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Singapore Math

Tuesday, July 30, 2019

Rabbit Math

Looking at the number of math questions that feature animals and birds, not even man’s best friend comes close to the rabbit—the beloved pet of math writers and teachers.

Think of the Fibonacci numbers, published by Leonardo of Pisa in Liber Abaci ("Book of the Abacus" or "Book of Calculating") in 1202, in connection with the rabbit population:

If every month a pair of rabbits produces one new pair, which begins to bear young two months after its own birth, how many pairs of rabbits will there be after a year?

Show that at the end of the twelfth month, there will be a dozen dozen pairs from a single pair.
An e-card I made before someecards banned users from designing their own. 

Why Singapore Math Loves Bunnies

Singapore math wouldn’t quite stand out from other foreign math curriculums, without its unhealthy number of brain-unfriendly math questions on chickens and rabbits (and goats and sheep). Even the smarter and (arguably) cleaner pigs unfairly lose out vis-à-vis the rabbits, simply because it's politically or religiously incorrect to use "infidel" pets or mammals and "haram" items in Singapore math textbooks, which are primarily targeted at a multiracial and multicultural student population. 

Through my dozen-odd supplementary Singapore math books, I'm guilty of contributing to the undue stress inflicted on millions of bunnies and their caring (or mathophobic?) owners around the globe. Below are two elementary math rabbit questions taken from my unpublished manuscripts:

A farmer has some chickens and rabbits. 
There are 60 eyes and 100 legs altogether. 
How many chickens and how many rabbits are there?

Since both chickens and rabbits each have 2 eyes, the total number of animals is 60 ÷ 2 = 30.

Suppose all 30 animals were chickens. Then there would be a total of 30 × 2 = 60 legs.
So the extra (100 – 60) = 40 legs must have come from the rabbits.

Each rabbit has (4 – 2) = 2 more legs than a chicken.
So there are 40 ÷ 2 = 20 rabbits and 30 – 20 = 10 chickens.

Challenge: Can you solve the above word problem, using a different method, say, the Stack Model Method, or the Sakamoto Method?

The next grade five or six question showcases two methods of solution, commonly used in Singapore local schools—students aren't expected to solve it by substitution or elimination methods, as these aren't formally taught in elementary school.

Guess Who's Suing Singapore?

A few years ago, I produced the bunny meme pictured below and posted it on the Imgur app, together with the accompanying wicked question:

Farmer Yan has almost twice as many chickens as rabbits. 
The total number of legs and heads is 184.
How many rabbits are there?

Now you know why these angry bunnies are "mathematically stressed," compared to the lazy, pampered cats and guinea pigs! Can you show why the answer is 17 rabbits? If as an elementary math student you could solve this, the odds that you might be born or blessed with the "mathematical gene" are pretty high.

Murderous Math—Let's Prey

In the wild, the rabbit is inarguably the most preyed-on animal in the world: from cobras, pythons, eagles, owls, lions, tigers, wolves, and hyenas, just to name a few common predators.

Guesstimate how many predators depend on the rabbits for their livelihoods every year. Or, how many rabbits have their lives cut short to feed their predators? Well, see these predators as playing their part in maintaining a healthy ecosystem for mankind—a proof that life isn't fair.

Political Rabbit Math

My childhood made-in-China candies
Recently, in the heat of the trade war between the US and China, as nationalistic mainland Chinese tried to promote their own brands of local products, I coined Rabbit Math and got it approved on Urban Dictionary, before some mean fellow probably with an axe to grind maniacally tried to continually downvote the phrase and had it taken down from cyberspace.

Beware of "digital terrorists" who just don't want to see even neutral mathematical terms or words floating on the internet—indeed, this sounds like the mathematical equivalent of Boko Haram.

One pair of rabbits can produce 60 babies a year.

Go Forth and Multiply

Before 1788, there were zero rabbits in Australia. That year, rabbits arrived on a boat from England; by 1950, there were 600-odd million rabbits in the Land of the Kangaroos.

If humans had babies at the rate rabbits do, show that our global population would double every three weeks. 

The Rabbit Habit

Early this year, I christened "5-Day Weekend" as a working template to promote creativity and productivity among time-poor workers, who always complain that their weekends are too short, and can't hardly get any productive work done on weekdays.

Rabbits by Numbers

Let me end with some tidbits about the idiosyncrasies of our beloved bunnies.

From: Mike Lowery’s “Random Illustrated Facts” (2017)

Those of you, who are bunny lovers, please share with the rest of us your favorite numerical factoids or numeroids about these cute animals.

As Productive as Fibonacci

Amateur-mathematician Fibonacci was a math popularizer and writer, who promoted the Hindu numerals during his European travels, besides blessing the mathematical brethren with a number of interesting or story arithmetic problems, one of which is the "rabbit problem" for which he's dearly remembered today. 

At a time when greying Singapore is historically experiencing its lowest fertility rate—which may lead the island-state to go the way of the dodo, if no disruptive measures are taken, other than conveniently (or simplistically?) depending on baby bonus incentives and immigration to arrest the population decline—for us, math educators, let's not stop being as mentally fertile and creative and productive as Dr. Fibonacci, although few of us would dare to promote the kind of productivity rate of his fertile bunnies!

Bibliography & References

Adam, F. (2014). The awesome book of awesomeness. London: Bloomsbury.

Fairbrass, M. & Tanguy, D. (2017). The scale of things. London: Quadrille Publishing Limited.

Lowery, M. (2017). Random illustrated facts. New York: Workman Publishing Co, Inc.

White Rabbit milk tea sells at 2,000% premium as Chinese consumers show support for local brands amid trade war http://bit.ly/2KPj43h

Yan, K. C. (2015). The stack model method: An intuitive and creative approach to solving word problems—Grades 5–6. Singapore: MathPlus Publishing.

Yan, K. C. (2015). The stack model method: An intuitive and creative approach to solving word problems—Grades 3–4. Singapore: MathPlus Publishing.

Yan. K. C. (2013). The chickens-and-rabbits problem. https://www.singaporemathplus.net/the-chickens-and-rabbits-problem/

© Yan Kow Cheong, July 30, 2019.

Thursday, January 31, 2019

Seven Irreverent Definitions of Singapore Math

Since I started christening mathematical words on Urban Dictionary, as someone who makes a living evangelizing the gospel of Singapore Math, it’s too tempting not to attempt defining the love-or-hate term, depending on your personal experience with the alien, hybrid math curriculum. Indeed, your geography or maturity would most likely determine your position or reaction vis-à-vis Singapore Math—for a number of you, not only you love Singapore Math, but Singapore Math loves you, too!

Since last December, I discovered that out of the hundreds-odd math terms or phrases I had contributed to Urban Dictionary—the "anti-Wikipedia"—under different pseudonyms, one “terrorist stalker” has been serially and wickedly downvoting a number of them on a daily basis to the point that the online dictionary had to temporarily suspend and eventually remove the most downvoted entries to prevent further digital abuse or digital persecution—two of those deleted definitions involve Singapore Math.

The Fear Factor in Singapore Math Education

If math teachers, tutors, writers, and editors were given the assurance that they wouldn't be punished, fined, jailed, or even caned for speaking up and speaking out on the good, the bad, and the ugly of Singapore math education, it's inconceivable why Singapore couldn't potentially become a global mathematical hub of choice for those born with the mathematical gene (let’s pretend that there’s such a thing) and a sense of humor or irreverence.

As a proof that we in Singapore aren’t the boring, exam-smart math educators that some outside the island-state would like to portray us, below are seven irreverent or light-hearted definitions on Singapore Math, which were approved and published on Urban Dictionary, the World's No. 1 online dictionary.

Could you figure out which two of the seven definitions were "censored" or deleted? At one point, I thought maybe there is a vigilante math squad, a subset of the small army of moral and political policemen and women, recruited by the Singapore authorities to monitor any citizens or residents who try to publish any mathematical thing, which speaks ill of the government, the police, the army, and the judiciary. 

Who knows that these e-censors might be on the lookout to report any "mathematical black sheep" to the authorities, who might then threaten and sue them, if they refuse to take down any content or comment that allegedly promotes the dark side of math or math education in Singapore?

Singapore Math with a New Twist

May I encourage you to redefine “Singapore Math” based on your personal experience and interaction with fellow math educators, students, parents, and caregivers (or maids-turned-tutors). Indeed, Singapore Math has many faces, and your unique perception and definition of it would allow us to peek at a hitherto unseen (sexier or darker) side of it. It's never too late to share your definition (or frustration) with fellow math educators.

In Singapore Math, we trust!

© Yan Kow Cheong, January 31, 2019

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.