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Comment by hintymad | Hacker News Reader

It looks how do do proofs is at university level in the US. I wonder why other countries start to teach kids how to do proofs from grade 7. They start with rigorous proofs in Euclidean geometry, the move to solid geometry, then to proofs in elementary functions, sets, number theories, and etc, then to polynomials and simple discrete maths and analytic geometry. By the time a kid graduates high school. using things like proof by induction or by contradiction is like a second nature. And no, I'm not talking about elite kids, but curriculum requirements for all the STEM students.

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We did proofs in 7th grade as part of geometry, in a semi-rural United States middle school.

Good to know. I guess education in the US has local standards? I have this impression of the US not teaching proof because in a number of introductory math classes in my college, the profs dedicated chapters to teach basics of induction, how to write proofs, and etc.

Every state sets its own curriculum, with varying degrees of freedom for the districts and schools within the states. The federal level has standards, which students are generally tested against in various standardized tests, that are tied to federal funding.

Multiple curricula can satisfy the same standards, at least on paper if not in practice. So states are, more or less, free to teach things how they want. However, they're also strongly driven by the textbook industry, which turns on the two biggest textbook purchasers: Texas and California. So a lot of the textbooks (and associated curriculum material) available for purchase in the rest of the states are driven by whatever those two states are pushing.

I would have still appreciated that refresher in a college class on content I learned 7-8 years prior.

> I guess education in the US has local standards?

Very much so! The US didn’t have a Department of Education until the 90s.

90s? You're off by a bit. The current Department of Education started in 1980, but it came out of the Department of Health, Education, and Welfare, founded in 1953. That, in turn, came out of the FSA which included an Office of Education (1939). Prior to that, the Office of Education had been part of the Department of the Interior. Before that it was its own Department, starting in 1867.

Though "90s" is delightfully vague. You're either off by nearly 1800 years, you're very old and meant 1890s and were only off by a few years, or you really meant the 1990s and were off by nearly 130 years.

Thanks. I have no idea where I read that, but have been carrying around that “fact” for over twenty years!

The “standard” place for geometry is 10th grade (after algebra 1 in 9th grade). A few geometric ideas have been moved from geometry to algebra 1 so that slope can be explained using similar triangles but this is just about memorizing explanations instead of doing proofs.

Today, if you aren’t in an honors geometry section, you likely learn a handwavy version of two-column proofs and do some pretty linear proofs that way. No symbolic logic, no mathematical writing.

Can't say I remember 7th grade ... but we were doing proofs in Geometry in High School. I also lived in a semi-rural US neighborhood.

10th grade is the “on level” time to take geometry.

So US school kids don't encounter any geometry in school till they are ~16?

Shapes, areas of simple polygons and circles, Pythagorean theorem, volume of solids, graphing, translation, all that stuff and more that one might call “geometry”, is scattered between roughly ages 6 and 12.

I think the high school level “geometry” class—which may be the only one named such, but primary school math is full of geometry—is an atrophied organ left over from when it was still common to teach directly from Euclid, which is why it tends be about introducing proofs more than covering new abilities and techniques in geometry (though it may cover some of that, too)

Thanks for the explanation! That is a lot less surprising.

No. The formal geometry class is usually age 14/15 (first or second year of high school). They should have seen a less formal treatment of geometry before then, though they may not know it.

which other countries? that's certainly not the case in Germany. you might see some proofs in geometry, and maybe some informal derivations of things later on, but "induction" is a university level thing (it's possible that some kids that focus more on maths in school see this kind of stuff earlier, but it's definitely not a universal experience).

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