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.

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

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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.

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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.

Singapore Math for 11-year-old Kids : Modelling

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Compare below the Singapore Math versus Algebra Method:
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Answer:
Mrs. Lim 68 (son 36, daughter 32)

Algebra Method: Try yourself !
(It involves solving 2 equations of 2 variables.)

My Comments:

There are certain types of problem easier to solve with Modelling (example: this one and the “Monkeys & Coconuts Problem” with Modelling Method); whereas there are some other types difficult to visualize in model, but straight forward with Algebra Method.

Modelling Math is excellent for lower primary kids (Primary 1 to Primary 4), while upper primary (Primary 5 – Primary 6) should be taught Algebra (1-variable to 2-variable equations).

The reason in PISA Test China (Shanghai) kids (PISA World’s #1) beat Singapore kids (PISA World’s #2) in Math is they learn Algebra in upper primary schools (11-12 year-old).

Algebra vs Singapore Math

Who wins?

This comic video illustrates Singapore Math’s Arithmetics Polya-style problem solving process vs Algebra’s mechanical method.

The problem is as follow:
R is 3 times older than S two years ago. From now 2 years later, their total age is 32. How old is R now ?

See my previous blog (search “Monkey”) the Nobel Physicist Paul Dirac’s problem “The Monkeys and Coconuts“, 3 methods are used: 2 adanced modern math (by Sequence, eigenvector & eigenvalue), and the easiest & intuitive method (by Singapore Modelling Math). High-school Algebra method is impossible, if not cumbersome, to solve the Monkey problem !