American parents are sending their kids to 'Russian math' (2017)

Hahahaha. Thanks for the lough.

This doesn't line up with all the other problems, which reward having some insight as well as the concrete algebra/arithmetic skills to finish it out.

If anything, your approach sounds more like what's expected in American schools: either you have been taught a foolproof way to solve problems matching Pattern X, or you stare slack jawed at the question paper thinking "I must have been absent the day they covered this question pattern". Exactly the opposite of the kind of thinking described in the article.

Besides, as in another comment of mine on this page, there is no generic method your teacher could have taught you here that always works. (If you think so, please set the right hand side to 1681 and solve that version...). The principal method I was taught for solving cubics was to make a guess. Numerical methods came later.

> Edit: this might make the kids think you need some 'magical' insights to do math and if they don't see it they are not apt for it, while the opposite might be true.

That's a valid point. However, what's the opposite to having insights? Is that following routines and/or exhaustively exploring the entire problem space (which the first problem in the GP comment seems to teach)?

Teaching those might have higher pedagogical value than conditioning children to find insights (as - at least at first sight - the increase in skill in those is more directly linked to the effort the child invests in learning) However, the von Neumann story in your sibling comment suggests that some people (and so, some children in the class) will perform routines faster than the other children no matter what. Seeing a "shortcut" solution gives a chance to those who are slower at routines to arrive at a solution fast, too.

Moreover, a lot of real-world problems (in academia as well as in business - from my limited experience in both) are exercises in pattern matching and finding shortcuts rather than in an exhaustive exploration of the problem space - and helping children to collect an arsenal of tricks (and more importantly, teaching them to look for insights and patterns by giving them multiple trick-based problems over the years) prepares them to handle those real-world problems.

I wonder what he older math-education in german schools is like, probably also more hard-core. After elementary school, germany has a three tracks Gymnasium, Realschule und Hauptschule. A Gymnasium prepares one for university and is still well regarded and its final tests, the Abitur, still carries a prestige. Looking back (I attended a Gymnasium), I think the quality of the education was quite high, especially in my english lessons and the social subjects. If the goal of the school was to produce good citizens capable of actively participating in a democracy and forming their own opinion, then it did it very well. Especially later, we had quite a few interesting, adult discussions with engaged teachers about various topics in history, society, art etc. So I think that the quality of my gymnasium was quite high and it really showed in subjects where capable teachers alone can make quite the difference.

But the gymnasiums should also prepare those capable for university, be more rigorous, and I think there's the problem. The division doesn't work anymore. Everybody wants their children to go to the gymnasium, because everybody has to study at the university. Even when they have no interest whatsoever in science and just want to work as a coder. Also, attending a Gymnasium can't be prestigious if everybody is doing it. I remember quite a few children struggling but getting pushed through by their parents because a Realschule is simply not an option. I was also struggling, but more because I just didn't care and there weren't really any consequences. I still passed each class. But a more rigorous math education would, I think, result in a lot of the children failing the gymnasium and a lot of angry parents who see the future of their children and their parental success in turmoil. So the Gymnasium really turned into a one-size-fits-all kind of education and I strongly suspect that especially in math (or physics) that leads to the lowest common denominator. So now I wonder what the math education was like when only few could attend the gymnasium, i suspect way more rigorous.

Is it similar in other countries?

By the way, it's totally different at the university level. The german university doesn't feel responsible for your personal success, you have to earn it. If you fail, you fail and the standard can be quite high. I also don't really see a lowering of standards in the "core" degrees, for the first big math exams I prepared myself by practicing with old ones going back into the 80s/90s. They were as difficult as the new ones. A lot of students failing out of the subjects they have chosen (can be as much as 2/3rds) just choose easier majors, for example a business-computer science combination because they have less math classes. A lot of the students that started studying with me ended up switching majors because of the more rigorous computer-science and math-classes (I think roughly 50%).

I still have a hard time in mental arithmetics. During my school days, this is one of the things which had instilled the "math phobia" in me. I never really took an interest in math, until I started doing competitive programming in college. I had to literally build a new understanding of division, multiplication, modulus, etc., it's difficult to explain. But I feel really ashamed in admitting that I still suck at math, probably because I just hated it during school days and no one was there to guide me. I don't really like blaming things on others, but I am not sure what else I could've done to learn math.