Creativity or Stupidity?

This week, I saw this attached (grade one?) test item or math meme on Facebook, which was initially posted by “The Language Nerds” group.

Based on the multiple comments to this ill-posed math question, it’s amusing, yet also disturbing, to read that most responders are praising the student for his “creative” answer, or criticizing the “uncreative” teacher for penalizing the poor child.

In this postmodern or polarized world we’re living in, you’d think that maybe only someone who’s a “very stable genius” would rationalize or argue that the student’s response qualifies as one of the equally valid answers. And if the biased teacher insisted on marking the creative child wrong, the parents might consider suing him or her for giving their son an undeserved zero.

Creative or Uncreative Comments

Below are some netizens’ replies to the math question from “Maths Jokes Daily,” which range from the hilarious to the ridiculous to the preposterous.

I think because the circles weren't closed properly 🤔

honestly think its possible for most people to understand what you are supposed to do here, so I would definetely argue that this is not a badly formed question :)

Were the correct answers 1.39, 2.17 and 3.96 ?

He got it wrong because he marked 3 numbers, and the question only asked for one, so the right answer is 15

He provided 3 right answers. He identified the smallest number in each row disregarding the periods and commas. LOL !

He circled 3 numbers. Number 1 is the smallest number and therefore should have only selected the 1 single number.

Also, why did the teacher put 3 lowercase "alpha" symbols?🤣

it’s evident smallest number and not smallest numberS so he should have circled only 1

Because he only circles 1 but not 1.39 Same with others

The fault lies entirely with the fool that numbered the questions with Roman Numerals and then used 1, 2, 3 instead of a, b, c

That kid is already smarter than the teacher.

Thats at least .5 for thinking outside the box

? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! ? ! 

Would you side with the teacher or the student? How would you respond to the “wrong” answer to this ill-posed or improperly posed question?

Creatively or uncritically yours

© Yan Kow Cheong, May 19, 2023.

Book-Smart Math vs. Street-Smart Math

 

Based on the picture and text, who do you think got a better deal? Which party ended up happier: Customer or Seller?

Would you agree that the young exam-smart customer was outfoxed by the old street-smart fruit seller? 

Aren’t we all guilty of this “book- or exam-smart syndrome,” when we’d buy more than what we needed because we thought we’re getting a good deal, or we didn’t want to be taken advantage of?

In the end, isn’t the supermarket or shop owner or fruit seller who’s having the last laugh, while the customer thinks they’re the “smarter one”?

Isn’t it a case of “more is less”? When A-students are being outwitted every day by C-students in the marketplace!

It’s probably no wonder that most exam-smart A-students around the world end up working for street-smart C-students. The former have so much to lose, compared to the latter who’ve far more to gain (if they do make it!).

If you’re a “math educator” (teacher, tutor, writer, editor, ghostwriter, lecturer, “moonlighter,” …), do you have what it takes to venture into the business of math or math education? 

Smartly yours

Photo © Anon.

Stole the attached picture from ex-colleague-and-friend WeePing Chun on Facebook.

© Yan Kow Cheong, May 9, 2023.

Math à la Japonaise

We need to thank Mrs. Marie Kondo for advocating that tidying up needn’t be obeyed as an eleventh commandment, especially for a significant number of us who can’t afford to live sans a mess, or who just refuse to be Konned by her enviable minimalist lifestyle.

Since the tidying consultant has been in the limelight recently after her long overdue admission that the art of tidying up could be an optional activity for those who can’t stand the sight of all kinds of oft-dated, sentimental, or hoarded items lying around the house (and in the office), I thought it’s apt to share about “KonMari Math,” which I christened two years ago, to show that even math educators too haven’t been spared by the gospel or philosophy of the organizing goddess.

Math word du jour

Photo from math prof @mathematicsprof on 17/2/19

Personally, I’m dazzled by most things Japanese: origami, sushi, wasabi, not to say, soroban (Japanese abacus—square-rooting, cube-rooting, differentiating, and integrating), Kumon math, Sakamoto math, Sangaku, and Wasan.

After being introduced to Mr. Kenji Wakabayashi by my ex-colleague and friend, Mr. O.K. Heng, to learn about the ABCs of the Sakamoto Maths Method, I was later offered the opportunity to attend a months-long series of math talks on the Japanese problem-solving heuristic (or “problem-solving strategy” as it’s known in some parts of the globe).

To certify that I’d mastered Sakamoto math, I reluctantly had to take an exam with fellow participants who’re much younger than me. I was already around forty then, and needless to say, by then, it’d been a while since I last sat for a math proficiency test or exam.

Front cover of the manual

Today, I’m thankful to Mr. Wakabayashi who gave me an opportunity to get a strong foundation on Sakamoto math, which has proved to be a more advantageous or intuitive problem-solving strategy than the bar model method in a number of problem situations.

What is even more amazing is that I attended all these Japanese math lessons without forking out a penny. Talking about being blessed mathematically (and financially), when other participants or franchise sponsored trainers have to pay hundreds of dollars to attend these twice weekly and weekend classes.

Indeed, Sakamoto math offers paid, sponsored, or guest attendees another method of solution to solving brain-unfriendly word problems. I think a Singapore math educator-turned-trainer ought to be versed with not only the bar model method, but also with the stack model method and the Sakamoto math method—a trinity of problem-solving strategies.

Recently, while working on a bar modeling manuscript, I accidentally came across some Wasan (or Japanese math) materials, which further solidifies my knowhow of Nippon math, especially some of the techniques I learned in Sakamoto math moons ago.

May I encourage all of you to expose yourself to the richness of Wasan, which would help broaden and deepen your appreciation and knowledge of multicultural math, if you’re open to learning different problem-solving strategies (or heuristics) commonly used in countries with a rich mathematical heritage.

Of course, to learn Sakamoto math effectively, do it preferably under a master-trainer from Japan—never mind their accent—rather than merely reading the notes of your child or nephew who’s signed up for a Sakamoto math course.

May the learning of Nippon math and multicultural math (Vedic math, bar model method, stack model method, line model method, …) spark mathematical joy in your life.

Wishing you many blessed joy-sparking or aha! moments.

Mathematically & multiculturally yours

References

Kondo, M. (2022). Marie Kondo’s Kurashi at home. New York: Ten Speed Press.

Yan, K.C. (2016). Sangaku — Japanese temple geometry. Geometrical quickies & trickies. Singapore: MathPlus Publishing.

© Yan Kow Cheong, March 10, 2023.

A New Yorker cartoon by Evan Lian.

Freedom from Crypto Addiction

Cure from crypto addiction needn’t be costly!

Help is now dearly available for those who’re hard hit by the recent crypto winter.

For those who can’t afford the nouveau-riche treatment, or who’re thinking of following Anthony Bourdain’s or Jeffrey Epstein’s template, because there seems to be no way out, know that there’s a (better) way to come out of that hell.

A better and faster (or cheaper) solution for crypto addicts would be to attend a counseling-and-praying session or two so that they’d be delivered once for all from the spirit of gambling.

Complete deliverance and healing is a mere prayer away if they’d turn to the Deliverer-and-Healer who has the power to free them from their short- or long-term addiction or affliction or persecution.

The Miracle Worker who turned water into wine, or who used five loaves of bread and two fish to feed five thousand people or families, is waiting and willing to deliver them from their gambling or years-long bad habit or addiction if only they agree or humble themselves to be delivered.

May their pride (or unbelief or negative faith or ignorance) not be a stumbling block to their being freed from crypto addiction, massive debt, or financial ruin.

Freely yours

© Yan Kow Cheong, February 8, 2023.

Crime Watch and Crime Math

Singapore is known for its low crime rate in the developed world, and those who occasionally peek at what’s happening in the island-state might be surprised to read about more local and foreign shoplifters being recently caught in CCTV-equipped supermarkets and shopping centers islandwide.

Dark Data

Below is an immoral statistics question that could serve as a “teaching moment” to warn both elementary and middle school (or upper primary and lower secondary) students against shoplifting and crime, especially when inflation around the world is at an all-time high.

The 2020–2022 estimated losses from the thefts of milk powder at retailers in Singapore are as follows:

2020: $18,000 (73 cases)

2021: $26,000 (96 cases)

2022: $27,000 (80 cases)

2023: $XY,000 (Z cases)

Based on past crime statistics, and in the light of a gloomy global economy that could bring about a financial apocalypse if the war in Ukraine dragged on, and should Mother Nature lose her patience with earthlings in spite of frequent natural calamities visiting the planet in recent years, predict the number of milk powder thefts and the accompanying monetary loss that would occur in the “fine” city of Singapore, in 2023.

How much revenue (or fines) could the authorities generate from these shoplifters-turned-resellers of milk powder (contaminated or not) in the coming decade?

Would there be a (higher) jail sentence for repeated offenders of infant formula? Or is caning in the pipeline for hardcore thieves? Or hundreds of community service hours for those unfit to be behind bars for whatever health or wealth reasons?

A Moral/Social Issue 

How many of these shoplifters genuinely couldn’t afford to feed their kids, especially when there is quasi-zero government assistance for the unemployed or underemployed, or for senior citizens with zero pension or savings in their “golden” years?

Do the shoplifters (and potential rioters) belong to some demographic groups that need the authorities to step in to avoid social disorders like public strikes and hate crimes perpetrated by racists-supremacists-turned-opportunists, which we’re witnessing in some right-wing political circles or red-pilled states?

From Profit to Profiteering

Like pharmaceutical companies that are notoriously known to overprice or overcharge their products, milk powder manufacturers don’t seem to be any morally different from them. Unless their dear milk powder came from holy cows or goats that have been anointed by Vatican-approved priests!

A Formula for an Equitable World

The social and political chaos plaguing many parts of the globe provides math educators worldwide an opportunity to step up and speak out against rogue politics and profiteering, poverty and inequality, and crime and robbery.

Some degree of equality or equity could come to pass via creative mathematical problem solving and active moral mindfulness on the part of math educators to help right some of the social ills, political hypocrisies, and business malpractices.

Remember: Low crime doesn’t mean no crime.

© Yan Kow Cheong, January 27, 2023.

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.

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.