Another question: why does he teach two different algebra sequences, Algebra 1, 2, & 3 and "Advanced Algebra 1, 2, & 3"? Both sequences seem to be high school algebra - yes?
I've been moving through Saxon Algebra 2 much more slowly than I'd like (Lesson 76 out of 129), so I'm thinking I may need to take a formal course pretty soon if only for the structure. Much of Saxon Algebra 2 is brand-new material to me -- brand new in the sense that not only do I not know it, I've never even seen it before. I didn't know this stuff was out there to know.
Which means that in the past couple of months I've gone from being a middle-aged person who had never heard of polar coordinates to being a middle-aged person who can convert polar coordinates to rectangular coordinates and and rectangular coordinates to polar coordinates -- and who can add vectors to boot. (What are vectors?)
Plus, as of this week I'm on my way to becoming a middle-aged person who can do all this using negative magnitudes, too. Introducing negative magnitudes, Saxon writes:
To make matters even more confusing, we note that it is also possible to use negative magnitudes to locate a point. [boldface in the original]
source:
Saxon Algebra 2
Lesson 76, page 305
Question: Am I the only middle-aged person on earth sitting around teaching herself how to add vectors?
If so, this might be too much outlier-ness even for me. (Though, given the fact that I'm the most mainstream person I know, I'm probably just slightly ahead of the curve. Six months from now every middle-aged mother in Westchester will be working mixture problems.)
I think I've mentioned this before, but it's worth repeating.
I took 3 years of math in high school.
Algebra 1, Geometry, Algebra 2
It turns out that what was Algebra 1 and 2 in my high school is Algebra 1 in Saxon Math. Algebra 1 plus.
I hate to even think what the real-math equivalent of my high school geometry course is going to be.
When I had algebra 2, we did not cover vectors, nor polar coordinates. I didn't get to that until senior year in what was a pre-calculus class, and yes, I admit, I did NOT take calculus in high school. Algebra 2 did a lot of work with exponentials, logarithms, imaginary numbers, solution of 3 equations in 3 unknowns, use of determinants to solve linear equations, solutions of simultaneous quadratic equations, and polynomial equations (synthetic division). Had our algebra teacher moved a bit faster, we would have gotten to combinations, permutations and the binomial theorem. That's what constituted Algebra 2 in the mid-60's. At least at the school I attended.
ReplyDeleteREMIND ME TO POST THIS UP FRONT!
ReplyDeleteI think Saxon has a pretty strong focus on "applied math" in the sense of heavily emphasizing the math you need for chemistry and physics.
I THINK that's why vectors are covered this early in the sequence.
Does that make sense?
imaginary numbers
ReplyDeletesolution of 3 equations in 3 unknowns
use of determinants to solve linear equations
solutions of simultaneous quadratic equations
and polynomial equations (synthetic division)
As I say, I'm on Lesson 76 in Algebra 2 (although since Saxon integrates geometry you really have to do all 3 books in the sequence to cover all of Algebra 2, I assume).
I've done:
* imaginary numbers (square root of -1)
* solution of 3 equations in 3 unknowns (just started this - I did learn this in high school)
* polynomial equations (synthetic division) if this is what I think it is, it was covered extensively in Algebra 1
I hate synthetic division.
ReplyDeleteI can't remember how to do it or which special case is the one case where it works (linear factors? monic linear factors?). And the notation makes no sense to me.
When I was taking algebra they taught us long division of polynomials (which always works) and never breathed a word of this synthetic division.
Because I went to school in NYS, I don't know what's Algebra 2, either, as I took the Integrated Course 1-2-3 sequence. Course 3 was functions, logarithms, lots of trig, the geometric series, and a bunch of other stuff that I can't remember now. Proof by induction, maybe?
I'm not sure when we did polar coordinates. Either in Course 3 or pre-calc. Probably both.
Tomorrow I'm teaching the calculus students how to find areas of regions given by polar coordinates.
What's the difference between pre-calc and trig??
ReplyDeletehmmm...
ReplyDeleteNow I'm not sure whether I learned synthetic division or regular long division of polynomials.
I'll have to check.
I'm guessing I learned synthetic...
more anti-synthetic-division rantage
ReplyDeletecan be found in
this classic thread (7/05)
in the late lamented "tall, dark, and mysterious".