing.

Good luck with it all -

polarbear

At some colleges one's score on the SAT Mathematics Level 2 Subject Test is used for placement, with a high-enough score indicating readiness for calculus. Prep books for this test could be useful, and it may be worth taking this test before college even if the schools you are applying to don't require it.