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Of all disciplines, mathematics is probably the only one which is close to being taught “right”. I finished what was the 3rd ranked high school in the country at that time, with a specialism in mathematics and intensive computer science. That entailed 5 hours of mathematics per school week, and 7 of computer science.The focus of that era in good schools was on low cost activities such as chess or mathematics. A chess set could be made from carved sticks from a garden, or other household objects. For mathematics, you just need a pencil, “mathematics” paper (obligatory 5mm graphing spacing), and a ruler and a compass if doing geometry.The curriculum was structured like this:grade I: basic operationsGrade II-IV: arithmetic. pupils learn to do complex algebra using the segment method. Pure logic was involved, and I could show you a 4th grade arithmetic problems that would make a maths PhD cry.simple geometry, names of figures, calculating perimeters and areassimple fractions and operations. natural (N) and whole integer (Z) number groups.rule of division with restGrade V: algebra. powers and common factor. lowest common divisor , rational number group (Q)simple graphing.Grade VI: synethtic geometry. Pythagoras, Thales, Menelaos theorems. 30 degree rule. Triangle and circle constructions.Grade VII: irrational and real number group (R), radicals and powers. quadratic equations.synthetic geometry: more ratio-based laws.Grade VIII: cubic equations. Newton’s binomial. more plotting. paramteric equations. 3D synthetic geometry. introduction to vector geometryFollowing grade 8, pupils would take a national test, much harder than GCSE level, on maths, romanian, and a choice between history or geography. The results would allow one to progress to a better or worse high school.If you managed to go into a high school like mine, you would have had:Grade IX: advanced graphing, more parametric equations, polynomial functions, row series and progressions, homograph and other functionstrigonometry, vector geometryGrade X: complex numbers (C), exponentials and logarithms, combinatorics and probabilistics, positional (r, phi) geometryGrade XI: advanced graphing, calculus: limits, Fermat’s least squares theorem, Darboux rule, derivatives,algebra: matrix operationsGrade XII: primitive and definite integralsalgebra: abstract algebra, isomorphisms, Abelian groups, etc., further matrix properties.Mathematics school books would have a very rigid structure:introduce the problem/backgroundprovide a theorem in elegant (minimal) wordingshow proof (or leave the proof “as an exercise to the teacher”)show corollaries and lemae (this often encouraged pondering and further thinking about the applications of what you just learned)lots and lots of exercises to get you develop confidence and a good feel of how the concepts would work.The exercises would vary from obvious, to tedious, to creative, to national olympiad level. In the same book. If you were able to do all exercises in the manual, chances are you’d actually like maths and would be encouraged to participate in contests.Those contests were opportunities to get free or heavily discounted transport and accommodation, often during a summer camp. These were normally unaffordable for many parents in post-communist Romania, and I suspect still unaffordable today.My experience wasn’t shockingly different from that of my parents. Looking at the 2020 Baccalaureate model exams http://subiecte.edu.ro/2020/bacalaureat/modeledesubiecte/probescrise/Bac_2020_E_c_Matematica_modele.zip, much of the subject was made a bit more fair than during my time, where getting a honest 85% without cheating was HARD, though it’s still tough.Basically, if you finished an advanced mathematics-oriented curriculum in Romania, you would hold equivalent knowledge of a mid 2nd year student in mathematics in a Western university (minus Fourier/Z transforms, ordinary differential equations, Taylor series, Hilbert spaces, but those are easy to pick up if you have the basics).This is somewhat of a historical perspective. I grew up in a time whenI didn’t have a computer till aged 11the first computer lab I entered had Motorola 68HC copies running CLI-only machines at KHz CPU clocks.First monochrome cell phone was given to me in 2003grew up with Sony Walkman copycats, flash-based MP3 players only became affordable enough by the time i was finishing high school.there weren’t many practical contests or interesting extracurricular activities in school (such as game development, robot wars clubs, astronomy clubs)