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Singapore Math

Friday, November 1, 2019

Panda Math

Two-odd years ago, with sporadic news on the low fertility rate of pandas, I cheekily coined “Panda Math”:


Panda Math was published on Urban Dictionary before its online presence was cut short.

Like the rabbit and the koala, the panda is much liked and loved by people of all ages and from different parts of the world. It's hard to imagine those who wouldn't like to be around a panda or two if they're given that rare opportunity. What are the odds that someone doesn't like both math and panda?

How could elementary and middle school math teachers leverage on the cute panda bear popular among school children to pose a number of brain-unfriendly math questions to sharpen their problem-solving skills?

Panda Diplomacy and Numeracy


To strengthen diplomatic ties, China loans pandas to countries around the world—a version of its soft diplomacy, aimed at winning hearts and minds abroad.

The practice existed as far back as the Tang Dynasty, when Empress Wu Zetian (625–705) sent a pair of pandas to the Japanese emperor. Giant pandas are very popular among the Japanese, and they symbolize the friendly ties between Japan and China then.

Guesstimate how many more pairs of pandas would be given as diplomatic gifts to other China-friendly nations in the next decade, as President Xi and gang expand their political influence worldwide.


Below are a sample of questions that could be used to spice the teaching of math, especially among panda-and-math lovers.


Philamath embraces the panda.
Sally bought some 50-cent and 65-cent stamps for a total of $5.10. How many 50¢ stamps and how many 65¢ stamps did she buy? Answer: Five 50¢ and four 65¢ stamps.

Chuang Chuang, a 19-year-old giant panda died unexpectedly in a Thai zoo. Assume that giant pandas normally live up to 25 to 30 years in captivity, in human terms, how old would the cute and cuddly bear be?  


Adult Math

Let's bring in some biology to hone students' mathematical problem solving.

The Mating Game

On average, a baby panda weighs 100 g, which is only 1/900 of their mother's weight, compared to 1/20 for a human. During the breeding season, when males and females come together for no more than 2 to 4 days, what would be the frequency for a male panda to mate with his partner before a baby bear is born?

What are the chances of a pair of pandas producing baby giant panda twins*? Or even triplets? Are the odds of a female panda giving birth to triplets lower than those of a human being being hit by lightning, or winning the lottery twice?

* In the wild, half of all pandas give birth to twins; however, it is rare for both cubs to survive as the panda mother is only able to raise one at a time and abandon the second twin—she has insufficient milk or energy to care for the twins.

Or, what about getting grades 1–2 students to indulge in some mathematical quickies such as the following?


The total age of Kai Kai and Lin Lin at an unspecified zoo is 14. Kai Kai is 4 years older than Lin Lin. How old is each panda bear? Hint: Not 4 and 10.

At a zoo, all bears are pandas except two, all bears are polar bears except two, and all bears are brown bears except two. How many panda bears are there?


Love at First Sight (or Smell)

Compared to African elephants, which can communicate over distances of one kilometer, or koalas up to 50 meters, pandas can recognize each other within a proximity of 20 meters. However, they can only figure out the gender of a potential mate if they are less than 10 meters away.

Guesstimate the total distance adult pandas in the wild must travel every year before lovemaking can successfully take place.


Bamboo Math

To maintain their energy needs, pandas must consume 12 kg to 38 kg worth of bamboo each day. Estimate how must bamboo forests needs to be allocated to provide enough food to sustain them.


Will the Panda Be Dodo 2.0?

Barring extreme climate change, which would make it pretty hot for the bamboo to grow, what are the odds that with mating and breeding challenges, the giant pandas might suffer the fate of the dodo?

Estimates suggest that there are fewer than 2000 pandas left in the wild. If President Trump and gang are allowed to promote their climate change hoax or "global warring" agenda, are the days of the pandas numbered? How many panda bears would still be around by 2050?


Singapore (Math) and Panda
The intersection is not empty.

On the surface, it looks like there is zero correlation between Singapore and Panda. Once we put on our thinking cap, it’s not difficult to come up with a number of parallels between these two items.


For example,


Singapore’s fertility rate of 1.14 is presently below replacement level. 
Pandas’ low fertility rate is a warning sign for possible extinction.

Singapore could have just ended being another Commonwealth developing country in a sea of corrupt, mediocre nations.
The panda could have been just another member of the Bear family, or a mere zoo attraction with hardly any global recognition.

Singapore math is a "success story" in math education: the island state's top rankings in TIMSS and PISA have attracted a fair bit of attention among math educators worldwide.  
Breeding panda in captivity is a success story (including a few births in some zoos), and panda diplomacy promotes friendship between China and other countries.

Singapore is a "Disneyland with a death penalty"—economic success and political stability at the expense of political freedom and an aversion to alternative lifestyles.
Pandas are a favorite attraction at zoos, which could be flown back if China's political system is questioned.

The panda is the logo of the World Wide Fund for Nature (WWF), which originated from a panda named Chi Chi that had been transferred from Beijing Zoo to London Zoo in 1958. 
Singapore math is associated with the "bar model method," a powerful problem-solving visualization heuristic to solve challenging word problems.

Products "made in Singapore" are no longer shun away; instead, the Singapore brand is well respected in many parts of the world for quality and honesty.
Pandas are beloved zoo animals around the world, although capitalist China pays lip service to the rule of law and copyrights, and is silent on human rights abuses, kidnappings, and torture.

It's your turn to list another half a dozen similarities between Singapore (or Singapore math) and pandas.



When the panda refuses to remain silent on illegal occupation.


Bibliography & References

Third time lucky? Pandas Kai Kai, Jia Jia get down to ‘serious business’ http://www.todayonline.com/node/2827076 

Giant panda death in Thailand leaves China asking questions https://www.bbc.co.uk/news/world-asia-49737215

Giant pandas can tell a mate from their calls http://www.bbc.co.uk/news/science-environment-45575604

Panda's habitat 'shrinking and becoming more fragmented' http://www.bbc.co.uk/news/science-environment-41366274

How did China save the giant panda? http://www.bbc.co.uk/news/world-asia-china-37273337


Yan Kow Cheong, October 31, 2019.


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