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Comment by testfoobar | Hacker News Reader

Wealthy suburbs are cutting advanced classes too. Palo Alto Unified School District is dropping dual-enrolled Multivariable Calculus and Linear Algebra (classes taken after AP Calculus BC).

https://www.paloaltoonline.com/square/2023/03/29/cancellatio...

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My kid is on this track exactly and I think it is a joke that some kids take multivariable calculus or linear algebra in high school. Enrichment and AP has become an arms race for the upper middle class to get their kids into good schools. Realistically, if you are STEM major you probably are going to have to retake these classes anyway. And if you aren't you probably won't need them.

I know some kids are really exceptional and maybe ought to take this much math that young. But I think a lot do it now to get into a college.

Couple of points. 1) Colleges expect students to take the most advanced curriculum available. With grade inflation across the board, AP and Honors classes are not the distinguishing factor they used to be. 2) With the entire world's resources at their fingertips an ever larger cohort of kids is advancing to higher level math classes at earlier stages.

Frankly, Multivariable and Linear Alg. is on the low end of the ability of advanced high school kids these days. The ease of deploying tensor flow has gotten a lot of kids motivated to learn linear algebra.

I did have to retake multivariable (calc 3) and linear algebra, but I'm grateful for that senior year HS class because: - the college versions were a breeze, which was a relief because the workload from other courses was high - having a good intuition about divergence & curl made physics (electromagnetism) easier, and linear algebra was used in differential equations before I actually took linear algebra

So I think for a high school student who knows they're heading for STEM, with room on their schedule, it can still be a good choice.

> I think it is a joke that

Standards change greatly with time and it is a joke to believe that applying the same standards to everyone will get a good outcome.

Anecdata: I would have loved to get the possibility to study higher math at high school level, at school. I had to dig it out on my own since the local school topped out after basic calculus, linalg, statistics. I was not alone.

Today I would estimate that top 5% could easily and happily handle multivariate, ode/pde, etc in high school given proper support and encouragement.

Top few percent learn several times faster than average. What is the point, other than ancient ideology, to slow them down and hinder their learning progress?

Math is a hard, abstract, mental discipline, so it’s very plausible that mere exposure to some concepts increases the subsequent understanding.

For example, I was one of the best students in class, yet it took me about a year to really get stochastic processes.

Taking advanced classes could be valuable even if you need to retake them.

I wholeheartedly agree. Exceptions to the rule always exist and I don't want it to be impossible, but they should be entirely optional and non-standard. You are going to re-learn it anyway (and learn it better, from first principles instead of patched together).

It's also an arms race that's misplaced. STEM majors are learning math anyway, there really are diminishing returns in cramming more of it into your school curriculum. A lot of different subjects are way more useful, ideally some that do exactly not prepare yourself for a major of your choice, otherwise you end up with over-optimised education. You need some social studies and discuss current topics moving america and the world. You need to write essays about these difficult topics. You need a little bit of science and a little bit of history. And a foreign language. It's about the abstract ideals of education, afterwards you can choose the major you want.

I'll cancel your anecdote with mine.

I didn't take any advance math in HS and actually did quite average. By some miracle I was admitted a very good Electrical Engineering program. However they made me take these advance math classes before university to prove that I could handle the task.

Removing these options from HS just lowers the bar for everyone.

I wish they would teach these classes with some context in high school. Rather than have a course on linear algebra, they could do something like Intro to Machine Learning or intro to writing a good physics engine, or perhaps computer graphics. Teaching linear algebra without context, especially to high schoolers, doesn't seem to be very useful, but adding in the context (at the expense of maybe depth) could be transformative.

I wish I had studied more math during highschool. University killed any free time I had and was so fast-paced that proofs were omitted, entire chapters skipped and I'm not even talking about building intuitive understanding of the subject.

In contrast, high school was three years of repeating the same equation solving with some calculus sprinkled on.

I have a hard time believing above average students (with parents with parents without engineering/science degrees) could take linear algebra and multi variable calculus at university rigor along any other courses they are required to take. Sure, maybe at Paly and Gunn there’s enough to fill a 20 person class, but those are still pretty steep courses which require math majors and not math education majors.

If the students are prepared enough for those classes, what’s the point in keeping them in High School anyway?

I had a strange experience where I had a bunch of AP courses lined up my senior year and then moved to a place which did not have nearly any of them. In hindsight, I should have really pressed for direct enrollment to college instead of faffing around my senior year in “communication skills”, AP english, and “Economics” - all three required by the school district but mostly useless.

At some point the answer should be to support students just taking a class or two at a local university. This is totally reasonable.

This is in fact how the programs are structured at many high schools with dual-enrollment. Most top high schools in the Bay Area offer such options for Multivariable Calculus and Linear Algebra. What Palo Alto is doing is dropping formal support of the program - in practice that has meant bringing college professors to school sites and providing these classes without fees for students. Without formal support, students have to pay and have to commute.

My senior year math course (after Calc BC in grade 11) was discrete math at the community college across the street. Felt a little embarrassing for us to take up half the classroom, sitting next to adults, and realizing that most of us high schoolers were towards the top of the class. But other than that unfortunate situation, I think it was a good system, and if anything, cheaper for the school district than finding someone to teach in-house.

I went to community college in California and there were high school kids in some of my classes.

Not that I was taking particularly hard classes or anything so I think they were just getting a leg up on the prerequisites for later on.

My school only offered one language and I wanted a different one. So I went to the nearby public university.

These courses are the next step after Calculus BC. Lots of kids take them with the support of their high school. Paly & Gunn combined have something like 90 kids who take Calc BC their junior year.

> I have a hard time believing above average students (with parents with parents without engineering/science degrees) could take linear algebra

Linear algebra is not hard. I had a math teacher who taught the basics of linear algebra in my middle school math class. While she was an exceptional teacher (incredibly good, we still talk over 25 years later!), I can attest that the concepts presented no great difficulty to any of the students (with the caveat that all of us were in an advanced learning program)

Now calculus, I feel that at least some high school students I've talked to really didn't "get it", even for single variable. Then again I get the feeling that most people who take calculus don't get it, which I find sad because IMHO calculus is absolutely phenomenal. For me, it was when math started really connecting to the real world and making an impact on how I saw things in my day to day.

For many advanced kids, math is not hard. It is a tool that must be mastered to solve the next set of problems. Profound understanding comes along the way.

> Linear algebra is not hard

Keep in mind that this term covers a huge range of math that can be introduced at very different levels of abstraction and generality. You might think linear algebra is mainly matrix multiplication and Gaussian elimination, someone else might think it's about the representation functor in Abelian categories.

We're talking about HS intro classes, so my use of Linear Algebra was at the same level as saying, well, Algebra. E.g. Non-math major uses of those terms.

Almost any subject in math can go really deep!

Yes. However, I read your post as suggesting (given the quote you respond to) that significant numbers of high school students can/should take university level courses of the same name as their high school courses, presumably because it's the same thing.

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