I will be rather short. There was a time when - I think - the US high school curriculum had several of the below topics (and none of the 'extra' topics) although analytical geometry was not a usual component (however, it did occur). For some students this seemed quite useful and some yet wonder, somewhat justifiably in my opinion, whether broadening our curriculum and incorporating calculus was wise. At the same time - for, I think, numerous reasons which involve a conception of mathematics and pedagogy - it wasn't particularly successful for the large majority of US high school students. Bracketing the calculus - as its incorporation seems to have been driven in part by US university admission policies - the other additional US topics may have, in part, have been introduced to address motivation and what might be termed a mathematical literacy need. That is, given that we suspect that large numbers of US students might be substantially bored by, for example, the teaching of solid geometry (please note I am referring to the teaching and not the subject matter), the tendency has been to introduce topics that seem more culturally relevant (note that getting into US universities is culturally relevant) - for example, being able to read newspaper statistics has been cited (and one may agree or disagree as to the appropriateness or importance). Are any of the considerations particular to US culture relevant to Chinese culture? I would expect some, but not all. For example, if one valued the ability of a Chinese teenager to read newspaper statistics and the ability to foster such was conceptually relegated to the mathematics classroom (it need not occur only there, for example), then probability and data analysis might become a point of emphasis. But the real difficulty seems to be a topical focus as if this were primary. I would hope that any mathematics curriculum would have as a primary focus the doing of significant and substantial mathematics. That is and has been a problem with the US curriculum although we do have teachers that succeed. Topical (re)organizations however well meaning, I suggest, incompletely address this problem. Do they in China? I don't know and can't tell from the list of topics. I do, for other reasons, suspect this is a not an inconsiderable problem.
>Which mathematical topics are the most important for high school?
Chinese mathematics education stresses the theory of functions, trigonometry and solid geometry.
[Background] The Chinese mathematics curriculum for high schools includes four courses: 1. Sets and functions, including all elementary functions--exponential, logarithmic, trigonometric. 2. Solid geometry. 3. Analytical geometry. 4. Algebra: equations, combinatorics.
No probability, statistics, data analysis, calculus, matrix theory, etc.