Most people do learn some math skills. Many kids learn more than the basics. Obviously experiences vary. Yes, there are a lot of out-of-classroom factors.
I think second language learning is a more extreme case though. Many language programs seem to produce very little. Math doesn't have that kind of variance. If kids' math skills are years behind another school system's... that gets noticed and acted on. If a language program produces almost no language skills, it tends to just be accepted.
I agree but I think the difference with languages is that it's almost impossible to avoid that for most people. Most children go to countries speaking other languages very rarely.
I live in the UK and "learnt" French in school. I went to France twice before I was 18.
Obviously there are places where it's different. I bet schools in California have some success teaching Spanish for example. But it's easier for subjects like Maths and English to answer "why will I ever need this" (even if they still usually do a pretty terrible job).
A trip to South Kensington is probably easier for almost the same result ;)
I also think that most kids do actually learn a lot math in schools. Some don't and are totally clueless, but most of them are acceptably good and most of them don't make all that much fuzz about having to learn it.
Math teaching in school? Maybe. It doesn't seem to be very efficient, and mostly a waste of time.
(And I say that as someone who has studied math at university.)
My father, who was a biology teacher, advocated that high school biology should be taught largely for the benefit of the vast majority of students who would never take another biology class in their life — a self contained curriculum focusing on nature observation and on practical interactions of biology with the world.
I went through a high school curriculum focused on classical languages, and went on to a math-heavy CS school. The entirety of my high school math probably helped me for less than one semester. The math of my colleagues who attended a math focused high school track helped them for maybe one more semester at most (Their drafting classes might have been more valuable). Yet my Latin and Greek, which I never studied anymore after high school, still occasionally comes in handy to prop up my vocabulary or read street signs in Athens.
The content of high school math is important only in the sense that it must interest the kids and might be vaguely useful later on. The real prize is systematic problem-solving skills and confidence.
Can you elaborate on this?
I have no idea how worthwhile that kind of instruction was; knowledge of anatomy hasn't featured in my career. I suspect it would have been very helpful if you decided to become a physician.
My view is biased, because I had some very good physics teachers in high school and an interest in the subject.
So here again, I doubt that a typical student at a typical school gets all that much out of the lectures.
Is there any interesting thought on how to incentivize quality in outcomes and content creation there? Where the usual pervasive failure doesn't get the disaster-triage-chain-of-care back-pressure of follow-on instruction? It's an issue I've been puzzling over.
Even first-tier college intro biology still struggles to leave students with a firm grip on even central dogma, something that can be taught down through middle-school. But at least improvement is incentivized when follow-on intro genetics is forced to remediate. In contrast, with mostly-terminal college intro astronomy, of the top ten-ish most used textbooks, most all have even the color of the Sun wrong, perpetuating the pervasive kindergarten misconception even into first-tier astronomy graduate school. A failure that's been long-term multi-decade stable, and seems unlikely to improve any year soon. And there's teaching order-of-magnitude size, a part of most-every science and engineering curriculum. But it's little used in subsequent instruction, so there's little selection pressure to teach it successfully. Leaving even first-tier medical school graduate students with little idea how big cells are. And even with narrow objectives and chain-of-care feedback, chemistry education content is described by chemistry education research using adjectives like "incoherent", and as leaving both students and teachers steeped in misconceptions. Science education content is pervasively very not wonderful, and would seemingly lose some of its very few quality constraints by not targeting follow-on instruction.
At the other extreme, in the context of pre-K science education, there's been a suggestion that students have a human right to make sense of their world. "Now", not a K-lifetime later in middle-school. We're very not set up for that. (Or even to do that in middle-school, or high-school, or undergrad, or ...). We are largely unable to even imagine what it might look like. Crafting content for it would seemingly require a massive collaborative effort from the science research community. But it's very not clear how to incentivize, or even to characterize it.
Which ties back to language learning. I talked with someone doing remote tutoring of French. For students with diverse objectives - the AP French exam, family culture, travel for tourism, and for work. And thus with diverse curriculums. Apparently the AP French exam tests for a particular type of conversational French, and is very hard. So even teaching to the test, it is a struggle to get good outcomes. So there's just not room for expanding scope, for other curricular objectives, for other aspects of what it can mean to learn French.
Which reminded me a lot of "physics" education, and physics education research. The pursuit of a worthwhile goal, and hard one. With even the rare excellence of best practices struggling for good outcomes. But also a narrow goal, with little room for scope expansion, with no room for much of the beautiful breadth of Physics. The old professorial lament, of "why would students be interested in majoring in physics, when they've never been shown any interesting physics?". (Or for a feel for reasonable values, etc). Which prompted me to wonder: Perhaps "making sense of the physical world" is fruitfully viewed as a goal distinct from normal "science" education? Rather than framing it as transformative improvement of science education?
If we take up a big hairy audacious goal like making sense of the physical world, in K or in college, or just a goal like a quality terminal self-contained "biology for poets", how do we avoid it being the usual dreck, but now without even the usual weak quality checks of high-stakes exams, of dependent follow-on instruction, and of pretending it's not largely a disaster? ... Thoughts? Thanks.
It seems like you could generalize this for most of the curriculum. Once kids arrive at the conclusion "I'm never, ever going to use this," it's over for most of them. And, naturally, that's self-fulfilling. Most kids who didn't learn math ended up not needing math – and some proudly trumpet that back at their teachers later in life! Should we shut down math?
Just anecdata, but among my friend group's children, I've seen a number of middle schoolers go from completely uninterested in a second language (English) to totally engaged once they discover YouTube or Netflix or a gaming community or whatever.
And classroom learning is apparently useful for those kids. The last time one of my linguist friends enlightened me, the research pointed at classroom learning being really important for those who don't learn the L2 in the home. If those learners are left to absorb the language solely through immersion, they most often end up at a middling level with the language.
That may be because with L2 immersion, a non-native speaker almost never gets feedback about language mistakes and so never has the chance to correct them. Instead, they see that what they say is understandable and keep repeating the same mistakes. (Maybe like, "Yesterday, I go to the store." Incorrect, but understandable.) That's not the end of the world, but it limits the speaker's opportunities with the language. Past a certain blurry threshold, they're unlikely to be hired to do a job that involves the language, for example.