Welcome to K C Yan's Singapore Math blog!

Wanting to be updated on Singapore Math news or new Singapore Math? You've come at the right place! Please leave your comments before leaving. A googol thanks.

Singapore Math


Thursday, October 15, 2015

Gross Singapore Math

© S. Mockus, & T. Millard, (2010)

Estimation (or guesstimation as it is more commonly known in the U.S.) is a creative mathematical activity that is seldom given enough curriculum attention and time in Singapore. For the lay public, and probably for a disturbingly large proportion of local math teachers, tutors, and parents, estimation is often confused with approximation (or rounding off numbers).

Like swimming, cycling, and driving, estimating ought to be a life skill that is indispensable for all responsible citizens aiming to be numerate in our quantitative world of bloated data.

A PSLE Estimation Routine

In this year Singapore's PSLE (grade 6) math paper, a routine guesstimation MCQ question has irked some parents, who "blamed" the Ministry of Education for posing an "unfair" question.

Ghostly Math from @MathPlus

How to Fermi-ize

Current Singapore math textbooks are often too Puritan, not to say, boring, to contain fertile exercises that could hone students' estimation skills. A dose of humor, without insulting or shocking the readers, will go some way in nurturing some Fermi disciples. Let's look at eleven non-drill-and-kill guesstimation questions, which could be posed to above-average math students bored by school math.

0. Zero Toilet Paper 

If all the toilet paper used in Singapore in an entire year were rolled out, how far would it stretch?

1. The Trillionth Heartbeat

Assuming an average human heart of 72 beats per minute, estimate that most folks would breathe their last breath around their billionth heartbeat, or by their near-666 weeks of life on this side of eternity.

2. Pools of Eyeballs

About how many Olympic-sized swimming pools would all the world's human eyeballs fill?

3. Death Nailed by Tobacco Sticks

© Chua Sin Yew

A medical association claims that a cigarette smoker shortens the length of his life by 9 minutes for each cigarette smoked. A student smokes three-quarters of a pack of 20 cigarettes every day for 30 years. Excluding leap years, by how many months or years has this student cut short his life to?

4. To Pee or Not to Pee

How much urine is in a typical public swimming pool? Or, how much pee in a pool would kill you?

5. Length of Intestine

If you were to pull your small intestine out and laid it in a straight line, how long would that be? Is it shorter than the distance from Earth to Moon?

6. A Nation of Vampires—Human Blood Aplenty

If you were to take all the human blood from all the living people in Singapore and pour it into the Singapore Indoor Stadium, how deep would it be?

© Mark Parisi

7. Zoo Poo

Estimate how much zoo poo is collected every week at the Singapore Zoological Gardens. How much of it could be used as fertilizers?

8. The Host with the Most

How many (unfriendly and not-s0-friendly) bacteria are living on and inside you right now?

9. Cash in on the Trash

Show that, on average, every square mile of sea on the planet contains 46,000 pieces of rubbish. How much cash could be generated annually by an entrepreneur involved in the trash business? [1 mile is about 8/5 kilometers.]

10. Green Pollution

© Sidney Harris
Thanks to Indonesia's mostly incompetent politicians and corrupt businessmen, its neighbors Malaysia, Singapore, and Thailand, have unhealthily been affected by the annual haze visiting them, as a result of illegal forest burning by local farmers to save costs for their bosses.

Guesstimate the number of people inside and outside Indonesia, who have been affected in the last two decades from this man-made pollution. How many natives, Mohammedans, and "infidels" will die prematurely because of near-zero political will from oft-corrupt Indonesian politicians?

Estimation Skills via Gross, Illegal, or Murderous Math

Be it via "Gross Math," "Murderous Math," or "Illicit Math," creative or fertile questions on the "shit," "death," or "illegal" business, could be posed to enhance students' guesstimating skills.

Indeed, gross Singapore math could serve as a catalyst to imparting real-life estimation skills to students, and to reducing more complaints from kiasu Singapore parents, whose children will be sitting for the PSLE oft-dreaded math paper in coming years.

Selected Answers
2. About 73 swimming pools.
5. About 18 miles long.
8. About 2,000,000,000,000,000 bacteria.

BONUS: Some Facebook Estimation Quickies

The Boring Talkative Math Teacher

500 GB of data can store X books. What is X?

Number of people in the picture

Grave Humor

Ballroom Readers' Institute (2011). Uncle John's impossible questions and astounding answers. Ashland, Oregon: Bathroom Readers' Press.

Krantz, S. G. (1997). Techniques of problem solving. American Mathematical Society.

Mockus, S. & Millard, T. (2010). How to speak zombie: A guide for the living. San Francisco, CA: Chronicle Books LLC.

Rimmer, G. (2005). How to make a camel smoothie and other surreal sums. Cambridge: Icon Books.

Teng, A. (2015). An informed estimate is worth its weight in coins. The Straits Times, Oct 9, 2015. http://tinyurl.com/q7ly7bx

The Bathroom Readers' Institute (2011). Uncle John's bathroom reader impossible questions and astounding answers. Ashland, OR: The Bathroom' Readers Innstitute.

Yan, K. C. (2012). Mathematical quickies and trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, October 15, 2015.

Sunday, March 1, 2015

A Dozen Numerical Deeds for the Chinese New Year

The Lunar New Year is often a time of receiving rather than a time of giving for most youngsters. However, like Christmas, for not-well-to-do donors, it's the worst time of the year, when they're expected to give hong baos or gifts to the younger generation, many of whom think it's their juvenile rights to receive these red packets.

An extra zero is always welcomed!
From: The Straits Times, Feb. 18, 2015. p. A24.

In recent years, more shops and supermarkets are open during the Chinese New Year, because foreign workers and non-Chinese Singaporeans are willing to work overtime to serve locals, who would otherwise be inconvenienced when it comes to buying household items; or having a wallet-friendly meal, while they go around visiting friends and relatives. Not to say, foreign-born doctors and nurses who are on stand-by to look after local patients, who are admitted to hospitals during the Chinese New Year public holidays. 

There is no better time than the Chinese New Year to show our appreciation to the financially disadvantaged and to tens of thousands of migrants, who help sustain the economy, when most Chinese Singaporeans are having a good time catching up with relatives and friends.

A Dozen Deeds for Singaporeans of All Sizes, Shapes, and Ages

Here are a dozen simple numerical deeds many could afford to do during this festive season, especially after receiving fat hong baos from senior family members and relatives.

12. Give some iTunes or Google play gift cards to children from disadvantaged homes for them to purchase some educational apps or ebooks.

11. Do
nate a math ebook, or offer a sample chapter, or book voucher to someone whose child might benefit from it.

10. Overtip a waitress.
The book may be unsuitable for non-geeks!

9. Give ten bucks to a street musician or blind person.

8. Compliment three strangers every day during this festive season.

7. Give a gift certificate or cash voucher to a beggar.

6. Bless a poor child with a Rubik's Cube.

Not all Rubik's cubes are made equal!
5. Offer ten percents of your income to charity, on top of your tithe.

4. Surprise an old friend overseas with a phone call.

A value-for-money grade 3 SG math book
3. Volunteer to teach or tutor someone how to use the model- or stack-model method as a problem-solving strategy to solve brain-unfriendly questions.

2. Settle the restaurant bill for a family of four strangers while they are enjoying their meal.

1. Buy a seasoned train ticket and give it to a poor person.

The time to spread happiness and joy is now, especially among foreign and migrant workers and the economically disadvantaged. For the young, it's never too early to be a cheerful giver! Let the spirit of giving be extended far and wide vis-à-vis disadvantaged Singapore citizens and residents!

© Yan Kow Cheong, March 1, 2015.

Tuesday, January 20, 2015

Another Math Ban from Singapore

Sorry, U.S. accounts ONLY!
A less-known disturbing fact in local educational publishing is that Singaporeans, Malaysians, and other nationalities can't purchase any Amazon Kindle and iBooks math e-books from their own local bookstore. For example, Singaporeans can't access to any free or paid e-books from Amazon or iTunes, unless they switch from the Singapore store to the U.S. store. This means they have to officially open a U.S. account with the bookseller, which is anything but a simple procedure. Why erect this wall to make it harder for Singaporeans and Malaysians to buy e-books in the U.S.?

Suitable for mathletes
Last year, I released a Kindle book with Amazon, and I asked them why there is such a restriction on locals to download free, or to purchase paid, Amazon Kindle e-books. The answers were vague and unsatisfactory, to say the least. For instance, you can't even test or preview how your e-book will look like on certain platforms with certain apps, as they're not available in the Singapore store, unless you've a U.S. account, which makes it eligible for you to download them.

What's the Motive behind the Ban?

Several reasons have been conjectured online as to why locals can't access e-books from the world's biggest bookstore. It looks like some decision-makers in Singapore and Malaysia are behind this ban to protect their vested business interests. If this is truly the case, then this augurs badly for the writing community or local publishing industry, especially for Singaporeans and Malaysians who plan to publish e-books under Amazon or iBooks. Interestingly, such a restriction doesn't apply for apps, though.

No Singapore!
It'd be understandable if such a purchase ban were to apply to, say, North Koreans and Iranians, because Amazon and Apple might not want to deal with countries ruled by dictators who sponsor or promote terrorism and violence. But to deprive ordinary citizens from countries whose human rights records are no worse than those in the Middle East and Asia, where women are often treated as second-class citizens, sounds like a business mockery! 

Few Value-for-Money Apps

With all these restrictions in place, one wonders whether this is the main reason why there have been few decent Singapore math apps (and far fewer math e-books) on both Amazon and iTunes so far. Presently, most math apps by locals on App Store are of little value—most just give away a sample chapter, or the Contents page, of their printed textbooks, unlike the paid Singapore math apps produced mainly by non-locals.

Singapore Math iBooks

Last week, I released two Singapore math books on iTunes; again, students, teachers, and parents in Singapore are unable to purchase them, because the titles are not available in the Singapore store. They need to have a US account to buy them. 

App Store: https://itun.es/us/JCU84.l
Google play: 
A few local math educators are willing to review the books to better assess their suitability to audiences that might benefit from these problem-solving books, but they gave up when they couldn't do so from their tablets, which is, by default, connected to the Singapore store. It's already a pain to update apps like Kindle (which isn't available in the local store) much less purchase or review e-books that can only be downloaded with a U.S. account.

It's an irony that our own local math students and teachers can't purchase Singapore math e-books, when others outside the country can freely and conveniently do so. The last thing we want is another ban that forbids us to assess mathematical knowhow, which has zero correlation with politics, democracy, or terrorism.

Google Play as a Last Resort

However, all isn't lost for those who still wish to access their free or paid Singapore math e-books online. They could download or buy them from Google play, if they are available there.

App Store: https://itun.es/us/fP384.l
Google play: 
The Future for Singapore Math E-Books

At a time when the days of printed boring math books are numbered, and more students and teachers are switching to smartphones and tablets as a new platform for learning and teaching, restricting them to buying or downloading math e-books online is simply a dozen steps backwards to encouraging local writers—often stifled by politically correct local publishers and faux math editors—in reaching out to a wider local readership and global audience. 

Math and math education must be free and be freely available, not to be dictated by some folks with a profit agenda.

© Yan Kow Cheong, January 20, 2015.

Wednesday, October 15, 2014

Stamping Up Singapore Math

Even if you are just an amateur stamp-collector, much less a professional philatelist, it won’t take you long to realize that not many people in this world are fond of collecting Singapore stamps, as compared to, say, stamps issued by other countries.

SingPost seems to have somewhat cheapened the value of Singapore stamps, by issuing First Day Covers, as if they're selling parking coupons—Singapore issues, on average, a dozen sets of new stamps every year.

Semi-circle stamps of yesteryear

In general, most Singapore stamps have an uninteresting theme or design; SingPost's commemoratives seem to have been issued more as a means to generating extra revenue from stamp collectors, with little attention paid to aesthetics and beauty.

Numeracy via Singapore Math Stamps

In general, although philatelists don't have a positive view of Singapore stamps, however, not all is bleak for our postal department. To promote mathematics and mathematics education in Singapore, in particular Singapore’s mathematical achievements locally and internationally, it wouldn’t be a bad idea if SingPost considers issuing commemoratives with a mathematical flavor. For instance, it can issue First Day Covers on the following themes:

· A set of three stamps featuring Singapore’s triple firsts at the Third International Mathematics and Science Study (TIMSS), which has since put Singapore on the Mathematics Education World Map—an economic by-product of this would be to produce more localized adaptations of Singapore math textbooks, hopefully from some politically unstable, resources-rich developing countries;

· Another set of three stamps featuring Singapore’s emphasis on the concrete-pictorial-abstract model in primary (or elementary) school mathematics, which arguably has contributed to our students’ better understanding of mathematical concepts, especially when it comes to solving word (or story) problems;
· A set of stamps highlighting Singapore’s model (or bar) method, which has prematurely empowered tens of thousands of local pupils to solve nonroutine and challenging word problems, which traditionally used to be set only at the secondary (or middle-) school level;

· A set of stamps depicting famous (dead or living) Asian (or Singaporean) mathematicians and mathematics educators—few as they may be—who have contributed much to raising the mathematical standards in Asia;

· A set of stamps celebrating special Math Days like the AbacusDay, Statistics Month, Metric Week, and Pi Day;

· A set of stamps debunking Asian superstitions, myths, and legends, related to annual festivals like the Lunar Seventh Month (or Ghost Month); or exposing pseudoscientific beliefs involving so-called auspicious and inauspicious (or lucky and unlucky) numbers, feng shui numbers, and I Ching;

· A set of stamps on the different types of abacuses, including those used in divination and superstition;

· A set of stamps featuring magic squares used by Asians in numerology and astrology;

· A set of stamps featuring Asian achievements in mathematics, whether at the International Mathematics Olympiad (IMO) or in regional contests and competitions;

The pentagonal framework defining
Singapore's math curriculum
· A set of stamps featuring the five components of the mathematical problem-solving model (attitude, metacognition, processes, concepts, and skills), which forms the framework of the mathematics curriculum in Singapore;

· A set of stamps featuring the most commonly used (or misused or abused) heuristics (e.g., draw a diagram, make a list, guess and check, look for patterns, work backwards) and some artificially forced thinking skills (e.g., classifying, comparing, sequencing, identifying patterns and relationshipsanalyzing parts and whole, induction, deduction, spatial visualization);

· A set of stamps commemorating the Singapore's Ministry of Education (MOE) visions:
1998: Thinking Schools, Learning Nation
2006: Teach Less, Learn More
2014 and beyond: ?!?!

Glocalizing Singapore Math via Philately

To promote an interest and appreciation of Singapore's (or Asia's) mathematical history and heritage in philately, traveling exhibitions may be held locally and regionally. For instance, rare philatelic gems such as mistakes, fakes, and forgeries—how mathematics can help detect forgery and fraud in philately—may be showcased.

So, issuing Singapore stamps with a mathematical flavor would go a long way to marketing and glocalizing Singapore math, while recognizing the contribution of local math educators, on leveraging the power of mathematics to help alleviate poverty, or lessen the economic gap between the haves and the have-nots. Let’s stamp mathematics firmly on Singapore postage stamps—glue is halal. Stamp up, Singapore!

For further reading
Wilson. Robin J. (2001). Stamping through mathematics. New York: Springer-Verlag.

© Yan Kow Cheong, October 15, 2014.