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CPA = Concrete – Picture – Abstract
Singapore Math = Chinese Math + English (UK/USA) Math
Chinese Math = Spoon-feeding 填鸭式|Computational focus | Applied |Memorization
English Math = Building-block 建构式|Practical focus |Less Theoretical
Singapore Math inherits both the strengths as well as the weaknesses of Chinese Math & English Math:
Strengths: Applied, Practical, Building-block. (Up to secondary school math level, good for daily math usage).
Weaknesses : Computational focus, Less Theoretical. (Bad for abstract thinking in further study of advanced math).
Singapore Math is only good for kids from 7 to 15 years old (PISA age is 15). From upper secondary Math (at 16) to A-level or Baccalaureat(at 18) or 中国高一～高三, the French Math is better for laying foundation in abstract thinking, paving the way for advanced math in university & beyond – evidenced by the majority of Fields Medalists are French. (Read “How do the French Excel in Math” )
【不擅长考试的大数学家—法国数学家埃尔米特 Charles Hermite】
He was 15 years junior of Galois from the same Math teacher Richard of Lycee Louis Le Grand. Richard gave him Galois’s student math homework books.
Charles Hermite proved ‘e’ transcendental, his German student Lindermann followed his method proved “pi” also transcendental.
Lindermann produced students Felix Klein, who produced Gauss, Riemann, David Hilbert…
Trying to explain elementary math using advanced math is like “对牛弹琴” (Playing guitar to Cow – it doesn’t understand) 。This book made fun of the “New Math” syllabus in the 1970s.
However, if you are an undergraduate suffering from the abstractness of Abstract Algebra, the above is a “God Send” enlightening example to grasp immediately these concepts:
Prime, Quotient Map, Ideal, Unit, Ring, Z/2Z quotient Ring, Field,…
Terrence Tao, the highest IQ (260) living person on eath today, won the Fields Medal at the 2nd youngest age in history (after French mathematician Serre at 27.)