Yes, this is exactly the point. The courses have to be taken in order for a reason and the only opportunity anyone has to complete the “optional” post-Alg2 courses is starting with the first year after Algebra 2 is offered, which is going to depend on the first year tracking is offered.
In Virginia, if the sequence including Alg2 cannot be completed before 10th grade, then nothing that requires a year or more of prerequisites can be taken before 12th grade and nothing that requires two years of prerequisites can be taken at all.
“Just take trigonometry and calculus at the same time!” is a ridiculous proposed solution for any number of reasons, not the least that it proposes to restrict accelerated math education to the kind of student who could handle doing that, which is going to be a tiny fraction as compared to the number who engage in a single-accelerated math course (which is something like 30% of all students in a lot of the larger Virginia districts).
For some reason, I read the last 2 words there as “differential equation”, and chuckled at the math joke.
Then I was disappointed to see it was just a trick of my own mind.
Well, how far did you really get? I don’t think that there’s anything “innate” about working through L’Hôpital’s rule, that just takes hard work. If it were innate, then Euclid would have invented calculus.
Personally, I think that it’s more of a lack of interest. They feel that math is boring, and doesn’t relate to the real world, so people just have a hard time learning it and doing the exercises. I never felt that way, I alway saw how the world was based on math, and was alway excited to dig deeper.
I found things like social studies to be incredibly boring, and even though I had an excellent memory, I had a hard time remembering people and places and events that I didn’t really care about.
Whether the student trusts the school system, the teacher, the textbook author etc. as to the value of the material even if it seems irrelevant in the moment, or has the delayed-gratification capability to understand that being bored now may pay off in multiple ways later, is based on the cultural and family environment that the student’s parents choose to instill in him or her and the quality of the school district. This is a problem that A) can be fixed B) will not be fixed by attacking those who had the benefit of coming from more adaptational circumstances.
In post 52, I lay put how my school does it. It works, but only because we dedicate a lot of time to everyone’s math and all the kids are pretty math centric. But basically, if you have some classes that go at double time, some at normal time, and some at slow time, you can skip around. You can also go to summer school.
I don’t think offering substantive classes tailored to their level or trying to address the root social causes of these problems is “attacking” them. That’s what I propose doing.
Are we maintaining the fiction that the new mishmash classes in which every ability cohort learns every math class at the same time will actually work for anybody, as opposed to transforming a system that isn’t broken into another teachers’ union sinecure where nobody learns anything except how to make excuses for failure?
That’s fair, and I certainly didn’t mean to imply that all teachers were lazy. But I do have some experience at the elementary-school level with teachers that are not willing to differentiate for students that are significantly ahead of their peers. I had a niece that literally begged to not to have to go to school anymore because she was so bored and her teacher was having her teach the other kids and even act as a “classroom monitor” to help with discipline. Now she has been moved into a special program the district has for gifted students (which comes with its own set of problems). I’ve had somewhat similar experiences with my own children that have been addressed in various ways.
I agree entirely. Our teachers are (in general) asked to do far too much with far too little.
The bolded part is what is in dispute: the people you oppose are saying that the system is broken. They have studies that lay out what they think is broken and in what way it is broken. They think it is broken despite what you point to as success.
Thus far you’ve done very little to convince me that they are wrong. Your points seem to mostly be, in fact, simply saying that they are wrong.
I worked my ass off to be good in math, for the problems to make sense, for the whole system to be comprehensible. I failed. For all my struggling and effort, I got just enough to bluff my way out of high school. To tell me that my failures are all due to “not working hard enough” or not “coming from more adaptational circumstances” is frankly insulting.
You throw around terms such as “dullards” and blame everything on “root social causes” and “family disinterest,” instead of recognizing that students have varying abilities and interests. It comes across as contempt for those who don’t meet your standards.
San Mateo says they have studies showing that “mishmash” classes work BETTER for elementary students than rigid tracking. Here’s an opinion piece describing San Francisco’s efforts to detrack math and the outcomes thereof; do you have actual refutations of their apparent results?
How would that work, though, at a more typical school? At a STEM magnet, you have more opportunity to do things like double-blocking and really concentrating on everyone’s math. From what I’ve read, there’s maybe a hundred public STEM magnet high schools in the US, versus 25,000 public high schools, so what solutions would be applicable to the overwhelming majority of American students?
I would say the difference between someone who’s good at maths and someone who isn’t is understanding the reason behind the operations you are performing, rather than simply rote-memorising them. Actually, that was why I found maths and science much easier than other subjects. You could simply understand the material, and then there’s little need to memorise anything.
And for sure a good teacher can help with this understanding - explaining things in different ways, knowing common misconceptions so you can set students right. Understanding should be the goal, but it observably comes easier to some than to others.
(I was not a good teacher. And at university it was notable that the smartest professors made the worst teachers. Give me someone average any day.)
So did I, but I think that’s a function of the understanding I meantioned earlier. Still, it’s always hard to disentangle interest from ability and say which came first.
Sure memorising things is tedious, but weren’t you interested to learn history and important events and how we got where we are today? We didn’t cover all that much in school, but now with the internet you can learn as much as you like, it’s great.
If you want kids to learn math better, they need more time at it. Math mastery takes time. If not enough kids want to accelerate, then it’s not really feasible (hence magnet schools to concentrate the ones that do)
I DO think a lot of school systems would better served if they offered a double blocked Alg 1 for students who struggle. The class could actually cover Algebra 1 and start into Alg 2, to give the kids a boost there. A poor foundation in Alg 1 just fucks a student so badly.
Most of the ways we accelerate are available to students if schools will let them. Alg 2 and geometry can be taken simultaneously. State can be taken along side pre cal or Calc. But most of the time, kids don’t want to dedicate that much of their time to math (totally valid choice) and acceleration is sorta pointless if you’ll run put of classes.
That does seem difficult when the progression is so rigid. In the UK pupils don’t progress through the same set of courses at different rates, but rather each year is divided into 3 different sets doing courses of varying difficulty. You always stay with people of the same age. And you can move around: in French (the only other subject we were tracked in) I was moved from the middle to the top set after year 9, and I don’t remember having any difficulty catching up at that point. And in my A-level maths class there was a girl who’d been in the middle set for GCSE; she did have to catch up on some concepts she’d missed out on, but she did okay in her A levels AFAIR.
Don’t the kids on your track 2 end up skipping whatever is in 8th grade math anyway?
So if the difference in outcomes aren’t due to anything inherent in the person, aren’t due to the amount of work put in, aren’t due to environment, and aren’t due to teachers, then what are they? Just random and unknowable? If some people just mysteriously end up understanding trigonometry and others don’t, for no identifiable reason, then do we need to worry about the structure of math class at all, or will this mystical process still manifest on people who are not enrolled in the apparently pointless math classes?
Some combination of these factors? I wish I knew what makes some people good and others bad at math, but I am at least highly skeptical of anyone who says there’s just one reason that makes the whole difference for everybody.
By the measure of “is the system teaching math” it is not broken. On one end, Virginia has the best single high school for math instruction, the best large cluster of high schools serving the entirety of a densely populated area, and thanks partially to its large number of advanced students, is overall ranked #5 in math education.
The average math scores for low economic status students in Virginia defined by federally subsidized meal eligibility exceed the basic proficiency standard of the NAEP.
In Henrico County, the largest suburb of Richmond, 50% of students are black or Hispanic and 54% of students qualify for free lunch. Every single one of the nine high schools in the county, including the one that is over 90% black students on free lunch, offers a college prep counselor and AP calculus classes. (The schools are considered very desirable and safe overall and many people choose to live in Henrico when their kids reach sixth grade for that reason, but I’m trying to focus specifically on the math angle here). The overall math scores for the county are at the median for Virginia, which as mentioned has very high scores relative to the country overall.
I’m not trying to cheerlead or say there aren’t many areas of potential improvement that I could identify in Virginia’s education system, but I want to know what in the above cries out for such a drastic overhaul if the measurement is “are we teaching math effectively to students at all ability levels and/or to students in groups that are supposedly disadvantaged by the existence of advanced math classes.”
Now, if the measurement is “equity,” we may have another story. That’s why equity shouldn’t be the measurement.
Eighth-grade math is mostly pre-algebra/very basic algebra anyway, so the topics end up getting covered in accelerated fashion at the beginning of algebra 1.
Differences may be due to any or all of those, plus others you haven’t even mentioned. You are giving the impression, however, that you’ve decided differences are ENTIRELY due to the moral worth of the individual and their family: if “those people” would just tell their kids that education is important, their kids would be math wunderkinds. It is this attitude on your part that so many in this thread are reacting to.
We worry about the structure of math classes in order to achieve the best possible outcomes for every student, not just the ones who “deserve” special classes. For example, in 2015 Thurston Domina found that enrolling more students in advanced classes early led to a decline in the average scores of a district’s 10th-graders on state math tests (abstract, although you probably need an account to see the full article). Why do you think he’s wrong? Would you not expect the opposite finding, and how do you explain his results?
This study analyzed California, where teachers’ unions have a strangehold on the system and there is no accountability for performance. What’s your explanation for why it doesn’t happen that way in Virginia or why education in Virginia should be more like California instead of the other way around?
If you want me to explicitly type out “throwing students at random into accelerated math classes taught by checked-out, unfirable California labor activists is not going to benefit them” then there you have it.
Putting properly qualified students into accelerated classes taught by accountable teachers in Virginia seems to be working just fine.