You can’t get much done in life if you only work on days when you feel good.
That’s both a good and difficult question.
Here’s a TL:DR;
Full answer below.
I don’t think I quite agree with where this answer is coming from. There seems to be a lot of emphasis on the student’s lack of ability to comprehend / practice mathematics and less on how mathematics is taught. Certainly the student has to take some responsibility but I think that’s less so in grade school math, and “math hate” seems to primarily stem from how students are taught it when they are young.
It’s very easy to make math be boring from the start. If you’re not making activities related to addition or division or geometry interesting (and more importantly, thought-provoking and beyond rote calculations) in the 2nd and 3rd grade, you’re gonna start losing kids. So by the time they’re even just in 4th or 5th grade (where maybe you can expect some more personal responsibility), you’ve already lost the battle, they already hate math. And this attitude will follow to high school. And high school mathematics won’t save them because, honestly, algebra and geometry and how they’re taught suck too. So you’re correct in saying that at some point it will be entirely overwhelming to even try and catch up. But the reason they fell behind in the first place is probably because the teacher did not do a good job introducing them to math years ago, not because they should have been practicing this whole time. Who wants to work at something that is taught in such an atrocious way?
I guess what I’m trying to get at is that answers like “it’s more demanding”, “it gets harder”, “lack of practice” all seem very student focused and I think it should be less aimed at the student who has a good reason for hating math, and more at the practices which are producing math hate. Kids are willing to work for the answer, but only when they feel like they can engage with a question. Your last answer “when students don’t see the purpose” seems to address this, but I think that should be the biggest part of the answer.
I’m with ryanandmath here - students get introduced to “math” as a series of rote calculations to be memorized, and it’s a losing battle from there.
He hit the nail on the head, so I’d like to delve into a related problem - I say “math” because I’d wager these students don’t actually hate mathematics, they hate arithmetic, computation, hate rote calculation, etc. (I do too!) They - and most of the population - have no idea what mathematics, as a field of study, actually is. Maybe I’m playing semantics here, but it always blows non-mathematicians’ minds that I could spend a day doing math and never see a single number (this is an especially delightful conversation to have with kids). I spend my time looking at rotation groups and metric spaces and homeomorphisms and ultraproducts and all manner of fascinating things, and the tools I’m using to do that are so far removed from what most people think “math” is that it isn’t even funny.
Show someone a bit of actual math - graph theory via the Bridges of Köngisburg, or topology via a Möbius strip, or just logical thinking via any number of interesting puzzles - and then tell me they hate it.
Cofinal, I agree with you that the higher level maths is the heart of it all, and that if people looked at graph theory and such, they would better appreciate math as a whole.
Ryan, Cofinal, as for the idea that math hate stems from the teacher, I am on the fence with that. I don’t think an engaging teacher can make every student appreciate math, but they can definitely make more of them appreciate math. Perhaps if we consider the base case - yes, this is getting tautological - that the first math teacher a student has, has to be engaging in order to start the student on the right foot. So when the student doesn’t yet have an opinion of math, if they are influenced in the right direction, they might stay on the right path. Whereas, if a student didn’t like math in elementary school - for whatever reason - might still not like it regardless of having an engaging teacher in junior high. This is a crude example, no doubt.
I do see where you are coming from, but my main problem with math hate being teacher-based is that it’s easier to blame other people for your problems.