What does your highschoolers math program look like? What influenced your choices/selection?
I just recently wrote as a guest blogger about high school math, though through the filter of teaching Euclid. I will link to those posts because they told a bit about our high school experience, but you don't have to follow them unless you want to!
Teaching Euclid Part I
Teaching Euclid Part II
My main theme in these Homeschooling High School posts has been something like "you plan and prepare with the ideal in mind, but you do what suits the child and your circumstances." The same thing is going to run through this post on math.
I was handicapped by not having a real ideal in math. There are plenty of criticisms of high school math out there; one recent one I read was Lockhart's Lament, and the corresponding book, A Mathematician's Lament. I also came across some strong criticisms when I was researching for the Euclid posts linked above, and some of them are linked in the posts.
They offer solutions, but generally the classroom type, not the kind of solutions that are easy for me, a homeschooling mom with not a lot of math background, to adopt.
Classical education and Charlotte Mason, my main influences, generally just incorporate the best of the conventional in math. They might advance the child the equivalent of a grade level or two, or add some Euclid and/or living books, but they don't really change it from the ground up, at least not by high school age. So you are stuck with the conventional math scope and sequence:
7th grade-- consolidation of basic math, plus prep for algebra
8th grade -- Algebra (at least now in California that's the ambition)
9th grade -- Geometry
10th-11th grade -- Algebra II and Trigonometry (usually a combined course in my experience, often 2 years worth of work)
12th grade -- no math, or advanced statistics, or calculus
If your child is especially strong in math, you may advance faster through this standard high school sequence. If your child takes a little longer to get to the abstract stage, perhaps it's as well to linger longer. My strongest two math students got up to Algebra II/Trig. The other two got most of the way through Geometry. The three that are in college or beyond all did very well in college math environments.
Curriculum we used for the older three:
Jacobs for Algebra I and Geometry
(if a child reached Algebra 1 during middle school, or seemed shaky on the transition to abstract conceptualization, we used Key to Algebra, which I highly recommend for those purposes)
One of my boys went on through Foerster's Algebra 2/Trigonometry. It is very good but at least in the older edition, seems to require much self-discipline and conceptual understanding.
The other boy who went past Geometry did so in a public school/independent study format. I think he used Prentice Hall's Algebra II/Trigonometry. He did not like it though he struggled on and got a decent grade. I helped him with some of the lessons and I had considerable trouble grasping the material though I did quite well in high school math, so I sympathized with his criticisms.
My present high schooler is somewhere between 10th and 11th grade (haven't quite decided yet). He is doing geometry using Jacob's. We use Khan Academy Geometry as a supplement.
The Great Courses also have some mathematics resources. My son and I geeked out the summer before last on this "Secrets of Mental Math". For us, it was a fun and energizing break. We plan to watch it again some time.
I don't know if Chari is going to post on math, but I know that she has found a solution for the challenges of teaching math in high school. She has a good friend who is a former homeschool mom, from a math background, who loves to tutor. Once Chari's kids reach high school age, they are tutored by this friend and do well.
I have looked up tutoring resources in our area, especially when facing some kind of challenge, and they are expensive and require driving 30 to 80 miles. So, yeah, no. But I've seen it work well, and I've considered moving nearer Chari not only to be closer to one of my best friends, but to join her great homeschool community, which we don't have here.
However, you can do it without a tutor, and to show it's possible, my oldest came close to acing his math SATs (he was pretty upset he didn't get a perfect score; he did get perfect LA results). I remember talking to a friend, a retired high school teacher, who was skeptical about homeschooling because he didn't think homeschool parents could teach all subjects at a high school level. I didn't normally talk about our kids' SAT scores because, well, you know, that's not the point, but I did mention my son's results then. Our friend was quite surprised and I think it modified his opinion at least a trifle.
The thing is that in the homeschool, teaching is not everything (though being a support and guide is important, and sometimes that does mean teaching or at least finding the right teaching materials or outside resources).
Learning is the thing, and realizing that it's the learning that is key can streamline things for the homeschooling mom who doesn't remember all her high school math and science courses.