Category Archives: Mathematical Humor

The lightest side of Singapore math with a slight dose of irreverence

The Joy of Swiftematics

Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Math, Theomatics, , , , , , , , , , , , , , , , , , , , , , , , , ,

Last July, millions across Asia competed for just 300,000 tickets to see Taylor Swift in the “fine” city of Singapore, which will host the only stop in Southeast Asia for the singer’s Eras Tour. Organizers said 22-plus million people registered for pre-sale tickets while online registrations passed the one million mark.

And last night, even pop singer Swift, who kicked off her six sold-out shows at the 55,000-seat National Stadium, couldn’t avoid creating some light-hearted political rift or jealousy among some ASEAN members.

Time magazine’s Person of the Year in 2023

Last month, after Thai Prime Minister Srettha Thavisin “complained” that Singapore had brokered a deal to “pay the pop star up to US$3 million for each of her six concerts—in exchange for keeping the shows exclusive to Singapore in Southeast Asia,” the Singapore Tourism Board admitted it “supported the event through a grant,” sans revealing its size or any conditions attached to it. Guesstimate the amount of grant that was given to stage these coveted events.

Even one unhappy politician from the Philippines said “this isn’t what good neighbors do” and called for his country to register its opposition with Singapore’s embassy. Go ahead, Mr. Joey Salceda.

Cartoon by Shannon Wheeler. #NewYorkerCartoons

Political instability, radical ideology that threatens violence to Western values, and poor infrastructure are oft-unspoken key factors for concert promoters to convince the pop superstar to give regional hubs like Bangkok, Manila, Kuala Lumpur, and Jakarta a miss as part of her “Eras Tour.”

Math in Pop Culture

With so much excitement (and concern from conservative or puritan parents) about Swift’s six-show tour in Singapore, how could math educators seize the opportunity to excite otherwise mathematically indifferent or apathetic students with some Swift-related math questions or activities?

For instance, what about coining some math or dismal science terms like Swiftematics and Swiftonomics to promote some creative problem posing?

A Singapore Math Definition of Swiftematics

Text © Anon.

Could the Boyfriend Make It on Time?

Posing real-life Swift-related math questions is only limited by our imagination. Below is a nontrivial question that was posted on Facebook, whose solution is anything but straightforward.

Posted by Judy Smith Hallett on “Maths Jokes Daily”

Swift’s Carbon Footprint

In 2022, Swift topped the list of celebrities with the highest private jet CO₂ emissions. If her jet pollution were about x times more than the average person’s total annual emissions, estimate x.

The next item is a Swift- or math-friendly question posted by news anchor Peter Busch.

A Math-Friendly Question for Swifties

The Numerology of Taylor Swift

Last month, after reading about Swift’s serial infatuation with her “lucky” number 13, I made an attempt to define Swiftie Math, which is based on the numerology (or pseudoscience) of Taylor Swift.

Since I’ve yet to receive any approval or rejection of the term—whether the editors see it fit for publication—I’d skip posting it online for now.

The Swift-Biden Conspiracy

Theomatically, MAGA evangelicals (or MAGA Xtians, where X ≠ Christ)—a subset of Christian nationalists—in red-pilled states haven’t failed to warn netizens about the “satanic” influences of Taylor Swift’s songs, but have hypocritically or selectively remained silent about the fraudulent, criminal, and sexual activities of their “political savior.”

Does Taylor Swift CAST SPELLS On Her Listeners?!

Conspiracies about the singer’s alleged support for President Biden have been rife in political and religious circles to paint Ms. Swift as an “ambassador of Satan,” who’s shown zero sign in supporting Trump and his cult.

Photo © 2024 CNN

Puritan Trumpublicans are hell-bent to warn millions of Swifties from unknowingly becoming witches lest they and their idol lose their souls, but, interestingly, hardly anything from these patriots calling for a nationwide corporate prayer for the soul of their beloved un-Christian ex-president.

Musically & mathematically yours

References

Taylor Swift named Time’s ‘Person of the Year’ https://www.cnn.com/2023/12/06/media/taylor-swift-time-person-of-the-year?cid=ios_app

‘Cruel Summer’ for Taylor Swift fans in Asia as Singapore shows sell out https://www.cnn.com/2023/07/14/business/taylor-swift-tour-singapore-asia-popularity-intl-hnk-dst

Taylor Swift’s journey from country icon to pop superstar https://www.cnn.com/2022/10/21/entertainment/gallery/taylor-swift/index.html

Does Taylor Swift CAST SPELLS On Her Listeners?! https://youtu.be/SDmzNDrj2NI?si=-gWMOb7CwsswytYV

© Yan Kow Cheong, March 3, 2024.

Thai Math

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Common sense has returned to Thailand, when the present government admitted before the Year of the Dragon ushered in that the recreational use of cannabis or marijuana is wrong, which was decriminalized in the kingdom in 2022.

Mr. Chonlanan Srikaew, Thai health minister, said that the government will soon be moving a new bill that will allow the drug to be used only for health and medicinal purposes.

Indeed, a big blow to hundreds of marijuana dispensary owners, and to millions of tourists who’re planning to visit the “Land of a Thousand Smiles” to get a kick out of marijuana.

And to a small extent, the ban will also affect recreational math educators who’ve started working on new and fertile questions that incorporate the legalized use of marijuana recreationally.

Should “Thailand math” questions be allowed in recreational math classrooms?

Marijuana Math

In an earlier post on “Marijuana Math” under “Math Word of the Day,” on LinkedIn, I poked fun that in tourism the “fine” city of Singapore would likely be losing out against Thailand. I mentioned tongue-in-cheek a few positives of Thailand being a “marijuana mecca” for adventurous or uninhibited tourists, especially those who come from conservative countries that criminalize the use of the drug recreationally.

With the new cannabis law in the pipeline, the number of tourists bypassing budget-unfriendly, family-friendly Singapore for wallet-friendly, pro-same-sex unions Thailand should be expected to be far lower than initially feared.

Math on a High

Let’s indulge in some recreational Thai Math questions, while there is some time to be on a high. The window of opportunity to enjoy these soon-to-be-banned word problems is closing in fast, unless the power-hungry military stages another coup to put in place a new pro-cannabis government.

1. A MAGA patriot, who recently visited Thailand, was caught with 24 cannabis candies and chewing gums in his locker at Mar-a-Lago. The fine is $80 for each candy, and $90 for each chewing gum. If the judge sentenced the culprit for a total of $2,010, how many candles and how many chewing gums were seized?

2. Which has the higher chance of occurring in the next quarter century: Singapore qualifying for the World Cup, or Singapore allowing tourists (but not locals and permanent residents) to use marijuana recreationally?

3. If the medicinal use of marijuana debatably proved to be a quasi-effective cure in treating math anxiety, mathophobia, or other mathematical disorders in a-not-too-distant future, would the “fine” city condone its use among its oft-self-professed semi-innumerate citizens?

Like the days of the legalization of recreational cannabis in Thailand, the days of the recreational use of Thai Math questions, too, look numbered.

Recreationally or restrictively yours

References

Thai government plans to ban recreational cannabis use http://tinyurl.com/mt6fhs2m

Number of young children who accidentally ate cannabis edibles jumped 1,375% in five years, study finds http://tinyurl.com/2mwb55d9

© Yan Kow Cheong, February 11, 2024.

Mathematical BS

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A math definition that has miraculously survived the attack of digital green terrorists.

Are you guilty of speaking (even mild) mathematical bullshit with your fellow math educators? How often do you use these BS phrases consciously or unconsciously to sound more educated or “mathematically civilized”?

If your math HOD talks about squaring the circle, thinking outside (or inside) the box (or cube), or going the extra (second) mile, do you really understand what the heck they’re talking about? Or are they just trying to impress or persuade their teachers to “walk their talk” (yes, another BS term); or worse, to cover up their shortcomings or confuse the new novice teachers?

What are the chances that they may to some degree be farting around some annoying and tiresome jargon to sound like a mathematical bore?

Of course, mathematical BS goes beyond language. Think of those sadistic statistics, data graphics, or infographics, which are often intended to mislead or confuse the audience. Misinformation, disinformation, and the Trump lies—you’re lured by them, because most are often music to the ear, especially if you love indulging in conspiracies, hoaxes, and white supremacist talks.

Context Matters

If a math teacher or educator talks about pushing the envelope, the chances that they may be legitimate are pretty high. If Pinocchios like Donald J. Trump, Boris Johnson, Vladimir V. Putin, and Kim Jong-un do, then it’s probably not—the odds are quasi-zero.

How to Be a Mathematical Bullshitter

How many of these phrases mostly convey empty words trying to sound smart?

always in beta
think outside the box
zero sum game
square the circle
make a 180° turn
the common denominator
360° appraisal
walk the talk
walk the walk
big picture
big ideas
blue sky thinking
pie in the sky
go the extra (second) mile
24/7 or 24/7/365
9 out of 10 agree
journal writing
push the envelope
back to square one
learning experiences
growth mindset
problem-based learning (PBL)
the new (new) normal
miss the forest for the trees
moral calculus

To Bull or Not to Bull?

Is spewing out mathematical BS a form of ineffective communication? A linguistic malpractice you’d try avoiding to reduce any chances of being misinterpreted?

Or do you like them because they make the speaker sound intelligent or educated, albeit their meanings or interpretations are often vague or even dangerous in some extreme cases or contexts?

In most cases, they arguably add spice to the conversation or impress the listeners, because most people who use them aren’t necessarily dishonest or evil-minded, unlike Trump and his gang of morally corrupt advisers and lawyers.

If BS can get Mr. Pinocchio into the White House or remove a country from the WHO, why not you? Your politicians, bosses, and pastors do it all the time (and probably you too), whether you want to admit it or not, so shouldn’t you do it as well since everyone else is guilty of it?

Until we meet again, know that my job isn’t to cure you from any honest or dishonest mathspeak. Why?* You can’t count on me to free you from a life of mathematical BS.

BS-freely yours

© Yan Kow Cheong, December 31, 2023

* The writer is currently undergoing weekly counselling sessions for excessively using BS or PC words in his formal and informal writing; he hopes (and also prays) that he’d find freedom from linguistic obfuscation in using only simple language that even his pets at home could understand him.

The Million Mistake Club

Humor, Mathematical Humor, Problem Solving, Recreational Math, Theomatics, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
Shot from Ed Rush’s “God Talks” (2023)

If we’ve been an employee rather than an entrepreneur or businessperson for most parts of our working life, most of us would probably not be eligible to join the Million Dollar Club.

Even for those of you who’re frequent flyers, the chances that you’d qualify for a Million Mile Club are probably not that high, too.

On the other hand, for an obscene number of us who’ve made at least a million mistakes, we’re likely to meet the criteria of becoming a member of the “Million Mistake Club.”

If you’re the lucky ones who’d never qualify for this notorious club, congratulations to you for living a life defined by manifold successes and few failures, either because you’re blessed with an Einstein brain (or born with a silver spoon in the mouth), or you’re simply averse to taking any risks (which would help reduce your failure rate).

An Age Problem

On average, guesstimate how young or old someone in most parts of the world would be by the time they make their millionth mistake. In their late 20s or early 30s? Go ahead and figure this out—it’s good for your left brain!

In TrumpLand (plagued by an unrighteous party and ruled by a self-righteous party), PutinLand (misruled by self-glory and orthodox church history), or XiLand (ruled by capitalist dictatorship and hostage diplomacy), what percentage of their politicians and prisoners (or even prosperity pastors) might have already joined the “Billion Mistake Club,” or are about to do so if they’d live beyond the three- or four-scores-and-ten lifespan?

A nation of aged oft-morally corrupt politicians and presidents

The Positives of a Million Mistake Club Member

Do you qualify as a member of the Million Mistake Club? If you’re a life member like me, what are the chances that you’d be a lot nicer to others by then?

Wouldn’t the world be a better rather than a bitter place if we celebrated members of the Million Mistake Club (instead of canceling or condemning them)?

Think of ex-convicts who’re now a free man or woman after paying for their mistakes. Or those who’ve been pardoned or released early for good behavior.

A screen shot stolen while attending a service

Why not uninhibitedly post on social media that you’ve joined the Million Mistake Club, and as a result your friends, fans, and followers could positively expect a different you—someone who’s less critical or condemning.

A new you who’s more understanding, forgiving and gracious, and less on comparing, competing, and complaining.

Of course, it’s easier preached than practiced, but nevertheless embarking on a life of contentment and consensus is the beginning of a life journey that would bear much fruit now and in future.

Remember: Your past doesn’t define you. What counts in the end: It’s not so much how you start, but how you finish.

Freely & truly yours

© Yan Kow Cheong, October 24, 2023.

Professor Calculus and Tintinology

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Remembering Prof. Calculus’s Inventions & Innovations

Meet Professor Cuthbert Calculus, a polymath—a geeky jack of all trades—who was at home in many disciplines ranging from astronautics and astrophysics to geometry and geodetics to mathematics and thermodynamics.

The beloved clumsy and eccentric professor, or the absent-minded mad scientist par excellence, applied his mathematical and scientific knowledge to launch his futuristic inventions and innovations.

A Tribute to Calculus

To celebrate Professor Calculus, who first appeared 80 years ago in Hergé’s 12th Tintin book, Red Rackham’s Treasure (1943), the recently published Professor Calculus: Science’s Forgotten Genius (2023) by Albert Algoud—the original French edition first came out in 1994—paid a funny tribute to one of the most endearing scientific geniuses in children’s literature.

Algoud’s English edition takes a voyeuristic look at Prof. Calculus’s achievements and the real-life innovations and people that inspired one of Hergé’s most popular characters. Think of Isaac Newton, Gottfried Wilhelm Leibniz, Auguste Piccard, Thomas Edison, Alexander Graham Bell, and Konstantin Tsiolkovsky.

Over the course of 54 years, Hergé (Georges Remi) who’s born in Brussels in 1907, completed over 20 titles in The Adventures of Tintin series, which is now considered to be one of the greatest, if not the greatest, comics series of all time.

The Harry Potter Series of Yesteryear

More than 230 million copies of Tintin’s series have been sold, which proves that comic books have the same power to entertain children and adults in the 21st century as they did in the early 20th.

Tintin’s Series for Girls

Moons ago, when my daughters were in elementary or middle school, I introduced them to some Tintin’s titles. To my surprise, they’d quasi-zero interest in Tintin & Milou’s (or Snowy’s) stories, because they couldn’t relate to the male or chauvinistic, not to say, colonialist, characters.

Flipping through the pages, and taking a deeper look at Hergé’s characters, I realized that the girls weren’t wrong. The number of pages in each book depicting female characters is probably fewer than the fingers in a hand.

It’s no surprise that Hergé had been accused of sexism for the almost complete lack of female characters in his “boys books.” In fact, few people would disagree today that most (white) men from that era were racist, sexist, and misogynist.

Hergé himself denied being a misogynist, saying that “for me, women have nothing to do in a world like Tintin’s, which is the realm of male friendship.”

Tintin’s Gender

On a lighter note, Tintin himself has been labeled as being strongly feminized, especially in relation to Captain Haddock, with the hypothesis that he’s of virtually indeterminate gender.

More than half a dozen years ago, French philosopher Vincent Cespede made the headlines when he claimed that Tintin is “an androgynous redhead with blue eyes” and “presumably asexual.”

A Christmas Gift for Boys (and Girls?)

If you’ve a teenage son, grandson, or nephew, I think giving away a few Tintin’s titles would be an apt Christmas gift for them; however, for a daughter, granddaughter, or goddaughter, you’d probably want to think twice or thrice before prematurely exposing them to any of Hergé’s predominantly male white characters.

In today’s politicians’ slogan of inclusiveness or political correctness, I wonder whether The Adventures of Tintin series might even be banned in some feminist or woke circles. After all, if we recall that the Harry Potter series was not only banned from some school’s library after educators consulted with exorcists in the US and Rome, but also in some conservative Christian and radical Islamist circles.

The same could also be said for math classics like Edwin Abbott Abbott’s Flatland (1884), which directly or indirectly exposes social classes and white supremacy. Or titles like George Orwell’s 1984 that was banned in both Soviet Union and China.

The Calculus Affair

Tintin’s puzzle: How to rescue Prof. Calculus who’s in danger.

In The Calculus Affair, Tintin witnessed some very strange events like the simultaneous shattering of windows, mirrors, and chandeliers, leaving him bewildered. After a shooting and a break-in, Tintin knew Prof. Calculus was in danger, but he had only one clue—an unusual packet of cigarettes.

Could he solve the mystery before a terrible weapon fell into the wrong hands? Could he act in time to protect Professor Calculus?

Calculus’s brain. Fr: Albert Algoud’s Professor Calculus: Science’s Forgotten Genius (2023)

The Adventures of Tintin Series

If you’re a Tintin fan old and new, especially a lover of graphic novels, mysteries, and historical adventures, how many of the 20-odd titles of Hergé’s The Adventures of Tintin series have you read?

What’s your favorite Tintin’s title?

Tintin in the Land of the Soviets Aimed at communicating an anti-communist sentiment to the young reader? Banned in Ukraine?

Tintin in America Placed in a restricted access section of the Jones Library in Amherst, MA in 2014 for its “racist imagery.”

Cigars of the Pharaoh

The Blue Lotus Would Japanese nationalists call for its ban?

The Broken Ear

The Black Island

King Ottakar’s Sceptre

The Crab with the Golden Claws

The Shooting Star

The Secret of the Unicorn

Red Rackham’s Treasure First printed 80 years ago.

The Seven Crystal Balls

Prisoners of the Sun

Land of Black Gold

Destination Moon

Explorers of the Moon

The Calculus Affair A mathematician’s favorite?

The Red Sea Sharks

Tintin in Tibet Praised by the Dalai Lama, who awarded it the Light of Truth Award. Banned in China?

The Castafiore Emerald

Flight 714 to Sydney

The Adventures of Tintin and the Picaros

Tintin and Alph-Art

Tintin in the Congo The racist content: colonial attitude vis-à-vis Congolese people and for glorifying big-game hunting.

In my childhood days, I read most of Tintin’s titles in its original French, which is probably the language of choice to reading them, especially for those who’re bilingual, trilingual, or multilingual. I hope to reread the series in another language in my golden years.

Adventuresomely yours

© Yan Kow Cheong, October 8, 2023.

Formula One Singapore: Blessing or Curse?

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Since 2008, except in 2020 and 2021, when the night race was cancelled due to Covid-19, Singapore Grand Prix has had its highs and lows.

Most locals would hardly shed a crocodile tear should the three-day noise-pollution event cease to be held in the “fine” city in future, albeit a record 302,000 “fans” turned up for the 2022 F1 Singapore GP.

In 2019, when the hazy event venue was at an unhealthy level, race organizers were giving away thousands of free F1 tickets to beef up the number of attendees for the F1 night race to avoid the sight of empty seats. Who says that begging and betting are mutually exclusive?

The environmentally unfriendly event appeals mostly to diehard F1 fans, as F1 fatigue had already set in among locals who’d attended a few more canned events after 2008.

The Singapore F1 night race looks more like a curse than a blessing for a segment of the population, especially retail shop and restaurant owners (with cancelled meal orders and table reservations), and service providers (few gym or tuition classes, haircuts, etc.) in the Marina Bay area.

Some of them have their sales dwindled this week due to customers’ difficulties of navigating around road closures, or the latter’s decision to give their venue of choice a miss to avoid any inconvenience.

And religious services and recreational activities in the area had to be cancelled as a result of noise pollution from this weekend event. Even the holy souls or health freaks, who need to be in the vicinity, rain or shine, pollution or not, would have to find alternative parking space to attend to their weekly rituals.

A Hell of a Race

Deemed the “most difficult race of the year,” Singapore’s Marina Bay circuit is notorious for its plethora of 90-degree corners along the 23-turn lap. And F1 drivers’ annual complaining mantra is the sauna- or oven-like conditions of warm and sweaty Singapore.

God in the Wheels—F1 Goes Spiritual

Pray for the F1 Singapore Grand Prix

In the aftermath of F1 race organizers seeking protection from God, gods, or goddesses, back in 2016, I’d irreverently coined “F1 Blessing”:

F1 Blessing: When religious leaders from various faiths come together annually to pray for the Singapore Grand Prix and to bless the Formula One night race.

Example: The public has no idea whether the F1 blessing requires the holy men to go through a list of prayer items; if not, what exactly are they praying about?—safety of drivers? good sale of tickets? no crazy spectators crossing the racing track when the race is on? God knows!

by MathPlus September 09, 2016

F1 Prayers

Let’s pray these three F1 prayers for 2023:

1. Pray that few diehard (or better still, zero) fans at the Singapore Grand Prix would be infected with Pirola, the newly recognized variant of Omicron (Covid-19 virus strain BA.2.86), and that no foreign spectators would bring any WHO-undetected variants into the local community.

2. In past events, we’d had unexpected guests like lizards and snakes at the Formula One Singapore event. Pray that no reptiles, giant hornets, or extraterrestrials would show up on Sunday.

3. Pray that all corrupt men and women, be they billionaires, ministers-millionaires, or organizers, who’re behind the “success” of the F1 Singapore Grand Prix, would be exposed, fined, and imprisoned for their illicit financial gains.

F1 Math

A math quickie on Singapore’s “Highest Noise Pollution Day”: Local drivers have so far failed to make the grade at the Singapore GP. Which is more likely: A Singaporean F1 driver making it to the top ten, or Singapore getting into the World Cup final?

Prayerfully and environmentally yours

© Yan Kow Cheong, September 17, 2023.

The Clock Problem

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On July 12, @PicturesFoIder x-ed (or tweeted) the following picture:

Picture © Anon.

Is this another ill-posed math question? Or just another arguably creative solution that put the teacher or tutor in a catch-22 response?

Let’s look at a sample of comments for and against the given answer.

They don’t want a digital clock!
This is the correct answer for anyone that is somehow confused! 🤔

Teacher needed to say clock with hour and minute hands.

The question says “small clock”, not “analog clock”, therefore the answer is correct.

This is everything what’s wrong with current educational system.
It sure does prepare you.
To think in the frameworks they want you to think. For example “there is only one right solution to a problem and that ain’t it”

thats what happens when you let kids use ipads at a young age

This student should be transferred to art school immediately

On one hand I’m scared that the new generation can’t read physical clocks, on the other hand, I’m surprised by the out of the box thinking

If my child received a X for that answer, I would challenge it. There is nothing at all wrong. It is a small clock showing ten past eleven. 100% accurate. IF they wanted a conventional clock face that should have been stated. I’d have given 2 ticks for innovative thinking!

The question doesn’t specify that it meant “analog clock” plus it says “10 minutes past 11:00” which implies digital time as opposed to “10 minutes past 11 o’clock” which would imply analog time.

I would have drawn an analog and digital clock with a note saying the request was ambiguous and next time be more specific. Also how small? Another ambiguous request

How many of these responses would you agree or disagree with? Valid or invalid, or preposterous in some instances, most of these comments can’t be discounted offhand.

Followers or Oddballs?

At a time when politicians, pastors, or even prisoners are often hypocritically or insincerely pushing for an overhaul of their rigid educational system (from which they themselves benefited much)—which promotes rote learning or regurgitation, or prepares students to the test—are math teachers ready for students’ unconventional or disruptive solutions, which often border on the ridiculous or irreverent?

If a child (or a trained chimpanzee) presented the solution below to the above problem, what would your response or reaction be?

Picture © Anon.

Would you mark it wrong or partially correct, because he or she had failed to take account that time on a clock is determined by the hour hand alone, with the minute hand acting as a mere convenience? Or in layman terms, the hour hand had also moved when the minute hand took a sixty-degree turn.

Or would you take this opportunity to introduce nonroutine (or more subtle faux) questions like the ones below?

1. What is the angle measure between the hands of a clock at 10 minutes past 11:00?

2. A clock reads ten minutes past eleven. What time would the clock read if the hands of the clock were interchanged?

3. Are there other times of the day when the hands of a clock would also show the same angle measure as when they were at 11:10?

The Positives of Ill-Posed Questions

An ill-posed question, or the unexpected answers to such a flawed question, is a gold mine for creative mathematical problem posing. It not only provides an off-the-wall sense of humor, but also gives math educators an opportunity to address students’ mathematical loopholes or their half-baked understanding of concepts.

Positively & creatively yours

© Yan Kow Cheong, August 13, 2023.

Calculus for Mature Students

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Math Meme from Math Lady Hazel

Like math, calculus needn’t sulk (to any degree)! In the hands of an excited middle-school or high-school math teacher, or with access to some creatively written (or online free) resources, the ABCs of calculus can even be taught to elementary school kids.

Think of Mr. Jaime Escalante who had successfully taught calculus to cohorts of Mexican-American students. There is zero excuse why we can’t emulate him to teaching it to financially disadvantaged or minority groups.

What’s Calculus to You?

Do you parrot the textbook definition of calculus to your students? The mathematics of (instantaneous) change. Or do you share it as the branch of mathematics that measures “how far an object has been going fast,” and “how fast an object has gone far”?

Moons ago, I cheekily approached or indirectly defined calculus via the division of zero as follows:

0 ÷ 0: The Raison d’être of Calculus

With some dose of irreverence, the bête noire of high-school or college math could turn out to be a much beloved topic even among the so-called innumerates or mathematically challenged.

Calculus for the Numerati

It’s debatably said that without an exposure of some delta-epsilon calculus, no man or woman can honestly claim to be “mathematically educated” or “mathematically civilized.” Sounds like mathematical pride or arrogance, isn’t it?

Or just an example of “mathematical elitism” à la Trump for those fakes who declare themselves as being a “very stable genius.” Even Einstein had remarked that calculus was “the greatest advance in thought that a single individual was ever privileged to make.”

Fr: Ryan Truong on Facebook’s “Mathematical Mathematics Memes”

Recently, while working on the Urban Calculus manuscript, I forced myself to reread some of the out-of-print pop calculus titles like David Berlinski’s A Tour of the Calculus, Steven Strogatz’s The Calculus of Friendship, and Mary Stopes-Roe’s Mathematics with Love to get an intuitive feel of the subject again.

For a long time, the thought of taking up the challenge to read Newton’s The Principia (even its annotated version) frightens me, because the complexity of the content is beyond me. I’ve a good excuse not to borrow the thick copy from the university library unless I want to look like a “mathematical snob” carrying it around, or use it as a temporary doorstop.

When Comics and Calculus Converge

Calculus for All

Let’s play our part in sharing the mathematical gospel of Newton and Leibniz that calculus needn’t be a four-letter word—how these two mathematical greats had exorcized the demon out of the division of zero.

Why not strive to be the “James Escalante” of your school, state, or country? You’d be the changemaker or mathematical savior in motivating some undecided or mature students to read a calculus course or module in college?

Differentially and integrally yours

© Yan Kow Cheong, July 30, 2023.

A Question on Inequality

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Fr: Ralph McConahy on Facebook

Many years ago, I read about the co-authors of a handbook for mathematics teachers in primary schools warning readers not to use the sign “<” or “>” (because the symbols were removed from the primary school syllabus); instead, they suggested using phrases like “more than” and “less than.”

For example, teachers were to avoid setting questions in these formats:

34 is 6 > ☐
8 > 43 is ☐

Instead, they’d rephrase them as “34 is 6 more than ☐.” and “8 more than 43 is ☐.”

Similarly, they’d refrain from posing inequalities questions such as the following:

7 < ☐ is 15.
9 < 25 is ☐.

And also avoid problem sums like the one below:

What is the largest (or greatest) whole number that can be placed in the box to make the statement true? 8 + ☐ < 40

Why the Ban (with or without a Fine)?

Based on teachers’ feedback that young (or even older) schoolchildren are often confused about the similarity of the two symbols < and >, that’s likely a key why that prompted local curriculum math specialists in the “fine” city to ban these “unequal symbols” in primary school mathematics moons ago.

Inequality Metaphors from the Sunshine State

Over the years, to reduce the confusion between < and >, some elementary math authors have come up with some witty ways to help schoolchildren remember which is which.

For instance, students are often taught to see the symbols as hungry alligators or crocodiles with gaping mouths—these reptiles always want to eat the larger numbers, so the open mouth will always face this.

Observe that the < looks somewhat like a lopsided L, which reminds us that it denotes less than. Or, in any true statement, the large open mouth of the symbol is on the side of the greater quantity, and the small point is on the side of the lesser quantity.

No More Ban

Like last year’s repeal of Section 377A in pseudo-puritan Singapore, based on the CPDD’s Primary Mathematics Textbook 2A (2022), the inequality signs too are now free to roam the pages of any MOE-approved primary 2–6 textbooks and workbooks.

In the aftermath of zero ban on inequality signs, questions that involve comparing and ordering numbers would no longer be symbolically penalized or criminalized for using the “>” and “<” signs (until further notice).

Below are a sample of three “uninhibited” Singapore math primary two inequality questions:

Which sign will you use, > or <?
(a) 45 ☐ 42
(b) 81 ☐ 71
(c) 317 ☐ 407
(d) 734 ☐ 724

Fill in the boxes with ‘<’ or ‘>’.
(a) 35 ☐ 53
(b) 65 ☐ 62
(c) 79 ☐ 68

It’s not uncommon to see once-banned open-ended questions now gracing the pages of primary math textbooks, such as the following:

In 38 > 33 + ☐, what could the missing number be?

It looks like we’ve come some way in restoring the inequality signs in the (lower) primary school syllabus. Now that the mathematical resurrection of these symbols has taken place, does their confusion among schoolchildren still remain a concern for both teachers and parents?

An Inequality Quiz

Let’s end with a math quiz that tests our basic knowledge of inequalities.

1. How many types of inequalities in elementary school math are there?

2. Which metaphor(s) would you use to help children who are prone to mistake one inequality sign for another?

3. Name half a dozen math inequalities in real life that schoolchildren could relate to.

4. “An inequality is an equation that forbids the use of an equal sign.” True or False.

Symbolically yours

© Yan Kow Cheong, July 9, 2023.

Singapore’s PSLE Math Paper

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There is an educational (or psychological or emotional) price a country has to pay if it wants its students to continually rank among the top three in international comparative studies like TIMSS and PISA, or in regional or international math contests and competitions.

An irreverent definition of Singapore’s most dreaded school exam paper

Understandably, parents in Singapore are unhappy about the difficult PSLE (grade 6) math questions that are used to assess their children, before they’d graduate from primary (grades 1–6) school to secondary (middle) school.

And the oft-politically correct or modeled answers from the city-state’s Ministry of Education (MOE) hardly ever pacify or satisfy teachers, parents, and caregivers; in most cases, the canned suggestions or quasi-laughable solutions only make them angrier or more cynical.

PC Slogans for Kiasu Parents

Be it the mantra that “every (local) school is a good school,” or that parents need to help or educate their children believe that “their self-worth or value isn’t dependent on their exam grades” is easier preached than practiced.

When politicians or MOE officials preach to parents that they needn’t be paranoid about their children’s PSLE exam or math score, because it’s not the end of the world, it’s like ex-loansharks-turned-philanthropists or ethically challenged ex-CEOs- or ex-bankers-turned-preachers now telling the financially struggling public that money isn’t everything, or that they’d not make money their god. For the haves to tell the have-nots, it’s utter hypocrisy, to say the least.

Answers and oft-ill-edited half-baked solutions are usually from tutors or teachers-moonlighters.

Tuition: A Necessary Evil for the Nation

Without compulsory tuition or heavy parental involvement, the majority of elementary math students in local schools would likely struggle to score a decent grade in their PSLE math paper.

Singapore’s PSLE math paper with its quota of brain-unfriendly questions looks like a necessary evil that would help define or maintain the “fine” city’s high standard of mathematics regionally and internationally.

From Mid-Year to Mock Exams

This year, Primary 6 students didn’t have to sit for mid-year exams at school, because last year, Education Minister Chan Chun Sing had said that the move would allow them to “focus more on their learning and less on marks.”

In the aftermath of the MOE’s move to do away with all mid-year exams for primary and secondary schools, tuition centers saw a golden opportunity to lure kiasu parents with their mock mid-year exams, whose questions are generally harder (not better) than those set in the PSLE math paper.

Other than parental or peer pressure to excel, most students’ undue stress could be traced to the difficulty of math questions set by neighborhood schools (driven by school rankings) and tuition centers (powered by profits), which are generally harder than those that appear in the PSLE math paper. Yes, they’re the two big culprits that set an unhealthy number of nonroutine questions that often demoralize the kids, by making them feel like they still “aren’t that good in math.”

A Promised Land for Geeks—and Tax Fugitives

Singapore is a “promised land” for those who’re born or blessed with the “mathematical gene” or for those who’d afford a private tutor. However, for the majority of average or math-anxious school children, we can only pray that PSLE math wouldn’t become their bête noire, and that God would keep them motivated and focused as they go through this oft-stressful rite of passage of their schooling years.

I might sound like a mathocrite (short for “mathematical hypocrite”) in giving mathematical or parental advice; nevertheless, let me end with this educational slogan that is worth reiterating, because I believe that the sooner we put it into practice, the less stressful (or peaceful) our life will be: Our math scores or grades don’t define us—in or out of school, and certainly not in life.

Grade-consciouslessly yours

© Yan Kow Cheong, June 18, 2023.