PSLE Singapore Math for 12 year-old kids

The “Singapore Math” , an invention by Singapore Prof. Lee Peng Yee 李秉彝 of ex-Nantah (now NTU-NIE) in the 1980s, is a combination of :

  1. The ancient Chinese Arithmetics (算数) Technique,
  2. Polya Problem Solving Methodology,
  3. Aided by Visual Modeling Diagram.

All Singapore kids learn this Singapore Math from 7 to 12 (‘PSLE’ Primary School Leaving Exams before secondary school). Singapore scores Top #1 in World’s Pisa Math Test (for all 13-year-old kids), beating China, Finland, Korea, Japan, Taiwan… and all Europe and USA.

Note: However, there are pros & cons of this Singapore Math, revealing its weaknesses in post-secondary / university Math education with too applied less theoretical foundation.

France has adopted Singapore Math since 2018 in the French primary schools, as recommended by the President Macron’s Education Reform Team headed by the Fields Medalist Cedric Villani, who praised the Singapore Math as ‘Une Méthode Miracle‘ . France is very strong in abstract Modern Math – the 19th century invention by the French prodigy 天才神童 Évariste Galois (Group Theory) . France wins 1/3 of the world’s “Math Nobel Prize equivalent ” Fields Medals , second only behind the USA, but is strangely weak in applied math (eg. Arithmetics, Euclidean Geometry, IMO Math Olympiad…).

[No Algebra please!]

Answer : Try before scrolling down

…Method 1:

…Method 2:

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Singapore Math’s “CPA” Pedagogy Leads to World’s PISA Top # 1 Rank

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Copy above, then open 头条, this article window will pop up:

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

Comment:

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” )

Why Math is so Sexy?

Cédric Villani (Field Medal 2010) the French mathematician becomes a deputé (equivalent to Member of Parliament) in President Emmanuel Macron’s new party “En Marche” consisting of 90% non politicians.

His new revolution in French Primary School Math Education is introducing “Singapore Math” : the 1960s Chinese Secondary School One Math (算术 Arithmetic) modified by the ex-Nantah (南大, now Nanyang Technological University) Prof Lee Peng Yee (李秉彝) with the Polya Problem Solving Method aided by visual Model diagrams.

France excels in Abstract (aka New / Modern / Bourbaki) Math but poor in Applied Math, while Asian countries (China, Singapore, Korea, Japan etc) are opposite. This demonstrates clearly in the Asian 15-year-old students scoring Top PISA Math Tests & Math Olympiad Championships (even in the USA teams), while the French young Mathematicians (< 40 years old) take 1/3 of the world’s Field Medals – “the Nobel Prize of Math”.

It is ideal to combine the Asian (applied) Math pedagogy for Primary school (from 7 to 13 years old) math and the French (abstract) Math (eg. Set, Group, Ring, Field, Vector Space, epsilon-delta Analysis…) in high-school math (from 15 to 18 years old).

The wise Cédric Villani is just doing this Ideal Combination of “East and West” for French Primary School Math Education .

Note: In the video (12:12 mins) Villani described his “Eureka discovery” inspiration at 4 am in Princeton Institute of Advanced Math. The same experience found by many mathematicians eg. Poincaré, Zhang Yitang, etc. Read Villani’s book where he called this “Strange Head Voice” (definitely not hallucination!!) experience as “The direct phone call from God “.

Singapour : Les Maths Singapour- Une Methode Miracle

“Singapore Math” was a derivative of ancient Chinese Math, modified and combined with “Polya Problem Solving Method ” by a Singapore Professor Lee Peng Yee (李秉彝) from Nanyang Technological University (NTU)’s NIE (National Institute of Education). Prof Lee was the first batch of Nantah University 南洋大学 (the precursor of NTU) Math undergraduate in late 1950s, who obtained PhD Math in Queen’s University (Belfast).

In 2005 during his public Math Olympiad books launching seminar at NUS bookshop, the 70-year-old Prof Lee started his talk on the genesis of “Singapore Math” idea with this famous ancient Chinese Math “Chicken and Rabbits” (鸡兔问题)。

Comments on Singapore Math :

1. The Pros & Cons

Pros: Concrete Chinese Arithmetic , Polya Problem Solving Pedagogy, Visualisation with Models. PLUS: well trained Math teachers, “educated” parents (revision class for them) or hire private Math home tutor.

Cons: Lack abstract training for Primary 5 & 6 kids (11-12 years old ) in Algebra equations (postponed to Secondary 1 @13 years old). The Chinese (上海) kids start Algebra before Singapore kids. Also French kids start abstract (Set Theory) concepts earlier than Asian kids.

2. UK Textbooks follow Singapore Math

La remise du rapport Villani au Ministre de l’Education nationale Mr. Blanquer préconisant 21 mesures pour l’enseignement des mathématiques en France, a mis à l’honneur, par ricochet et par voix de presse, la méthode de Singapour pour l’apprentissage des maths.

Note: French Mathematician Cédric Villani (Fields Medalist 2010) joins President Macron’s Political Party as a deputé (= Member of Parliament).

https://lepetitjournal.com/singapour/les-maths-singapour-une-methode-miracle-224015

Why are Singapore school kids so strong in Math ? (World #1 PISA Test in 2016)

https://lepetitjournal.com/singapour/actualites/education-pourquoi-les-eleves-singapouriens-sont-ils-si-forts-en-maths-46043

Every (Singapore) school is a good school” – Mr. Heng (Former Minister of Education of Singapore)

UK Textbooks à la Chinese / Singapore Math Style

[Original Financial Times Article] Google: UK maths books fail DfE test

\boxed {\text {Ideal Math = (Chinese + English) * French }}

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.

Note: Shanghai used to represent China to be the World Top PISA in math for decades till averaged down by other chinese cities.

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 ).

Singapore Math for  Primary School Kids

Singapore scores the 2016 PISA Test World’s First in Math.

Below is the “Singapore Math” shown by a USA School adopting the pedagogy.


I had the opportunity to meet the inventor of the “Singapore Math” Prof Lee PengYee (李秉彝) in a Math seminar at NUS few years ago, who took the inspiration of the 1960s ~ 1970s Chinese School (P.S.L.E.  / Secondary 1) Math 算术 (literary means “Counting Technique” sans Algebra), combined with the Polya 4-Step Problem Solving Methodology [Video by Polya], with a visual tool called “The Model Diagram”.

See here a tougher “Singapore Math” example for the 11-year-old kids at P.S.L.E. Exams.

Note: This pedagogy is based on Concrete Visualisation, while good for majority of young students (7 to 13 years old) to learn computation and problem solving, it doesn’t train the opposite skill from young in “abstractness” (eg. Basic Set Theory) which is the foundation required in university Advanced Math, where the French, Russian and USA university students excel more than the Asian cohorts.

The Ideal Math Education for the next 22nd Century

1) Singapore Math (Computation for Primary schools ) +
2) English Math (Applied Math for High Schools) +
3) French Math (Abstract Math for Universities)

Current Math education is biased towards any one &/or two (out of the three): 

Singapore PSLE 2015 Math

image

PSLE is “Primary School Leaving Exams” for 11~12 year-old children sitting at the end of 6-year primary education. The result is used as selection criteria to enter the secondary school of choice.

image

Hint: Without seeing or feeling the weight of the $1 coin, you still can guess the answer. This is the essence of “Singapore Math” — using “Guesstimation“.

Answer (below):
Try before you scroll down.
If wrong answer, please go back to primary school 🙂
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Answer:

By elimination using ‘guesstimation’ method:
A) 6g too light,
D) 6 kg too heavy.
Left B & C…
C) 600 g > half kg for 8 coins ($1), not possible.

Ans: B = 60 g.