Virginia educrats drop the hammer on advanced math education

[Kimstu]

@ZosterSandstorm

85% of Fairfax County students who take the BC exam score 3 or higher, out of easily 2000 or more who enroll in the class every year.

Could you provide a cite so I understand exactly what quantitative claim you’re making here? Is that 85% of 2000 students who take the BC Calc exam every year, or 85% of some subset who actually take the exam among the 2000 enrolled in the course?

And as Jas09 noted, there’s nothing about the Virginia Math Pathways proposal that will prevent students from taking BC Calc.

@ZosterSandstorm

We should track students who will not be using math after high school into a few years of practical economics and statistical reasoning classes […]

We should track students who will be attending college as humanities majors to cap out around Calculus AB […]

But this is exactly the sort of thing that the Virginia Math Pathways proposal is advocating! Did you read that “Case for Math Pathways” document on their website you linked to?

In 2015, the MAA, along with four major mathematical professional associations—the American Mathematical Association of Two-Year Colleges (AMATYC), the American Mathematical Society (AMS), the American Statistical Association (ASA), and the Society for Industrial and Applied Mathematics (SIAM)—reaffirmed this recommendation, calling for multiple mathematics pathways that are aligned to fields of study, some of which should include early exposure to statistics, modeling, and computation (Saxe & Braddy, 2015). […]

This document cited in the above “Case” document makes a similar argument for such pathways in high school.

Good heavens ZS, you’ve spent a dozen posts or so fulminating against a pedagogical redesign proposal that apparently you actually agree with. The chief difference is just that what you call “tracking”, they call “pathways”. (They’re using “tracking” in the more usual pedagogical sense of just assigning students into perceived “ability” cohorts from an early age, without reference to particular areas of study.)

[ZosterSandstorm]

No, the new standards replace tracking from 4th grade up, which is the current practice, with a much more restrictive tracking in 11th and 12th grade only. This not only removes years of benefit from advanced instruction for students who are more skilled than the “vast majority” but it effectively cuts off the top of one of the tracks entirely.

[Kimstu]

@ZosterSandstorm

@Kimstu

the 1-3% of all high school students who really can benefit from such extreme acceleration as reaching calculus early in high school, and moving on to advanced college math before graduation

Why should these students be denied opportunities to take the appropriate courses at the schools they attend? In Northern Virginia you have 30+ high schools offering Calculus BC with over 85% of students passing the exam.

As Jas09 has also noted, we seem to have a persistent communication disconnect here. The vast majority of students who take Calculus BC, even in places like Virginia’s Fairfax County, are not doing so early in their high school career.

Yes, it’s absolutely reasonable for all students to have the opportunity to take high school math up to the BC Calculus level if they want to, and AFAICT there’s nothing in the Virginia Math Pathways proposal that would prevent that.

But no, IMHO a standard high school curriculum should not be routinely offering math courses above the BC Calculus level. The proportion of high-schoolers 17 or under who have really learned enough algebra, geometry, analytic geometry, trigonometry, single-variable calculus, and possibly some linear algebra as well, in enough depth and precision to meaningfully understand a multivariable calculus course, is too tiny to be a reasonable priority for high-school curricular development in mathematics.

@ZosterSandstorm

but it effectively cuts off the top of one of the tracks entirely

“Cutting off the top” of the standard high school mathematics curriculum above BC Calculus, as I said, seems eminently reasonable.

[Kimstu]

@ZosterSandstorm

This not only removes years of benefit from advanced instruction for students who are more skilled than the “vast majority”

I’m not at all persuaded that just dumping some subset of students at an early age into a cohort called “gifted” or some such necessarily leads to “benefit from advanced instruction”.

I am absolutely all in favor of allowing flexibility in student learning at the individual level, with individual acceleration and enrichment opportunities and so forth. But just shuffling a bunch of nine-year-olds (which is what fourth-graders are) into a few permanently (or nearly so) assigned categories labeled “Smart”, “Average” and “Dumb”, or some paraphrase thereof, has very little to do with actually providing individual learning opportunities.

[Jas09]

Right, the big change, such as it is, is that in 9th and 10th grade you just take “Essentials of Mathematics” (or something like that). It teaches a wide range of concepts relating to functions, trigonometry, etc. It’s all the groundwork you need for advanced courses in your Junior and Senior years.

What is supposed to happen is that more apt students are able to dive more deeply into the various topics rather than race ahead checking off curriculum boxes so they can jump into Algebra II, etc. And more to the point if a student doesn’t do great in 9th grade but then loves various pre-calculus topics in 10th grade they still have a chance to do calculus even though they weren’t in the “top track” as a freshman.

From what I’ve seen, and what I remember of HS math, it’s probably not a terrible idea. There was a lot of pressure on getting on the “right track” as early as 7th grade because if you didn’t you would never get to Calculus and then never to go Harvard (or whatever). It was pretty dumb. It happened in science too, but not nearly as bad as math.

[Snowboarder_Bo]

@ZosterSandstorm

We should track students who will not be using math after high school into a few years of practical economics and statistical reasoning classes that will help them be better citizens and managers of their lives, then let them use most of their time in 11th and 12th grade on learning skilled trades so that they are prepared for life after high school.

Actually, it seems that the studies say that we should not be tracking students as you describe.

Also, what indicators would be used to determine which 11- and 12-year-olds “will not be using math after high school”?

[MandaJo]

The practical applications of the proposed policy are not clear to me, so I have no comment there.

However, I will say that it is ABSOLUTELY possible to end up with kids that are good at Calc and bad at Algebra 2/geometry. My school has a quarter of kids finishing AB by Freshman year and another 50% by the end of sophomore year. We have a 99% pass rate on the AP exam for years. But the science teachers will tell you that the kids struggle with slope, isolating variables, graphing. As the SAT lady on campus, I can’t tell you how many easy slope questions they miss on the damn thing because they don’t get what slope IS.

I love advanced math. Having advanced math available is a joy to my kids, truly. But the arms race does lead to weaknesses in fundamental skills (especially when Calc teachers prioritize keeping that 99% pass rate above all things.)

[Kimstu]

@Jas09

From what I’ve seen, and what I remember of HS math, it’s probably not a terrible idea. There was a lot of pressure on getting on the “right track” as early as 7th grade because if you didn’t you would never get to Calculus and then never to go Harvard (or whatever). It was pretty dumb.

Yup. Although as former Mathematical Association of America President David Bressoud said in one of the articles I linked to above, the ultimate source of that problem is the colleges, not the high schools. If colleges stopped telling high schools that calculus was necessary to be a competitive applicant, high schools would stop trying to rush so many students into calculus before they’re ready for it.

@Snowboarder_Bo

Actually, it seems that the studies say that we should not be tracking students as you describe.

This whole controversy is doing none of us any favors with its persistent ambiguity around the terms “tracking” and “pathways”. Here’s how I think the terms are generally being used in the pedagogy literature:

Tracking: In its typical use, AFAICT, this refers to a system of assigning all students into broad “ability-based” cohorts, generally beginning under ten years old and sometimes as early as five, and allowing them to enroll only in courses approved for their cohort, irrespective of subject.

From reports I’ve seen, it’s not clear that this accomplishes much for anybody except to convince students who aren’t in the highest cohort that they are comparatively “dumb” and can’t expect any high academic achievement.

The body of research is made up of a variety of different studies looking at the academic effects of separation for gifted and high-achieving students, including research on de-tracking efforts, gifted programs, and alternative approaches to enrichment. The common finding across these studies is that a system of sorting and separating students based on academic level is neither necessary nor particularly helpful for supporting gifted and high-achieving students. […]

More than a dozen studies across four decades point to a clear result: academic tracking—the practice of sorting students based on perceived academic ability into different classes—harms the students assigned to lower levels. […]

Furthermore, several recent studies, specifically examining elementary school gifted programs, have found that separating gifted students does not help their academic achievement. […]

While the studies on separate gifted programs show lackluster results, research on approaches that make enrichment available to many or all students in a school are promising. One such approach is the schoolwide enrichment model(SEM), which was developed at the University of Connecticut.

SEM is an approach to teaching and learning that draws from the pedagogy of gifted education to enhance opportunities for all students in a given school. Schools using this model typically identify “gifted behaviors,” including above-average academic abilities, creativity, and task commitment, rather than attaching a binary (“gifted”/“not gifted”) label to each student. SEM advises schools to use flexible student groupings that change throughout the course of a year and bring together students with different achievement and interest levels.

Pathways: This is the sort of “career-path” specialization in (usually) secondary education that groups students based on their goals and interests rather than on some generic “ability” score, and tailors courses of study to serve different types of goals and interests.

Student Tracking vs. Academic Pathways: Different…or the Same?

What the OECD data show us is that in the United States social class and parental education are more predictive of educational achievement than in most other industrialized countries. […]

Now along comes the idea that we ought to provide pathways for the kids in our secondary schools. That word means different things to different people. Some […] use it to describe ways that schools, working with business, can provide real opportunities for kids who now leave school with no useful credential and can provide apprentice-like solutions that will lead to a far better future, something that some European countries do far better than we. When those kids are offered a strong academic education, combined with a work-based training that can lead to a rewarding career with no dead-ends, everyone wins.

@MandaJo

But the science teachers will tell you that the kids struggle with slope, isolating variables, graphing. As the SAT lady on campus, I can’t tell you how many easy slope questions they miss on the damn thing because they don’t get what slope IS.

Oh so true. And if you were hoping that that problem magically solves itself in the summer before they head off to college, I’m afraid I have bad news for you. (I didn’t really suppose you really thought it did.)

[What_Exit]

Modnote: I don’t see a magnet school ban for you listed anywhere. I have seen a clear instruction for you to avoid making attacks on other posters in GD and P&E. So from what I can see, you can talk about magnet schools as long as you can avoid attacking other posters.

[Czarcasm]

@ZosterSandstorm

The people who illegally replaced test-based admission to TJ with a “holistic evaluation” aka race-balancing

@Czarcasm

I don’t remember that court case-got a link?

Asking again-got a link?

[amarinth]

@MandaJo

However, I will say that it is ABSOLUTELY possible to end up with kids that are good at Calc and bad at Algebra 2/geometry. My school has a quarter of kids finishing AB by Freshman year and another 50% by the end of sophomore year. We have a 99% pass rate on the AP exam for years. But the science teachers will tell you that the kids struggle with slope, isolating variables, graphing. As the SAT lady on campus, I can’t tell you how many easy slope questions they miss on the damn thing because they don’t get what slope IS.

I don’t get this at all. How can you possibly do well in calculus without understanding slope? How can you understand derivatives without understanding slope?

I used to tutor students who were placed in advanced math who didn’t have math fundamentals down (basic algebra, sometimes even fractions), and that was apparent in their grades. It seems odd that the AP tests don’t pick up on the lack of foundational understanding.

As far as the proposal, I’m old and went to a highschool that was vehemently anti-tracking. There was a progression for math, but any student could double up or learn outside of school. So while the majority of students in the more advanced math classes had been taking math together all the way through, there were always a few who hadn’t taken that more obvious route. It worked well. Much better than deciding which children should be given opportunities when they’re in 4th grade and locking the rest out.

[Eonwe]

@Jas09

What I’m getting from it is that they are trying to get away from the Algebra I → Geometry → Alegebra II/Trig → Pre-Calc - > Calc I → Calc II tracking path where you just plop down and move to the right every year or semester. Instead you build up skills in the areas you need for the careers you are thinking of pursuing and only need the common foundational stuff. And they are adding a bunch of half-credit courses at the HS level so folks that don’t need Calculus for their career can take things like financial modeling or advanced geometric or statistics courses.

You forgot, the other important part, which is that evil left-wing Democrat dogmatic cultists hate America and want to destroy our schools and our economy, just to give a hand out to black people who don’t deserve it.

Which is what this whole panic amounts to.

[MandaJo]

I think they just quit recognizing it in Algebra 2 contexts. I don’t teach math, but those kids DRILL specific problem types. They never see a problem you could solve with just algebra. I do know that we had a department chair who really focused on spiraling in Alg 2 concepts in continuously, and while he was here the kids were better at it. But he left, and now it’s all chanting derivatives.

We have a similar system: it’s not a track, but if you are behind, you’ll have to hustle to catch up.

For our “top” kids: Ninth grade year they take Geometry (separate class) and a double blocked class called “Freshman Calculus” where they meet 90 minutes every day and do Algebra 2/Pre-Cal before Thanksgiving and start AB at Thanksgiving. They have “Trig week”. But those kids are really strong and really love math and it works. They take BC as sophomores, Stats as juniors, and a post-AP survey course as seniors.

For the middle 50%: Nine grade, they take geometry as a separate class, and a double blocked class (90 minutes every day) that covers Alg 2 in the fall and Pre-Cal in the spring. Because it’s a “double” class, it goes at the “normal” speed: they are just in Freshman, Sophomore, and junior math all in the 9th grade. Then, as sophomores, they take AB (which we also double block, so that everyone has the time they need) and BC as juniors. Senior year they take Stats and can opt in to the Post-AP math survey if they want (so they are “caught up” to the first group)

For the bottom quartile: Geometry as a separate class (and these are all mixed together) and then a double blocked (90 minutes a day) Algebra 2 class. This is much slower than at a “normal” high school, albeit a year earlier. The idea is that these are typically kids that are average at math but want to go into STEM fields, so lets take a year and give them deep support. Then pre-Cal as sophomores and AB as juniors. Senior year they take BC. If they want, they can take Stats as juniors as well, and the post-AP survey as seniors–so they finish the same as the top group.

We used to have much more rigid tracks. This system has worked really well (although, as I said, we do sometimes leave Alg 2 behind, when you don’t really see it after Freshman year, and then find you really need it in AP Chem as a junior, or on the SAT).

[GIGObuster]

@Eonwe

You forgot, the other important part, which is that evil left-wing Democrat dogmatic cultists hate America and want to destroy our schools and our economy, just to give a hand out to black people who don’t deserve it.

Which is what this whole panic amounts to.

Incidentally, one way to check for the sources the OP is relying on is to enter keyword combos in the search engine from his OP like “Virginia educrats” and advanced and math, then cites from right wing outfits that are not even recognized as reliable by NewsGuard pop up. So far it is indeed a very exaggerated panic from the right, and with very bad sources of information harping on it.

[ZosterSandstorm]

@Kimstu

Tracking: In its typical use, AFAICT, this refers to a system of assigning all students into broad “ability-based” cohorts, generally beginning under ten years old and sometimes as early as five, and allowing them to enroll only in courses approved for their cohort, irrespective of subject.

From reports I’ve seen, it’s not clear that this accomplishes much for anybody except to convince students who aren’t in the highest cohort that they are comparatively “dumb” and can’t expect any high academic achievement.

Tracking in math class based on demonstrated math ability is worlds apart from the misguided notion of identifying who is and is not “gifted” and making every decision based on that.

There are, obviously, more than zero people who can handle being taught math at a faster pace than the average denizen of the public school system. The total abolition of acceleration is not appropriate for serving the needs of students as individuals and is bad for society as a whole. This is only going to further bifurcate schools into a public school feedlot-and-warehousing system and a private alternative where only people with money can get a decent education.

[Kimstu]

@ZosterSandstorm

The total abolition of acceleration is not appropriate for serving the needs of students as individuals and is bad for society as a whole.

There is no indication that the proposed Virginia Mathematics Pathways initiative is advocating “the total abolition of acceleration”.

You seem to be taking your talking points from this Fox News article, which quotes but largely ignores the statement of a VDOE official contradicting that claim.

VDOE spokesperson Charles Pyle indicated to Fox News that the courses would allow for at least some variation depending on students’ skill level. “Differentiated instruction means providing instruction that is catered to the learning needs of each child (appropriate levels of challenge and academic rigor),” Pyle said. […]

Pyle added that VMPI “aims to support increased differentiated learning opportunities within a heterogeneous learning environment, that will promote greater access to advanced mathematical learning for all students before high school graduation. […]”

As I said, I think it absolutely makes sense for standard high school math curricula to “abolish acceleration” beyond advanced single-variable calculus. There are far too many students being rushed through math curricula to get to, or beyond, introductory calculus when they don’t have a good grounding in pre-calculus subjects.

Even if you choose to ignore all the previously posted anecdotes and articles about this problem, you might want to check out this one:

The rush to calculus is bad for students and their futures in STEM

[…] It is quite possible for students to learn the mechanics of many categories of calculus problems and to answer questions correctly on exams without really understanding the concepts. To quote the MAA’s report:

In some sense, the worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus. […]

Many students take Calculus I again at their universities, even if they have a passing score on the AP exam. There are many reasons for this: some colleges insist (engineering programs in particular) and many medical schools demand that applicants take the course at a university. Or students may not feel particularly confident about their abilities. In my own experience, the number of students retaking the calculus course is very high – in a typical section of engineering calculus, up to 90% of my students have taken it in high school. While there are some positive aspects to retaking the course, there are downsides, the most notable of which is overconfidence and a student’s misplaced certainty that he or she already knows the material.

A typical first-semester calculus course consists of 45 lectures delivered three times per week over a 15-week term. The pace is quick. Contrast that with a typical high school Calculus AB course, which meets five days per week for 180 class meetings. The college course covers the same material in a quarter of the time; students must therefore have solid skills in algebra and geometry along with good study and work habits to succeed.

So this is the crux of the problem: students lacking the requisite foundational abilities may not succeed because the college faculty member expects them to be at ease with these more basic ideas, freeing them to absorb and understand the new, more conceptual material. The rush to AP Calculus has instructed students in the techniques for solving large classes of standard calculus problems rather than prepare them for success in higher mathematics.

Demanding to retain a curriculum structure that encourages the “rush to calculus” is not doing any favors either to high-achieving high school math students, to all the rest of the high school math students, to high school math teachers, or to college math and science professors. If the Virginia DoE is trying to break free of this counterproductive structure, then good for them.

[ZosterSandstorm]

As we’ve already gone over in the thread: It’s entirely clear that one of the core changes involved in this proposal is that everyone has to take the same “essential concepts” classes through grade 10, which will replace the old prealgebra/algebra/geometry/Algebra II sequence with a mixture of those classes. Everyone has to take the same classes through 10th grade, no one can take trigonometry/analysis/precalculus before grade 11, and thus no one can take calculus before grade 12.

Taking geometry in 9th grade and Algebra II in 10th grade is the standard, non-accelerated expectation for students in Virginia today. Forcing everyone to follow that pace and forbidding taking precalculus classes before 11th grade is, in fact, getting rid of accelerated math classes. I don’t know what you’re looking for here - unless the proposal is called “Accelerated Math Is Banned” it doesn’t count, even though it does in fact ban accelerated math?

The idea that this isn’t going on, or that NO ONE should be allowed to take calculus in high school because SOME people take it too soon, isn’t supportable. There obviously are nonzero students who should not be hobbled into the “average” curriculum, and refusing to meet their needs by pretending they are going to benefit from being forced into mediocrity is just more equity cult nonsense.

[Snowboarder_Bo]

Is the opposite of the Equity Cult the Inequity Cult? Or do they prefer to be called the Unfairness Cult? The Lopsided Cult? What’s the proper nomenclature?

[Kimstu]

@ZosterSandstorm

Everyone has to take the same classes through 10th grade, no one can take trigonometry/analysis/precalculus before grade 11, and thus no one can take calculus before grade 12.

Wrong, according to the infographic in the VDoE site you linked to. Students can not only choose to mix and match their half-credit courses in any order and combination they’re individually prepared for, but they can also take their one-credit courses, including calculus, with dual-enrollment and advanced placement options.

So yes, I’m sure that plenty of students in this system will end up first encountering calculus before grade 12.

Furthermore, the proposed differentiated-instruction model as part of the Math Pathways means that students who master the basics in their various “concepts” math courses can learn additional material and techniques in that subject as well. That’s generally a better approach to a subject in mathematics than just drilling all students through the same rote algorithms and formulas to cover the same material.

@ZosterSandstorm

The idea that this isn’t going on, or that NO ONE should be allowed to take calculus in high school because SOME people take it too soon

As has been explained to you many times already, this proposal is in no way suggesting, much less requiring, that “NO ONE should be allowed to take calculus in high school”.

When you can’t argue against a proposed reform without setting up inaccurate strawmen that misrepresent it, that should be a signal to you that your attempted arguments are not sound.

@ZosterSandstorm

There obviously are nonzero students who should not be hobbled into the “average” curriculum

The whole point of this proposal, ISTM, is that no students end up “hobbled into” an “average curriculum”.

Instead, the goal is for all students to gain a solid grounding in core subjects while absorbing additional related topics and concepts to the extent of their individual interest and capacity. Then each student moves into a chosen “pathway” providing a custom curriculum adapted to their own goals and interests.

[ZosterSandstorm]

@Snowboarder_Bo

Is the opposite of the Equity Cult the Inequity Cult?

“People who recognize that differences among people are real, that not all differences are bad, and those that are bad should be solved by improving the situation of those who are at a disadvantage rather than penalizing achievers.”

If you need a shorthand, “people who live in reality” or “sane people” work fine.