Category Archives: Mathematical Humor

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

Calculus for Mature Students

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:

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.

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

A Question on Inequality

July 9, 2023Humor, Mathematical Humor, Problem Solving, Singapore Mathcomparing numbers, decimals, equality, equals sign, equation, greater than, inequality, inequality signs, less than, math metaphor, math symbols, math textbook, problem sum, symbolismKow-Cheong Yan

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

Singapore’s PSLE Math Paper

June 11, 2023Mathematical Humor, Problem Solving, Singapore Math, Theomaticsassessment, coaching, education, homeschooling, math anxiety, math competition, math contest, math exam, mathophobia, mid-year exam, mock exam, parenting, peer pressure, PISA, PSLE Math, PSLE math paper, school ranking, self-esteem, stress, tiger parents, TIMSS, tuition, tuition centerKow-Cheong Yan

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

What’s Your Life PhD?

March 25, 2023Humor, Mathematical Humor, Recreational Math, Singapore Math, Theomaticsacademia, Bible, consultant, Covid-19, deliverance, disciples, eternal destiny, fishers of men, healing, Ivory Tower, parody, PhD, Political Math, politics, praying, preaching, salvation, Song of Solomon, Song of SongsKow-Cheong Yan

For the majority of people around the world without a PhD, the academic title is often creatively or cynically assigned a different meaning. Talking of poking fun at those who make a living in an ivory tower—the image of an “ivory tower” is used in the Bible in the Song of Songs (7:4) to describe a woman’s purity—the lay public’s general impression or perception of most PhDs is often anything but positive. Could this be due to some subconscious “intellectual envy”?

Maybe because when they think of academics becoming politicians or of them serving as consultants or advisors for an oft-inept or corrupt government (or of an educational consultant for a publishing house hoping to boost their school adoption rate), many have mixed feelings about these exam-smart folks, who are mostly “un-street-smart,” when it comes to solving everyday life or real-world problems for their fellow citizens—their oft-halfwitted decisions often serve as a living proof of their (practical) unintelligence rather than their intelligence.

PhDs to Save the Planet from Covid-19

Below are three entries I submitted during the lockdown two-odd years ago.

Was Cummings, ex-PM Johnson’s “corona jerk”?

One rule for the Cummings and
one for the common people.

Be it the canned “Permanent Head Damage” or “Post Holiday Depression,” new meanings associated with the acronym are only limited by our imagination.

Boosted Jabs at PhDs

A few years ago, I started relooking at new meanings of a PhD. Two such revised definitions were:

What’s your life’s PhD, especially when you respectfully compare yourself with those with big titles, most of whom often have infinitesimally positive or quasi-zero impact on those around them?

Meanwhile, why not pray, help, and do rather than just preach, hope, and delay?

A North Korea without the Kims

March 4, 2023Humor, Mathematical Humor, Recreational Math, Singapore Mathannexation, Caliphate, Crimea, Dictatorship, Ignoble Peace Prize, ISIS, Islamism, Kim Dynasty, Kim Jong Un, math, Missile, Nobel Peace Prize, North Korea, parody, politics, Putin, reunification, Russia, Singapore, terrorism, Trump, Ukraine, unholy trinity, warKow-Cheong Yan

Way back in 2017, when ISIS or radical Islamist ideologies were making inroads in a number of developing or war-torn countries, and North Korea then looked like the safest place on the planet from green terrorism, I coined North Korea as follows:

North Korea: Where jihadists daren’t go in trying to Islamize infidels unless they don’t mind going to hell sooner than later to meet up with ex-dictators Kim Jong Il and Kim Il Sung.

ISIS or the Taliban is no match for Dictator Kim Jong Un’s trained killers, if these Mohammedan jihadists dream of going to North Korea to set up their Caliphate.

by MathPlus May 31, 2017

The Kim Dynasty

The Kim dynasty is “like grandfather, like father, like son.” Would the world witness a gender change at the top, if a sister (and subsequently a daughter, legitimate or not) were to be reluctantly appointed, thus breaking the decades-long patriarchal political order? A modern-day Jezebel in waiting!

North Korea & Math Education

Imagine if North Korean students were to take part in TIMSS and PISA, what are the chances that they would outrank or outwit their Singaporean or mainland Chinese counterparts in both math and science?

Or, if you needed a part-time or freelance value-for-money coder (or licenced hacker), would you choose one from Singapore, India, or North Korea? The choice is pretty clear, isn’t it?

Dark Political Math

After Comrade Kim’s last heartbeat, what are the odds that the two Koreas might be reunited as one? Or would this reunification happen earlier, say, if the hermit nation was forced to surrender following a series of bombings on Pyongyang or on its nuclear sites by the Allies?

Broken Bromance Blossomed

Imagine that Donald J. Trump is miraculously re-elected in 2024, and the Trump-Kim lukewarm bromance is rekindled with a flurry of more “love letters.”

*Reel* Leaders Nominated for Nobel Peace Prize

What are the odds that they’d eventually have a tête-à-tête at the White House? A post-pandemic reunion between two vainglorious rogues that could help raise their chances of being nominated for the Nobel Peace Prize for the nth time, as their actions (or inactions) arguably prevented a WW3!

The Peacefakers Sans Clothes

What if fearing that he’d end up on the wrong side of eternity, and also be remembered as a modern-day Hitler or Stalin, comrade Putin decided to return the annexed lands, including Crimea, to Ukraine? Would the world witness a peace prize being shared by the unholy Kim-Putin-Trump trio? Or would all three be re-nominated for the Ignoble Peace Prize instead?

The *Leadershit* Series for Rogue *Leaders*

Fake Missile for Anti-NATO*

Would the US and allies (yes-nations) only stop playing the more-sanctions game when Kim Jong-un’s patience ran out—when he decided to launch a “fake” missile targeting one of its neighbours, which would force them to take the rogue nation seriously or to treat the Kim dynasty with respect or reverence?

Peacefully & prayerfully yours

* NATO = No Action, Talk Only

Numbers vs. Letters

February 11, 2023Mathematical Humor, Problem Solving, Recreational Math, Singapore Mathalphabet, brain, language, learning, letters, lingua franca, literacy, math, memorizing, memory, mother tongue, neuroscience, numbers, numeracy, recall, recitationKow-Cheong Yan

A while ago, I tweeted the following math or language or brain question, hoping for a layman answer from math educators or linguists or brain specialists, who might offer a quick-and-dirty explanation to that puzzle.

Another nontrivial question is: “For a number of us who’d no choice but to learn or master a few languages or dialects to survive, why do we feel at home decades later still vocalizing or reciting numbers in the (foreign) language we used while we’re growing up rather than in our mother tongue or lingua franca?”

Personally, I find it easier to recite or utter a sequence of consecutive numbers, or to work with mathematical symbols, in French rather than in English or Chinese—or in my Hakka dialect. I find it puzzling because French has now been relegated to my third or fourth language, and I hardly ever use it in my daily communication, or in any tête-à-tête meetings, other than occasionally dropping some French jargon in my writing to appear like a faux Francophone.

Although today English is my second language and lingua franca, French remains my language of choice when it comes to self-talking (or maybe even daydreaming or dreaming) in numbers or numerals.

It looks like if we learn numbers and symbols in a certain language or dialect in our formative years, we’re brainwired to recall or recite numbers in that particular language later in our adult life. This occurs especially when we’re on our own, even though we may be equally versed or quasi-fluent in other languages or dialects.

Like cycling, driving, or swimming, it appears that reciting numbers in the language of our childhood days in later years is something that stays with us for life.

When self-talking about numbers, do the majority of you who’re forced to be bilingual, trilingual, or multilingual to survive (or thrive) in school and in the workplace also share my experience? Sounds like it’s a neuro rather than a numero question we’re trying to address here!

Linguistically yours

Lunar New Year

February 5, 2023Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Mathastrology, calendar, Chinese, Chinese New Year, dragon, fertility rate, hongbao, horror-scope, luck, Lunar New Year, math, money, mythology, pattern, prosperity, puzzle, rabbit, Singapore, Singapore math, superstition, traditionKow-Cheong Yan

Today is the last day of the annual 15-day Chinese New Year (or Lunar New Year) festival in China and Chinese communities around the world.

The Lunar New Year is so-called because the dates of celebration follow the phases of the moon—the new moon could fall on dates between January 21 and February 20, which is similar to Easter that could take place between March 22 and April 25.

Due to its “movable” date, the Lunar New Year (which is unspokenly steeped in superstition and divination, but unquestionably or expectantly celebrated by a billion-odd mainland Chinese and the forty-plus million faithfuls in the Chinese diaspora as part of Chinese tradition) serves as a rich recreational math or calendrical activity for teachers or educators worldwide.

In the Year of the Ox (or “Covidox”), which ushered in a palindromic date (12/02/2021), I pondered: “Any sexy formula that tells us when the Chinese New Year falls in a given year? Not calendrical recipes meant for symbol-minded geeks, but one for the majority of us, the simple-minded folks who’d key in the year and out come the CNY date & day of the week.”

With superstitious couples unfairly or irrationally treating baby tigers and bulls as “inauspicious,” but don’t mind baby bunnies, could supposedly conservative or puritan “fine” Singapore with a frightening low fertility rate of 1.2—below its replacement rate of 2.1, which could see its population heading the way of the dodo sans selective immigration and baby bonus cash incentives—expect a mini-baby boom in the Year of the Rabbit?

With few Covid restrictions still in place, would Singaporeans and permanent residents (and tax fugitives fearing political persecution or prison) be more excited this year to play their part in producing an above-average number of newborns-bunnies? And with Valentine’s Day around the corner, could the nation expect an overbooking of hospital beds or single wards in November?

I completely forgot that I wrote A Dozen Numerical Deeds for the Chinese New Year eight [sounds like a numerologically Sino-auspicious number?] years ago. If you want to keep the spirit of giving alive in the new bunny year, help yourself with some of the suggested gifts to bless others, Chinese and non-Chinese.

Generously yours

Math Word of the Day: Formula Feeding

January 28, 2023Humor, Mathematical Humor, Recreational Mathbaby, bonding, breastfeeding, cancer, cow milk, father bonding time, formula, formula feeding, goat milk, heath, infant, math, milk, milk allergy, milk powder, mother’s milk, parenting, shared parenting responsibilities, Singapore, skim milk, zero fatKow-Cheong Yan

On May 26, 2021, I hypocritically posed the following:

Family Math: The positives and negatives of formula feeding vis-à-vis breastfeeding. How to get millions of fathers involved in parenting, while giving the mother a break if formula feeding isn’t an option.

Below are three tweets, two of which are more than a decade old.

Got 🥛 : 🐄 or 🐐?

Lactose intolerant? Allergic to cow milk? Nature “next best thing to mother’s milk”: Singapore’s Goat Milk vine.co/v/i7OiHuQW62K (@MathPlus on 12/6/15)

Zero Fat ≠ No Fat

Beware of labels: Zero fat, no-fat (skim milk) contains 0.4 grams of fat per cup (or 86 calories per cup). A “zero lie”! #zero (@Zero_Math on 1/7/11)

Meeting & Milking the Cow!

You don’t get milk from a cow by sending a letter, or by calling on the phone. You get milk from a cow by sitting by its side & milking it. (@MathPlus on 12/2/12)

You may also be interested in Crime Watch and Crime Math, which is related to infant formula or powder milk.

Dutifully & responsibly yours

Pi versus WHO

January 17, 2023Humor, Mathematical Humor, Singapore MathChina, Covid-19, Greek numerals, humor, lawsuit, libel, math, mutant, pi, Pi Approximation Day, Pi Day, politics, recognition, Singapore, Singapore math, variant, WHO, XiKow-Cheong Yan

Pi recently took a page from Singapore’s only ruling party’s decades-long successful template how to stay in power perpetually, with quasi-zero public protests, strikes, and riots.

Will Pi win her viral legal case against the World Health Organization (WHO)? Millions of math teachers worldwide are unspokenly hoping that the WHO won’t alienate or betray Pi, just as it did for the marginalized and unrecognized variant Xi.

Would Pi be vindicated for unfairly being discriminated by those who’re playing politics to prevent her from being admitted as a bona-fide corona variant worthy of WHO’s recognition?

Imagine how excited math educators globally would be if Pi won her legal case against the WHO.

Come Pi Day or Pi Approximation Day, if the 16th letter of the Greek alphabet were officially declared a WHO-approved variant by then, schools and universities would be electrified in conducting an eclectic mix of pi talks and lectures to promote Pi’s ambivalent “murderous” new status.

I, for one, have started to work on Murderous Pi—the title of a math e-book to celebrate Pi’s evolution from a humble mathematical constant to a proud corona variant, which would be plagued with devilish or wicked problems on mathematics’s most beloved irrational number.

Are you looking forward for Pi’s long-overdue recognition by WHO’s health professionals in the Lunar New Year of the Rabbit?

Until she’s virally credited for her fatally mixed impact on earthlings before she’d rest in peace to make way for Rho and Sigma, who’re lining up to be WHO-recognized, Pi’s rejection would be perceived as an irrational [mathematical & viral] injustice or betrayal, whose aftermath paranoiac behaviors among math educators and virologists worldwide could potentially be unpeaceful, to say the least.

Like the “infidel” Zero, who’s ostracized by the Church Fathers of yesteryear, may the “agnostic” or “devilish” Pi be vindicated as she longs to gain formal approval to be in the company of fellow corona variants.

Math Word of the Day: Mathemachicken

June 28, 2022Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Mathban, chicken, egg, humor, inflation, kampong chicken, Malaysia, math, mathophobia, organic chicken, philosophy, problem solving, profiteering, Singapore, Ukraine, warKow-Cheong Yan

I can’t recall what prompted me to coin “mathemachicken” three-odd years ago. Was it the aftermath of setting or solving an unhealthy number of word problems on chickens or eggs, or both?

Not too long ago, in Organic Chicken Rice for the Rich, I hatched up a meme and offered some math questions on organic and kampong chickens. https://bit.ly/3y1fXvL

Early this month, the world read about Malaysia’s decision to ban the export of chickens (but not eggs) to its frenemy neighbor Singapore. In fact, even before the ban, the prices of chicken eggs were already skyrocketing in supermarkets, which sounds more like a case of synchronized profiteering strategies among exporters, distributors, and supermarkets than anything else, but after some Opposition members had denounced the unjustified inflated prices, things have since stabilized more or less.

Ukrainian Eggs 4 Singapore

During Singapore’s “circuit breaker”—a PC term for “lockdown”—we’re blessed with white eggs flown from Ukraine. I recall that some supermarkets had promotions like “Buy One, Get One Free” or “Buy Two, Get One Free” to lure locals to try Ukrainian eggs. Since the war, the import of these bigger and cheaper eggs seems to have come to a halt.

Probably no animal is more popular than the chicken in math word problems—even the beloved bunny comes a distant second. Be it the use of their heads, eyes, legs, or eggs, the chicken remains the animal of choice among mathematical problem posers.

Tens of thousands of brain-friendly and unfriendly math questions on chickens and eggs around the world make their way into canned and creative math textbooks every year, which makes millions of math-anxious students worldwide to “chicken out” to avoid being given all kinds of labels by peers and parents for their oft-irrational fear or failure to solving them.

Philosophically Speaking

If you were a chicken, would you feel privileged or pissed off by the way your name is being used, abused, or misused in school textbooks and workbooks?

Do you think it’s long overdue that you and your feathery friends and foes sue the publishers and the Ministries of Education around the world for showing disrespect or even disdain towards the chicken community?

On a lighter note, if it looks like a chicken and clucks and counts like a chicken, you never know: it might be a mathemachicken.

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