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Singapore Math

Friday, March 12, 2010

Immoral Algebra


Here is an online algebra question, forwarded to me almost every year, which has been circulating the globe many times:

Maya is 21 years older than her son Raju.
In 6 years from now Maya will be 5 times as old as Raju.
Question: Where's Maya's husband?

My reply to the sender was: My limited algebraic knowledge leads me to infer that the "normal-child-to-be" was some one year away to see the world (Answer: x = –1). Challenge: Try solving this problem using the Singapore model method.
So I can only conclude that the "conservative couple" was in some "missionary position" then.

My sender's forwarded answer was: 

Current age of Raju is -0.75 ie -9 months ie he is 
being conceived therefore husband is on top of wife

And my reply following the e-mailer's answer was:
I bet is that if we've a few of these CRE8TIVE word problems in our traditionally sterile MOE-approved textbooks, more students would be excited to reading algebra until they're old enough to have kids of their own. Students would be begging teachers and tutors for more algebra and more word problems – two bĂȘtes-noires of school mathematics. Who knows? This may turn out to be an inexpensive cure to addressing our declining birthrate! When most students' favorite four-letter word would then be MATH MATH MATH ... and MORE MORE MORE!

Stripping Off Your Maths

The above online algebra word problem reminds me of a math workshop organized by the Singapore Science Centre in late eighties, when the speaker-and-author, Mr Ang Tok Woon, shared with fellow teachers that a good metaphor could help weak or uninterested students recall mathematical concepts or formulas rather effectively.

He used the idea of ‘stripping off’ some unknowns when teaching the topic on "Subject of Formula" to a group of academically challenged [ITE or SAF mature] students. For instance, given E = mc2, ‘making c the subject of formula’ means expressing c in terms of E and m. And he was surprised that years later when some of his ex-students met him, they reminded him that they had forgotten everything else he taught them except for that part on stripping off.

Sexing Up the “Sixth Factor”

Only a lack of imagination and creativity would deprive hundreds of thousands of pubescent teenagers from experiencing the joys (and pains) of algebra.

As we explore how best to incorporate the sixth factor — the ‘context knowledge’ — as suggested by Assoc. Prof. Wong Khoon Yoong from the National Institute of Education, Singapore, to extend the present two-decades-old Singapore Mathematics Curriculum Framework comprising of the five factors (Skills, Attitudes, Concepts, Processes and Metacognition), diagrammatically placed along the sides of a pentagon, I think posing ‘real-world problems’ with a recreational or cultural flavor would go a long way to arousing the algebraic interests of our students who might otherwise give algebra a miss, once it becomes an optional topic. 

Indeed, we need a fertile dosage of algebra to debunk the myth that the common language of mathematics is difficult and boring. Algebra, or any topic in mathematics, for that matter, is amoral and neutral. Mathematics can only be boring as long as we’ve boring teachers and writers (and editors, math consultants and math specialists) — or all five — churning out unexciting textbooks. However, matters would have been a notch above boring if we had had fewer boring reviewers and curriculum specialists.

Some Nudity May Promote Numeracy 

Another episode proves that infusing some perceived elements of decent nudity – art for mathematics’ sake – to enhance numeracy (quantitative literacy, as it is commonly known in the US) may not be a far-fetched idea. Years ago I was attending a two-day teachers’ course entitled Andragogical Principles, an in-service program for those teaching working adults or mature students, when the lecturer confided to us that by letting his students write about their [wild?] fantasies, they actually improved their language proficiencies. In fact, I wouldn’t be surprised that some of them are now working as freelance writers or editors for some adult publications!

Indeed, numeracy spiced with some exciting part of human biology may act as a catalyst (‘mathematical aphrodisiac’) to attracting even mathematically dull students to sign up for some extra-mathematical activities to enhance their quantitative literacy. As mathematics educators, we critically need creative methods to promote our mathematical trade; otherwise, we’ll end up losing potential candidates with a mind for the abstract to major in other disciplines that often promise more tangible rewards.


Like guerrilla marketers, we need to go all out to promote and sell the idea that MATHEMATIC$ I$ MONEY! Some born with the ‘mathematical gene’ definitely stand a high probability of becoming millionaires, by cracking some unsolved mathematical nuts – for example, a few million-dollar prizes are on offer by the Clay Mathematics Institute to whoever can find the solution to some fiendishly difficult mathematical puzzles. For the majority of us, we can at least hope to secure some decent jobs thanks to the logical, analytical and deductive skills acquired through years of toying around with notions and notations.

If the oldest profession on earth continues to thrive because of the money factor, there is no reason why it cannot share a common denominator with the most disliked subject in school. With some financial carrots, more people would be motivated to speak the language of science and technology. Like sex, mathematics is money — and it can be enjoyable, too!

Thursday, March 11, 2010


For a few years now, I've secretly been writing mathematical words and terms, to be categorized under a so-called MATHESAURUSI wanted to christen the title A Politically Correct Mathematics Glossary or A Quick-and-Dirty Mathesaurus Dictionary.
Offhand, here's a sample of my irreverent definitions:

  • Abacus A primitive calculator that questionably originates from China. The Japanese version, called the Soroban, claims to be able to perform square and cube roots, as well as differentiation and integration. Unlike the calculator, its batteries last a lifetime. 
  • Actuary One who misuses or abuses statistics to justify the high premiums charged by one's insurance company.

  • AMC Abbreviation for “Australian Mathematical Competitions.” The world’s popular competition, AMC caters for those mathletes who do not qualify for the IMO, but hope to be medalists, nonethelessSee IMO.

  • Boolean Algebra The Arithmetic of “Or” and “And.”

  • Coordinates A way of describing a location on a grid. For instance, the author's e-mail coordinates are: kcyan.mathplus@gmail.com Some common daily use of coordinates are: (a) A cab driver looking for (5, 8), 5th Avenue and 8th Street; (b) Finding a seat in a theatre, say L25 (Row L, Number 25), and the like.

  • Mathophobia Anonymous A gathering of people who pride themselves of their mathematical ineptitude. The members meet clandestinely to avoid being overcharged and conned by unscrupulous agents. 

  • Quadratic Equation A misnomer for naming an equation of degree 2; should be renamed “biratic equation.”

  • Trial-and-Error Method A hit-and-miss approach. The mathematical equivalent for looking for a word in the dictionary.

  • World Wide Web (WWW) Comprises virtual cities of bits; the world of 1s and 0s. A city of bits. A communications medium that encourages gossip, freedom of speech, and gambling; sale of pink pills, yellow literature, blue movies, and so on.

  • NCTM’s Standards An ideal list of guidelines and recommendations for mathematical excellence in K-12 by the National Council of Teachers of Mathematics, to be implemented in a non-ideal classroom.

  • One-to-one correspondence The most primitive and also the most sophisticated method of counting. Used by farmers to count sheep, and by mathematicians to study different sizes of infinities and to come up with some visual (look-see) proofs.
Would you, readers, be keen to co-author with me the above irreverent guide to relevant mathematical terms? Any takers (friends, fiends or foes) who would be excited by such a general math-lite title? Please direct them to me. 

I couldn't be more serious about this funny title. I think it's going to be exciting to co-write and publish such a MATHESAURUS.

Irreverently yours
K C Yan 

© Yan Kow Cheong, March 11, 2010

Monday, March 8, 2010

The Thinking Like a Mathematician Series

The Thinking Like a Mathematician Series

In an age when apparently human beings use only ten percent of their brain, the public hasn't been spared of the Think Like a Genius syndrome. We've titles like Think like Da Vinci, Think like Einstein, and the like. Interestingly, but not surprisingly, we've yet to see a Thinking Like a Mathematician Series.
Probably we won't see such self-help series for some time, if the rate of innumeracy among writers and journalists doesn't dip in future. It's unlikely that untenured professional mathematicians (whose rice bowls depend on the number of published journal papers) would be lured into writing this type of pop math titles. However, non-fiction writers with post-graduate qualifications in science and mathematics are potential candidates to popularize such math-lite titles to the lay public.

Those who are fluent with abstract ideas would undoubtedly want to read about their mathematical idols of yesteryear – the habits of those highly successful mathematical minds. Monkeying the language of positive thinking, our chances of becoming a mathematician or mathematics educator would presumably be higher if we started acting or thinking like one. It is the intention and going through the motions of being or thinking like a mathematician that counts. 

Self-help books and circuit speakers tell us that if we want to think like a mathematician, and actually go through the motions of being one, we will become at least an adequate [probably, third-class] mathematician. We may not become another Archimedes, Gauss or Newton, but we'll be much more of a pseudo-mathematician than someone who doesn't practice the yoga of applied positive thinking. 

Meanwhile, let's look forward to some of these feel-good math titles, which may give the mathematical brethren some psychological boost to their often-unappreciated vocations.

Chicken Soup for the Mathematician Series
Chicken Soup for the Pure Mathematician
Chicken Soup for the Applied Mathematician
Chicken Soup for the Math Professor
Chicken Soup for the Math Assistant Professor
Chicken Soup for the Math Associate Professor
Chicken Soup for the Math Adjunct Professor

Chicken Soup for the Algebraist
Chicken Soup for the Geometer
Chicken Soup for the Group Theorist

Chicken Soup for the Number Theorist
Chicken Soup for the Probabilist
Chicken Soup for the Statistician
Chicken Soup for the Topologist 

© Yan Kow Cheong, March 8, 2010