On the other hand, arithmetic for very young kids like second-graders is probably also a waste of time. If you waited till they're older (or they express a genuine interest) I expect they'd learn it quickly enough and with less chance of learning mainly to hate math.

Perhaps it made sense in ye olde days when many students would not go on to junior high.

You mean adding and substracting numbers? Personally I think it should be taught (and is here) to first graders. Also here no kid hates math before 5th grade (overly generalizing).

It's nice to hear there are places that don't implicitly teach math-hate -- where is it?

My sample number might be too small (so it is probably anecdotal evidence at most), but I would say german primary schools (which is grade 1-4). To me it looks like the math hate is coming later starting somewhere in secondary school between grade 5 to 7.

Thanks. I based my 'probably' on a few things -- it's admittedly not strong:

- There was an American school about a lifetime ago that tried that strategy, and the principal claimed it worked fine.

- A general impression that before mass education it wasn't uncommon for people who got schooling to start years older than our start, with no impression that they learned arithmetic any worse. E.g. http://www.scientiasocialis.lt/pec/files/pdf/vol57/90-101.Pi... "In general the pupils began their arithmetical instruction at 10–11 and this education prosecuted for two years."

- Piaget's picture of stages of development (in my vague understanding) suggests that arithmetic beyond a very concrete level would be developmentally unnatural for younger kids, and more natural later. Apparently Montessori schools do better on this score?

- Unschoolers sometimes reach adulthood with less understanding of math than state-schoolers, but if the average is worse, I haven't heard of it. Anecdotally they're fine.

- Hate and ignorance of math is very widespread (I've read similar claims about average French people with their substantially different school system)

- This jibes with my general experience, having gone to school, etc.

- There's not much reason to expect a claim this far from mainstream to have been carefully studied. Maybe it has been and refuted -- I just don't very much respect the status quo and so I expect there are improvements that would 'easy' except for the obstacle that it's very hard to meaningfully change the system. And this strikes me as a plausible (though unambitious) one.