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Comment by gowld | Hacker News Reader

Note: The article is about the high-school math ("College Algebra" and "Finite Math", material covered in "Algebra II" and "Precalculus" in high school) that is taught in remedial classes in community colleges.

From my perspective as a tutor of several students (one who was a libarian, another in nursing school), it's a very popular but strage class to offer, as it's of no use to the nearly students who take it after high school -- it's too abstract for those students, which is why they didn't learn it the first time they saw it in high school, and aren't going to use it in their careers as nurses or office workers or other community-college careers.

"Business mathematics" and "personal finance" would probably be more helpful to these students.

Of course, it's not the OP's fault that community colleges demand these weeder courses.

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It's probably the thinking in your antepenultimate paragraph reinforcing itself. Instead, abstract skills can offer a gateway to the application of more rigid rules, so to speak, because it shows that they are strong, but the applicability is flexible.

Math grad student lecturer of various university entry level to intermediate mathematics courses at UF and ASU here. Over 30 years ago, but the following anecdotage is still vivid in my mind:

I taught many hundreds of students quite a variety of courses ranging from 'Finite Math', entry level algebra, all the way up to honors calc and linear algebra. Unique among all the courses, 'Finite Math' was so entirely abstract I, the math grad student, could not understand the point of the exercises.

I only taught it once, but after two weeks the coursework was so incoherent I stated in class that I would teach them exactly how to solve the problems, and if they learned that, they'd pass (all they cared about). I explicitly stated I wouldn't try to teach them anything at all about why any of it was relevant to their external problems.

Exactly the opposite of my approach to every other course, all without fail entirely satisfying to teach. I loved teaching college math! I'd do it again for very little, but the absurd adjunct rates are strongly discouraging.

That is, I'd teach anything but these ridiculous stand ins for math courses like 'Finite Math'.

OTOH, there's a deep beauty in real math starting with calculus and I dunno I find it calming and even though abstract and not really applicable to the external world these days it might be useful for some prisoners' mental health. There are a lot of stories of the prison library opening up some otherwise hopeless cases.

> I taught many hundreds of students quite a variety of courses ranging from 'Finite Math', entry level algebra, all the way up to honors calc and linear algebra. Unique among all the courses, 'Finite Math' was so entirely abstract I, the math grad student, could not understand the point of the exercises.

Yup. The stuff we teach in trig and precalc provides some preparation for calculus, but it seems pretty broken.

Even early calc instruction tends to be broken-- we make things complicated over various historical analytic crises, but then we take enough shortcuts in explanation that we still need to relearn half of everything when we take an actual analysis class.

I have a 5th grader who's taking Algebra I now and will rapidly run out of math classes he can take while in middle school. I'm hoping I can find him a better path for preparation for calc.

I have a 5th grader who's taking Algebra I now and will rapidly run out of math classes

Have you tried giving him more challenging problems based on his existing math level? Work on his problem solving skills could benefit him a lot. Most high school math is just repeating the example solution with different numbers.

One nice source of challenging problems is the past contest page of the CEMC [1] (disclosure: my university runs these contests and I have participated in grading for them). They have contests for a variety of grade levels and both the contest PDFs and the full solutions are available for download, entirely for free!

[1] https://www.cemc.uwaterloo.ca/contests/past_contests.html

Hey, thanks for the link!

He's doing well in the MOEMS Math Olympiad stuff and is going to be taking a class on inductive and deductive reasoning this summer.

To some extent, we have a different problem-- a lot of what "more challenging problems" tend to be is word problems with lots of distractors and often even vocabulary he doesn't know yet. He has great math intuition and ability to symbolically manipulate and spatially visualize problems, but he reads like a smart 10 year old, not a 13 year old.

I'm sort of assuming this will sort itself out as he gets older-- and he still got an A- in his pre-algebra class (which had enough shuffling of radicals, etc, that it was pretty decent fraction of Alg I).

(Also a little gripe about the online math class having a nominal 3 hour final... you can see his accuracy in the last half of the test was a fair bit lower than the first half).

Does he like to read fiction? When I was that age I excelled in math but I also loved to read fiction, mostly fantasy novels. I read Lord of the Rings at a very young age and it really expanded my vocabulary.

I'm not sure how English is taught at your son's school, but I have the sense that a lot of schools give kids material at grade level. I think this is an unambitious approach. Reading to challenge yourself is the best way to get better, just as solving challenging math problems helps you get better at math.

Admittedly, it's hard if the kid is not interested in what you're getting him to read. I am a bit dismayed at what appears to be a broad decline in fiction reading among boys. I think there needs to be more emphasis on finding books that boys will enjoy reading while also challenging them.

> Even early calc instruction tends to be broken-- we make things complicated over various historical analytic crises, but then we take enough shortcuts in explanation that we still need to relearn half of everything when we take an actual analysis class.

Take a look at Calculus Made Easy. It's non-rigorous - it uses infinitesimals without the machinery of non-standard analysis, instead of limits - but it presents the material in a clear and concise way such that just about anyone who can do basic algebra and computations can learn the material and develop an intuition for how calculus works. Once the intimidation factor is gone, they can go back and learn about epsilon-delta etc.

Thanks for the suggestion-- I'll pick it up! It looks like there's a recent revision with modern notation (though the reviser couldn't resist adding a chapter based on limits).

> antepenultimate paragraph

“Second paragraph” is a simpler way to put it.

"Second to last"

"Third to last"

I was confused, I meant "second to last" indeed, but you are correct.

By that I did mean you should have called it the second or third sentence instead, not that antepenultimate means second from last. Doing otherwise in a four-paragraph passage (and nearly any other context, frankly) is absurd and makes most people think you’re trying to sound well-read, and you end up where it is unclear even to yourself what you said.

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