IME, almost no one gets through two years of Algebra before 9th grade. Less than 1%. In part because even the talented math kids will run out of math that the high school can offer if they start pre-calc in ninth grade.
Our districts math progression for talented math kids is Geometry, Alg II, Trig and Precalc squeezed over two years (they call it squeeze math - normally Geometry is a year, Alg II is a year, and Trig and Precalc are a year). If you start that in 9th grade, in 11th you take AB or BC AP Calc. As a senior you take CIS (College in the Schools) Multivariable Calc and - if you have the elective space - Prob/Stat. The 1% (in my daughters class its one kid out of 400) who take that as a Junior have to go to the University of Minnesota to get more math - which eats up four hours out of the day three days a week (in class and travel time), and makes it nearly impossible to take the other classes you need to graduate. For this reason, even if you are really talented, districts hate to accelerate you.
It isn’t easy to find high school teachers who can teach AB or BC Calc, and harder to find them that can teach Multivariable Calc. My ex was a math education major - and he didn’t even need to take Multivariable for his degree. Which is part of the problem with teaching those courses - especially in smaller communities. Our calc teacher moves between two schools and just teaches Calc. One hour AB one BC and one Multi then moves to the other school to repeat it in the afternoon.
About half of kids take Pre-Alg in ninth grade, Alg in 10th, Geometry in 11 and Alg II w/Trig in 12. Once again, they have to pass Alg II to graduate, or get an exception. About a quarter of the kids do the squeeze progression and most of the rest the non squeeze progression which gets them the opportunity (but not requirement) to take Calc (but not necessarily AP Calc) as Seniors. A small percentage of kids - less than 10% - are on an exception program for special needs and will graduate by simply taking four years of math, regardless of how far through the progression they get.
One of the big issues here is that to get that exception, you need to spend a lot of time getting doctors to say your kid is special needs and working with the school on an IEP. And know you need to do that. Don’t make the meetings, your IEP risks being dropped. So middle class white kids graduate without Algebra II - without Algebra I in some cases, while kids that don’t have the advantage of parents who know how to (and can afford to) work the system don’t graduate.
It depends in part on the sequence. A third of my class took Algebra I in 7th grade, and the Saxon math books don’t have a separate year of geometry, or at least they didn’t used to. A school I went to had geometry after both algebras, although I wasn’t there to take it.
I don’t understand the problem of running out of math classes. Does your district require everyone to be enrolled in a math class? I don’t see any college objecting to a student running out and taking something else. Correspondence courses are also an option; I took two in high school, and I imagine the quality has improved from those dusty ancient days of the internet.
I’ve been straying from the question of what should be taught as opposed to what is and can be. While I bristle at the notion that something routinely mastered by children is “advance math”, that doesn’t mean everyone should learn it. But I don’t really know what anyone * should* learn about any topic. I think that hinges on the purpose of secondary school, which I don’t see many agreeing on.
Our older son is in a math/science magnet program. He took algebra in 6th and algebra in 8th. By the end of his junior year he’d finished AP Calculus BC. Obviously schools like this are the exception. Younger son is taking Algebra 2 as a sophomore, which I would guess is more the norm. Things have changed quite a bit since I was in high school (early eighties). We didn’t even have AP classes.
The problem is that colleges look for four years of math.
This is REALLY stupid, but I’m assured by my daughter’s (who is good at math) counselor that it is true. She doesn’t want to take multivariate - she wants to major in PoliSci and minor in theatre :rolleyes:, but she’ll need four years of math to “get into a good college.” I keep telling her (the counselor) that AP B/C Calc is probably adequate with no Senior year math except a Tri of Stats (which she will probably take next Summer through a local college, she hates the Stats teacher who is currently her Pre-Calc teacher) unless she’s looking for a Stanford engineering degree, but apparently, I’m wrong (I don’t think I am) and the gap of a year worth of math is going to tank her chances of ending up in a respectable four year school.
That’s exactly where my daughter is…in an ordinary public school where probably 20% of the kids are on that path - so around here it isn’t rare.
One of the things that bugs me - and it isn’t just Math - is that we push kids so hard. Its possible to exit my kids’ high school with enough college credits to start college as a Junior - between CIS coursework and AP coursework and PSEO options. She’ll take five college level courses next year as Junior - AP Chem, AP English, APUSH, B/C Calc and CIS Spanish (5th year high school Spanish - and she’ll have no Spanish option her Senior year without driving into the city to go to the U). And this isn’t an Ivy League kid by a longshot - she isn’t even a type A personality. (Actually, I think I talked her into college prep chem so she’ll have time to, I don’t know, do extracurriculars…look at Snapchat…read for entertainment.)
But on the other end, there is little left for the Mike Rowe fans of the world. Tracking kids (ala Europe) would be great, but we have two major tracks for my kids - to college or you are in college while still in high school. Everyone else can work fast food.
I’m talking about the kids who finish two years of Calc in High School, which you are pathed for if you finish Alg II in 8th grade. - Both years of Algebra before high school and high school starting in 9th grade.
It does assume that you’ve also fit in the year of Geometry before high school. If the progression is Geometry after Alg II, then you’d be on the schedule you are talking about.
That is starting to bother me too. There is this idea that American public schools are all terrible and something absolutely has to to be done about it. I am sure that it is true in many schools ranging from the inner-cities to tiny little rural towns but I know it isn’t true in suburban Massachusetts where my own daughters go to public school and I hear that it is much the same in other non-poor areas.
They are working the kids to death even with the median level expectations. It is literally hours of homework every day including weekends, school vacations and even during the short summer break. They get on the bus at 6:30 am, stay in school for the regular period, go to extended school until 6 pm because both of their parents work like most families these days and then come home and do homework until 9 pm when they have to go to bed to repeat it again. It is like somebody took every one of the most strict and extreme ideas they could find from every other educational system in the world and decided that those all sound great as long as you kick them up a notch.
I am happy that they are getting a good education in public schools but they are just kids and I think they should have other priorities as well. It really screws up family life as well. If even one of your kids has a big test coming up or a project to work on, you can’t really go anywhere and you have to keep the whole house quiet until they finish which may take hours or days. I don’t think junior high and high school should be purposely made to be that difficult and it should be at least somewhat fun.
We took my daughter off to tour colleges, and we hear the same thing from the college students over and over again - keep in mind, we aren’t talking top tier colleges here, but respectable four year schools. (By the way, one was Clark - in Massachusetts, so you have a pretty good idea of what we are talking about).
“You will have so much time compared to high school! Its so much easier!”
College should not be easier than high school.
In the meantime HALF of Minneapolis public school kids don’t graduate.
Our younger son (HS sophomore) has already had major anxiety problems in school. A friend of our older son dropped out, got her GED, and started at the local community college. Our oldest basically decided he wasn’t going to “play the game.” Despite being a National Merit Semifinalist he made D’s in English all through sophomore and junior years. His test scores and overall ok gpa got him a good scholarship at his first choice school. His brother is too stressed to even think about college at this point.
I hear this a bit from maths fans, but I’ve yet to see many concrete examples of using higher maths in real life for the average person. What examples would you suggest?
My loathing of maths isn’t encoded by teachers at all - I had some wonderful teachers who tried their best, but the reality is I Just Hate Mathematics. Trying to work out anything beyond basic arithmetic gives me a headache and I’ve long been of the view we have calculators and computers for that stuff now, so unless I’m planning on becoming a literal rocket scientist, I’m best putting my energies elsewhere.
Fortunately my high school English classes were pretty light on poetry. We did have some (not the titles you mentioned) and a few Shakespearean Sonnets, but our teachers basically knew that there was no universe a class of teenage boys was going to be interested in poetry (even with comparison to song lyrics) and we did a lot more critical analysis of novels and short stories etc.
In addition to “American schools are tough” kids and their parents are being told that to get into a good college, they need challenging coursework on their transcript - and need to do well at it. And because college is so expensive, their kids are competing for scholarship dollars or spots at schools that offer great financial aid to middle class students - that come to the kids who take that challenging coursework, get good grades, and test well. Hence the “four years of math, even if that means a future Liberal Arts major will end up taking Multivariable Calc.”
I’m not denying your experience, but anecdotally, I’ve had plenty of people tell me something like “I used to like math until…” and the “until” was often a bad teacher who turned them off to the subject.
This doesn’t make sense. The “basic arithmetic” is the part the calculators and computers can handle for us. The “higher math” is the part we still need to know how to do so that we can tell the calculators and computers what to do for us. This is a point Keith Devlin (whose blog I linked to upthread) made in an earlier article “What Is Algebra?”
So we should make people listen to Opera until they hit one that gives them an appreciation for Opera? Or Heavy Metal Bands? Or require people to wander through Art Museums having the art explained to them until they like it?
What makes math so special? And not arithmetic. You need to be able to perform arithmetic to get through life with some success - even if you end up being an English teacher or a car mechanic. But polynomial functions?
I’d make the same argument about English - I know a lot of people who had no appreciation for books until some teacher or some book hit them, and a whole new world opened up. But I don’t know that creating that experience for those people is really worth forcing high schoolers to read Jane Austen, or anyone to read Jane Austen - though Austen was one of those authors that opened worlds for me, personally.
When I homeschooled my son, those were pretty much exactly the sorts of math problems Algebra had. They didn’t reach him. He can do them, but reading a graph someone else creates is easy - and he simply showed me how to Google relative values of cell phone plans. In his mind, he doesn’t need to do the math, he knows how to do the research to avoid the math.
I thought you were saying that it was worth pushing until indifferent math students had a breakthrough - either a talented teacher or the aha moment when math became the wondrous structure and incredible problem solving skill set math fans see.
I’m confused how this follows from what I said. What did you think I was trying to say?