no answers to any of this.
but, part of me agrees with how students should have more depth, rather than being accelerated.
my 4 were all accelerated - from a parents’ view point i think the junior high years of algebra and geometry were lacking and didn’t have as much substance. It was a “thing” to be in those classes; people were begging teachers & having their kids re-tested; but I think that was all mostly for prestige rather than the actual learning. My kids all had dips in scores in the algebra/geometry areas on their ACT test.
At the same time, the recognition of being in these tough classes was an encouragement; my s15 - who did not make varsity sports teams in HS because only the best get to compete - is now an actuary and rocking it! the math boost gave him that encouragement and drive.
It’s not a good situation at all for sure - for anyone, students or teachers. Our schools have so many problems in all areas that at this point, I don’t know what the solution is. And I know so many teachers, especially in the younger grades, try so hard to engage students and parents. I suppose if you’ve been labeled as failing year after year, going on 2 decades now, it just takes it toll everywhere. However, we have a new superintendent that appears to be promising. (For awhile we went through a new one every year, plus a new HS principal, and often major schedule format changes.) But thus far, I have liked what I’ve seen from her. And she has strong local roots, so hopefully she can stay and make a difference long term.
Why not, rather than accelerating Calc AB, BC, MVC, offering a path where the top students take Calc AB OR BC then the following year an introduction to Proof Based Calculus, spiraling knowledge for mastery and learning new skills and new ways of thinking?
In my opinion, it’d also be more useful to very advanced future STEM majors in that it’d teach them the type of thinking they’ll need for the colleges and majors they’re aiming for.
Fewer algebra/trig minutiae, more data, stats, etc. for all seems to be an excellent initiative.
The big issue IMHO is if the default path becomes 8th grade Algebra1+ data/stats, without separate groups for the +1, -1 and -xxx groups. In other words, those complaining shouldn’t be the parents of advanced and would-be accelerated kids, but rather the kids struggling, the kids who need numeracy remediation, and the teachers who will NOT be able to create one size fits all class for all these levels, so you better hope they have separate groups/classes with special means allocated to each group.
Proof based calculus would be real analysis, normally considered a difficult college junior/senior level math major course. A more introductory proof based course would be discrete math or proof focused linear algebra. However, not all STEM majors will need proof based math.
Once past calculus BC, STEM majors diverge in math needs. High schools seem to default to multivariable calculus for +2 track students (if there are enough of them to offer courses to), although not all will need it. For example, biology majors would benefit more from calculus based statistics. The relatively small number of +2 track students and the divergence of their future math needs makes it more difficult for a high school to fulfill all of their math needs after calculus BC.
oops
I’ve seen classes offered that are Calculus1 with introduction to proofs. So there has to be a way.
I agree that offering a choice of Regular Stats, AP Stats, and Calc-based Stats for seniors would be a great possibility. Even non bio majors would benefit from seeing how calculus (taken junior year) can be used for stats.
Caltech would be an example, but the expected prerequisite is a regular calculus course.
But students who are able to and want to handle something like that after calculus BC is probably only a small subset of +2 math track students these days (where most are probably parentally pushed ahead cases).
I’ve seen classes offered that are Calculus1 with introduction to proofs. So there has to be a way.
I agree. Not all proof based calculus needs to be at the abstract level of real analysis. Students can build up a fairly good amount of intuition and conceptual understanding with analysis of functions, and going deeper into the consequences of the theorems that are usually glossed over in first year calculus. With free, sophisticated programs like wolfram|alpha and Octave available easily, there are some really interesting ways to do this at a high school level.
I would be happy if schools would figure out how to help students truly understand algebra. I feel that, for most, that is key. Most students won’t actually need calculus, but the skills and concepts learned in algebra are really helpful. Logic is required to solve algebraic equations, and learning to solve actual problems that relate to the real world helps students gain critical thinking skills. Calculus is a means to an end (and for many, the end is getting into a particular college). Algebra is something that I think should not be glossed over in terms of its importance.
For mathematically talented kids, the answer should lie outside the standard HS curriculum. They should be offered to study subjects such as geometry, combinatorics, probabilities, etc. in more depth, instead of completing their HS math curriculum early. The problem is that few HSs in the country have the resources to offer more in-depth studies.
That is always going to be the problem for the true top math talents – in most high schools, there are too few of them for the school to devote resources specifically to them, so they just say “get on the +2 (or higher) track”.
Of course, many of these same schools have difficulty saying “no” to parents of good-but-not-great-at-math students when those parents insist on putting their kids in the +2 track when they really should be in the +1 or +0 track. And then you get the forced two year calculus AB - calculus BC sequence to accommodate those pushed students, to the boredom of the true top math talents.
Yup, that’s why I said “for juniors who took calculus” (so, the +2 track: rather than taking AB-BC-MVC, they’d take whatever calculus in 11th grade, intro to proofs in 12th).
They should be offered to study subjects such as geometry, combinatorics, probabilities, etc. in more depth, instead of completing their HS math curriculum early.The problem is that few HSs in the country have the resources to offer more in-depth studies.
A single school or district may not have all the resources, but maybe contract out to the AOPS folks or something similar and use zoom-based synchronous classes. It can be done - whether there is the will to get it done is something totally different.
Agree with this. AoPS is the gold standard for online math instruction and no need to reinvent the wheel. They have classes ranging from pre-algebra to those preparing to take the USAMO exam (roughly top 250 high school math students nationwide). Everyone I know who has qualified for USAMO has taken AoPS classes for many years. They are also accredited by the Western Association for Schools and Colleges, the same people that accredit places like the UCs and CSUs.
I’m sure that the various teacher organizations will embrace that, right? 
Just like students are different, so too are districts. If you have a district with a large number of “T20 or perish” families (particularly if there are more such families than there are kids from that schools who make it into T20 schools), I expect there will be a lot of groveling to get into advanced classes. But for the vast majority of students (and even the majority of students at those schools) that just isn’t the case because the obsession doesn’t exist.
Only a handful of the kids in accelerated math with my kids didn’t belong. Most of them took the off ramp when it was available. At least they were given the opportunity to try. There were some kids who probably could have handled it but didn’t want to (lack of motivation).
In a highly ranked school district, many kids received mediocre educations. Wasn’t district’s fault. Or the teachers’. Education wasn’t a priority for them (or their parents). They didn’t want to be pushed or challenged. They wanted to have fun. And for the vast majority of them from what I have heard, that doesn’t suddenly change after high school.
While online / distance education may be the only practical way to hold a class that is only of interest to 30 students scattered across 20 high schools, it does have the problem that not all students do well in online / distance education (as the whole COVID-19 situation has shown).
Math would not be the only subject that this could apply to. Less common foreign languages, specialty elective topics in history, social studies, and English, and perhaps other courses where the student interest is too small for any one school would be courses to offer as online / distance, but that means accepting the limitation of online / distance.
“Yup, that’s why I said “for juniors who took calculus” (so, the +2 track: rather than taking AB-BC-MVC, they’d take whatever calculus in 11th grade, intro to proofs in 12th).”
Very few high schools have teachers that can teach an intro to proofs class, especially to kids taking calculus in 10 or 11th grade. If they could teach that, they could teach Linear Algebra, as someone posted earlier, but LA has to be taken at the local community college or UC/CSU if they’re close by.
"good-but-not-great-at-math students when those parents insist on putting their kids in the +2 track when they really should be in the +1 or +0 track. "
You keep bringing this up, the many kids who struggle with Calc in 10 or 11th grade because they have pushy parents. Do you have any data on this, or it just anecdotal posts on c/c? I know a lot of kids that are fine with Calc in 10th or 11th, don’t have pushy parents and are at places like MIT, Cal Tech, UCB, highly competitive OOS flagships like UM, Purdue, UIUC, et al.
“there are some really interesting ways to do this at a high school level”
Again, the teachers are not there for any kind of Cal Tech course, even the most fundamental, at least at public high schools. Even the better AP teachers have a comprehensive curriculum from the college board that they follow. Also, if you could teach proofs like that, you probably would be at Cal Tech.
It is pretty common to see students posting that they feel that they are “not that good at math” even though they are in the +2 track.
Then again, there are also parents who are extremely unrealistic. There was one recently who was worried that a B grade in one out of four college math courses (others A grades) taken by a student who completed calculus BC in 9th grade would disqualify the student from admission to highly selective colleges. The student was clearly a top student in math, but that apparently was not good enough for the hypercompetitive parent.
Since this program would be phased in in 2025, this leaves time to VA’s public universities to train and prepare math teachers who’d be ready for that level - perhaps providing good college scholarships to attract math talent in exchange for a 4? 5? 10? years commitment to teaching at a VA public school and offering that course to a district’s students; in addition, those completing the program could presumably command a bonus that the DOE could plan for.
In other words, if this were a plan, there’d be way to make it happen.