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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.
7 comments:
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.
REMIND ME TO POST THIS UP FRONT!
I 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
solution 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.
I 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??
hmmm...
Now 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
can be found in
this classic thread (7/05)
in the late lamented "tall, dark, and mysterious".
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