Bob and Alice have 10 candies in total, and Bob has 2 more candies than Alice. How many candies do Bob and Alice each have?

TAL's solution: this is called addition-subtraction problem. Add the two numbers and divide the sum by two, you get the bigger value for Bob. Subtract the difference from the total and then divide the result by two, and you get the smaller value for Alice. No mention of why. No mention of underlying intuition. No mention of any mathematical concepts. This is the most abhorrent teaching I've ever seen.

(Tangent: Has anyone yet tried to prompt GPT3 to generate "deep" word problems?)

10-3 / 2 = 3.5 candies for Bob.

You may think that's a strange solution, but it's the only one that matches the problem statement. What was your solution?

Considering the problem as follows: "Bob and Alice have 10 candies in total, and Bob has 2 more candies than Alice. How many candies do Bob and Alice each have?"

My own solution would be to just define the variables as follows: Bob = Alice + 2; Bob + Alice = 10; 2xAlice + 2 = 10; Alice = (has) 4 candies; Bob = (has) 6 candies.

Adjusting the problem with an odd difference instead of an even number we have: "Bob and Alice have 10 candies in total, and Bob has 3 more candies than Alice. How many candies do Bob and Alice each have?" Bob = Alice + 3; 2xAlice + 3 = 10; Alice = (has) 3.5 candies; Bob = (has) 6.5 candies.

I find my solution to be easier to understand and somehow more logical than "let's add/substract this and that and divide by two". Probably my main issue was explaining to a kid how having 3.5 and 6.5 candies works seeing candies I known all my life are basically unbreakable (unless you have a kid's teeths which is known to be able to devour metal).

As an anecdote I recently dated a lady who has a teenage daughter and she showed me the math exams her youngling has been taking. Having never been one to withdraw from a challenge, even mildly implied, I printed the things and started working on them only to be horrified how much I've forgotten in terms of elementary mathematics. I genuinely felt shame even though I scored a decent number (but nothing to write home about).

I feel we're failing our children in how we're pumping them with information but without always teaching them how to learn and that makes me really sad :(

Another difference between China and the US is the philosophy towards achievement. The US tends to bias resources towards underachievers, whereas China tends to just give up on them and focus on the overachievers. So again there's pressure to compete, because as soon as you fall behind you'll just be at a further disadvantage because nobody is trying to help you (unless you pay them).

Honestly, the end result is kind of the same in both scenarios - the best and brightest (strongly correlated with wealth) go to elite universities, with the occasional feel-good story about rural kids making it in. They're pretty much set for life, while everyone else is stuck with a useless degree. Although many menial jobs won't hire you unless you have a degree, so it's good for that.

And I’ve never heard that high schools don’t teach calculus. The Chinese people I know who went to the US in later high school years and for college all found that the calculus classes were repetitive for them.

About calculus: https://www.gaokzx.com/c/201901/33164.html

Using the elite students from private schools who you know as a counter argument is really not that strong. Only 14% of the high school students are in private schools.

The top results (for me) all say that it's not literally correct that only 50% of middle school students make it to high school, but most (suspiciously) only mention numbers for Beijing. https://zhuanlan.zhihu.com/p/368135272 has a table covering every province, showing that the rate goes from 53.11% in Henan to 70.49% in Heilongjiang.

It's interesting that there's no calculus on the gaokao. It's an elective in high school (same as the US). I wouldn't have guessed that. However, some very basic linear algebra does seem to be in the compulsory high school math curriculum(1). More than I learned in high school in the US, anyways.

Also, generally the private schools are considered worse options. The elite students with the highest middle school test scores mostly go to public high schools. Maybe students at the private high schools are more likely to go overseas, and so they are more likely to take the calculus electives. But even among the private school students, only a small percentage will go overseas.

For the vocational school thing, I had no idea it was so extensive. Very interesting. I knew about sports high schools, where most of the graduates go on to teacher colleges and become PE teachers. What other kinds of vocational high schools are there? How does it work for smaller cities - how many special types of vocational school can they really support?

(1) https://baike.baidu.com/item/%E9%AB%98%E4%B8%AD%E6%95%B0%E5%...

My wife took the art/liberal arts track in high school and most definitely didn’t learn calculus (she still got into one of the best arts academies, though). So at least on that track, you won’t learn calculus (you generally take the same classes together, unlike the USA). I’m not sure about the STEM track, but my bet is first tier Shanghai and Beijing would be way different from a tier 88 like Chenzhou. I also can’t imagine kids at a school like renmin zhongxue not learning calculus, and that’s just a middle school.

Teacher schools (normal universities) require high school. I’m not sure about tourist or sports schools. But the tourist college I visited (in Zhangjiajie) seemed more like a college than the vocational schools I’ve seen. I didn’t ask, though. I assume Beijing Sports university is a real university, but I’m not sure about the other more provincial ones.

OTOH, friends of same age who were in Shanghai did get exposed to linear algebra.

I'm not sure where the original commenter is at in China where 50% are not going to high school. "Ailun" is also right about the private school thing. It's big in China. Finally, the idea that Chinese students are not learning calculus is patent nonsense.

I assume that is because entrance exams are forced not to cover material outside the national high school subjects?

Brazil’s hardest entrance exams (ITA and IME) are not bound in any way, so they go arbitrarily deep.

1- Table 1 and 2 of that document: https://www.fraserinstitute.org/sites/default/files/math-per...

My province, the NCEE had Calculus, linear algebra and inequality and it's choose two from three.

Students tend to choose this (if it's availble in that area) because it's generally easy. And if you're like me, not good at computing numbers, you would choose inequality (mean inequality and Cauchy's Inequality in most cases) as you only need to do some transformation to the problem. Some students will do matrix if they cannot solve this quick enough.

These were my experience, I do heard that recent education revolution was moving inequality to compulsory but removed Cauchy and so on.

BTW, I don't understand how analytical geometry can be replaced by calculus and linear algebra.

I looked up analytic geometry on Wiki and it looks like stuff that would definitely be taught in the U.S. Usually in the weirdly named "precalculus" course, though some of it would even be covered in previous courses.