Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.
- Symmetry of a Square
- Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
- What is a Group (群 “CAN I” ) ? = Closure Associative Neutral Inverse
- Monster Group = God ?
- String Theory: Higgs boson (玻色子) aka “God Particles”
Note (*): “保距映射” (Isometry），是指在度量空间 (metric space) 之中保持距离不变的”同构“关系 (Isomorphism) 。几何学中的对应概念是 “全等变换”。
[Original Financial Times Article] Google: UK maths books fail DfE test
UK, USA, France are copying Chinese Math (from which the “Singapore Modeling Math” derived) in Primary schools, this proves my above-mentioned “Ideal Math” formula is correct. The 2 Asian countries were top in 2015 PISA Math Test for 15-year-old students, while UK was ranked 27th.
It remains to see if China / Singapore reciprocate the French Math theoretical foundation rigor in High Schools (Junior Colleges) and in the first 2 years of undergraduates for STEM (Science, Technology, Engineering, Math) students.
Compared with Fields Medals (equivalent to Nobel Prize in Math), the picture is reversed – where USA, France and UK are top. The secret lies in the formula : the multiplying factor – (* French), ie the math theoretical foundation notably in French Math.
Note: 2 Chinese Fields Medalists are listed in the nationalities of “British / HK, now China” (ST Yau 丘成桐), Australia (Terence Tao 陶哲轩 ).
Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.
The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:
Note: Lewis Carroll: the author of “Alice in wonderland”
Cambridge Professor Tim Gowers (Fields Medalist) suggested the similar pedagogy of “Memorise by First Principles”.
C = Chinese 中文 = Primary school Arithematics sans “Algebra” (= Singapore Modeling Math). Abacus-Algorithmic thinking.
E = English = Secondary School Math
=> Applied, Tricky, Math Olympiad-style
=> Engineering, Business, Applied Science.
F = Français (French) = High-school / Baccalaureate & University Math = Theoretical, Abstract
=> Rigorous Math Philosophy for Advanced Concepts
=> New frontier Scientific Research.
Why (C+E) ?
C + E = Basic Math Foundation.
Why * F ?
If multiply by Theoretical F, like flying with added wings (如虎添翅)。
if (C+E) -> 0 (less applied), or
if F -> 0 (lack theories),
then Total Math Education -> 0.