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.
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.
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 AffairA mathematician’s favorite?
The Red Sea Sharks
Tintin in TibetPraised 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 CongoThe 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.
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?
A math definition that has since been hijacked by digital terrorists.
Early this week, we read in the news that the Taliban were stopping female Afghan students heading to the university from leaving the country to study in Dubai.
What kind of society or ideology would prevent girls and women from pursuing an education that would empower them to live productive or fruitful lives, and to help raise the literacy and numeracy rate of their country?
If a government don’t respect the human rights and fundamental freedom of women and girls, it speaks volumes what kind of radical thinking is behind their spiritual or ideological decision and action.
Just when the civilized world thought that forcing people to be attired in a certain way based on man-made laws is bad, banning them from attending secondary schools and universities makes a mockery of all the rites and rituals that are practiced to moralize or de-infidel-ize them.
In most developed or semi-democratic societies, not sending your children to school, or depriving them of a formal education, for no valid reasons, could land parents and caregivers in deep trouble with the authorities.
Singapore: Lifelong Opportunity for All Minority Muslim Girls & Women
In multicultural Singapore, even educated parents can’t simply homeschool a child just because they want to without a valid reason from the Ministry of Education. For example, religious-minded parents can’t conveniently send their children to a madrasah for their formal education if they can’t convince the authorities that their children’s educational, emotional, and social needs would be well taken care of.
A government that fail to provide formal education for its citizens, male and female (or whatever other labels some might prefer to be identified themselves with), or discriminate against girls and women, or alienate certain racial or religious groups, and minorities, makes us wonder how far these people have been radicalized, or are ideologically brainwashed or spiritually blinded.
When rogue rulers or radical religious leaders in a theocratic state control the lives of millions of men, women, and children based on radical ideology, by dictating them how they ought to live and be taught, one can imagine what kind of citizentry they’d produce for future generations.
The marginalization and objectification of girls and women is condoned in many Mohammedan milieux or Islamist circles, and these practices hardly ever make the headlines, compared to the misinformation or disinformation on the repression of Uyghurs and genocide in Xinjiang.
As someone aptly commented, it sounds like Americans “don’t like Chinese and also don’t like Muslims, but they seem (or pretend) to like Chinese Muslims.”
An e-card that proves ISIS values math education.
For “infidels,” selling or marketing Singapore math titles to the Taliban or Boko Haram (which outwardly or publicly abhor and denounce anything Western or Christian) is like running a half-priced campaign for ice cubes in Alaska.
Politics 1 Math Education 0
Since the U.S. pulled out of Afghanistan, after trying to free the people from terrorism and radical Islamism for two-odd decades, arguably, both Trump and Biden are directly or indirectly responsible for the current deprivation of education among girls and women in the country.
It’s a back-to-square-one situation before 9/11, when radical Islamists and terrorists religiously relegated girls and women to domestic slaves.
The Western media put a premium on “radical democracy” but pay lip service to the lack of educational and job opportunities for millions of girls and women in Afghanistan and many so-called “moderate Muslim” countries.
Radical Math Questions
Below are some previously x-ed (or tweeted) politico- or religio-mathematical questions non-NATO [no-action-talk-only] math educators would like to reflect on if they wished to play an active part in the education emancipation of girls and women in many oppressive or rogue regimes around the world.
1. Guesstimate how many millions of girls and women in Afghanistan would be denied of their human and educational rights, as the Taliban start enforcing their man-made Sharia law to oppress or enslave them in most spheres of life.
2. How many Afghan girls and women would be robbed of an education under the Taliban in 2021 and beyond, as radical Islamists and terrorists force them to be subservient to men?
3. If Section 377A humiliates and hurts gay people, doesn’t the men-designed Sharia also “discriminate or disadvantage girls and women”? Shouldn’t those discriminatory laws against them be repealed?
4. [Fake] Math News: Trump & the Taliban. Afghan judges are deliberating what sharia punishments should be meted out to Trump for his financial, political & sexual crimes. What are the odds that he’d be spared of barbaric amputation, caning or stoning?
5. How many Malala Yousafzai’s Afghanistan and other Muslim-majority nations like Iran and Saudi Arabia—where women and girls are often discriminated and enslaved—would need to fight for women’s and children’s rights against the Taliban and the ayatollahs?
A math definition that appeared to have been hijacked by Al-Qaeda or the Taliban
An unspoken commandment among parents and homeschoolers is: Thou shalt not introduce algebra to young kids without close adult supervision.
Looking at the unhealthy number of pre-school math titles in local bookstores, some Singapore math authors have set questions that directly or indirectly help promote algebraic thinking among toddlers and kindergarteners, particularly via the bar model method and number patterns, whether they’re pedagogically conscious of it or not.
Kiasu parents or tiger mums would buy assessment (or supplementary) math titles (often disguised as “parents’ guides”) to give their kids an “unfair advantage” over their peers.
On closer look, disappointingly, these preschool “enrichment math” books are often mere rehashed primary one (or grade one) assessment math titles.
Fr: Cartoon from Judy Smith Hallett
I decided not to showcase any covers of these oft-drill-and-kill kindergarten math titles here to avoid any perception that I’m endorsing some local authors or their publishers.
Notion, Not Notation
Debatably, it’s no harm getting preschoolers to start thinking algebraically long before they’re formally taught generalized arithmetic. Yes to pre-algebraic thinking but no to algebraic notation or equation for kindergarteners.
Personally, I’ve yet to see any decent locally published K–2 Singapore math titles in bookstores (other than through some questions in children’s puzzles books), which creatively or systematically promote algebraic thinking skills.
In the last two decades, there had been a number of journal articles and a few NCTM (and even some AMS) titles that feature activities or nonroutine questions that champion pre-algebraic thinking at the kindergarten level.
It’s a pity that Pre-K and kindergarten teachers (and mathepreneurs) haven’t leveraged on these rich resources to come up with supplementary math titles to evangelize the algebraic gospel to K–2 students.
The raison-d’être of premature algebra teaching
In Singapore, a mecca for brain-unfriendly, budget-friendly assessment (or supplementary) math titles, it looks rather surprising that local Singapore writers have so far not come up with an “Algebra for Babies or Toddlers” when local libraries already carry catchy foreign titles like Bayesian Probability for Babies and Pythagorean Theorem for Babies.
Ripe Harvest but Few Workers
The time is ripe for creative math educators, local or foreign-born, to publish a creative algebra series for toddlers and kindergarteners of kiasu parents, but it looks like the writers who’d help pluck up the fruits are few. An untapped market for publishers that want to move away from canned or drill-and-kill preschool math titles.
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?
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.
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?
Mask Art as Therapy. Original un-memed photo from Hunny & Lummy’s “Masks of Singapore” (2021).
What mathematical or nonmathematical crisis are you presently facing or undergoing? Mid-life crisis? Existential crisis? Financial crisis? Relational crisis? Post-pandemic crisis?
Have you forgotten what it means to enjoy math? If you’re a school teacher or university lecturer, are you planning to leave the [Singapore’s or US’s or XYZ’s ] rigid educational system to pursue your mathematical dream?
If you’re an editor, are you longing for the day when you don’t have to handle those quasi-uneditable manuscripts once you’ve paid up your mortgage or send your children to college?
And if you’re a writer, do you long (or pray?) for those pseudo-math editors to get promoted to their next level of incompetency, where they’re less likely to adulterate your manuscript?
Math & Mask
Beyond the mask that we wear to function in our daily lives as math educators (lecturers, teachers, tutors, editors, writers, consultants, managing editors, publishing managers, …), who are we?
Do you see yourself enjoying the mathematical journey while you’re building your career or struggling to pay the bill? When you take off your daily masks, when you don’t feel the pressure to pretend, when you’d simply be yourself, what does it feel like? What does it smell like? What does it taste like? What does it sound like?
A Commandment to Deal with the Mask of Pride
Mathematical Synesthesia
Can you visualize the color of infinity? Taste the number zero? Smell the fragrance of pi? Or you think these synesthetic experiences are only reserved for autistics or idiot savants?
We all came into this world with zero, and we’ll also leave it with zero but the [mathematical] spirit of life we’ve lived in our lifetime. Are you always waiting for permission to write that math book? Or hoping that when you retire, you’d have the time (and space) to explore and pursue that math pet project?
Are you petrified that others might witness that you’ve been a victim of the imposter syndrome, as you get promoted and being tagged with bigger flowery job titles? Still struggling to fake it until you make it?
Unmask Your Math
To make a mark in math or math education in the local, regional, or international community, you need to strip your mask away. People want to see and work with vulnerable or fallible folks, who’re prepared to make a fool of themselves, to be a laughable stock or mathematical clown, and not to take themselves seriously.
What are you waiting for? Not some other time when you’ve accumulated enough zeros in your bank account, or next semester (or pandemic?), but today. Because when you’re financially free, you’re unlikely to have the energy to do that math thing you so desire.
Don’t die with a book inside you! Or miss tithing one or two years of your life to volunteer as a math teacher in some low-GDP countries to help raise the numeracy level of the locals. Or fail to resurrect that off-atrophied “math & art” project for a solo exhibition. It’s better to fail or experience the journey than regret on your deathbed.
Remember: Let not pride, insecurity, or failure prevent you from fulfilling your God-given purpose on this side of eternity, as you embark on your mathematical journey.
You needn’t do it alone: Seek Him and His wisdom for your mathematical needs and wants. Be fearless and free.
On May 23, 2023, @OrwellNGoode tweeted the rate question below, with the “teacher” marking the student’s answer of 20 minutes wrong, and showing why it’d be 15 minutes instead.
Who the heck takes 10 minutes to saw a board?
I’ve no idea what grade level this math question was being assigned to. Although questions on ratios and rates are formally introduced in grades 5–6 in most parts of the world, however, it’s not uncommon to spot these types of mathematical quickies in grades 1–4 Singapore math olympiad papers to trap the unwary.
Assuming that the word problem didn’t come from a bot or from ChatGPT, the teacher’s intuitive reasoning may be said to be ratio-nally sound but rationally incorrect in solving this pseudo-proportional math question.
Logically or mathematically speaking, few math teachers would disagree that the student was right and the teacher was wrong.
This arguably “badly worded” or “ill-posed” math question provides a fertile ground for a number of possible (valid or creative?) answers, probably much to the annoyance of most math teachers and editors, who often feel uncomfortable or jittery about questions with more than one possible answer.
Indeed, there is no shortage of supporters to defend a “15 minutes” answer. For example, since there is zero mention that the length of each board is of equal length (and we can’t assume it to be so), or as each sawing might take place in a different direction, the “logical” answer of 20 minutes can’t be taken as mathematical gospel truth.
That three pieces need two cuts or sawings is unanimous among problem solvers. The bone of contention is the assumed length of the second cut. Say, if the second cut was half as long as the first one, then it’d take half the time of the first cut, in which case the answer of 15 minutes would be practically plausible.
A creative solution from @A_MGregory
It looks like we’re only limited by our imagination or creativity to rationalize why the answer can’t in practice be 15 minutes or any other duration, by using a different (creative) reasoning from the flawed one provided by the “teacher.”
Like most artificial or impractical word problems in school math, this rate question debatably falls short of design thinking and is thus open to different interpretations or assumptions, which might also weaponize some “anti-woke” math educators to ban or censor these types of “confusing or tricky” math questions.
Ironically, this is why injecting a dose of realism or creativity to these oft-ill-posed or contrived math questions would help open up the minds of uncritical or unquestioning math educators.
Don’t just answer the questions, question the questions.
Long before the TikTok saga, when the quid-pro-quo ex-president and his gang were entertaining the idea how they’d extract any financial or political gain from the mainland Chinese company on the pretext of security concerns, I was thinking how local math teachers (who’re dissuaded from using social media to share their personal or professional views on math or math education) could leverage on this fast-growing platform to popularize the gospel of mathematics to billions of people.
During the Covid-19 pandemic, I’d christened “TikTok Math” as follows:
Is “TokTok Math” a four-letter word for MAGA patriots?
TheTikTok Factor
Last month, following TikTok’s CEO’s four-odd hours meeting with US lawmakers, I tweeted the following:
TikTok’s “theoretical threat”: Blessing or curse? Unlike Singapore that welcomes (or sometimes reluctantly allows) foreign competition as its people mostly benefit from their presence, the US—and the yes-nations—would rather use politics or paranoia than creative power to be a leader.
TikTok “Theoretical Threat”
Does it pay to be a technology leader if for decades your competitor has dominated the industry?
The TikTok saga is an eye-opener to the outside world, as it shows that even the United States, when technologically challenged or militarily threatened, would abandon its own playbook of business ethics, or concoct some theoretical or imaginary security threats, to neutralize the competition or enemy.
Today, the world’s policeman, which has caused more pain than inciting peace, has lost its moral compass on the global stage. A divided polarized nation that doesn’t walk its talk, with promises often turning into pains, or where perks and profits trump people and principles.
The democracy deliverer has inflicted more human pain and suffering than any other country since the last world war. Think of Vietnam, Iraq, and Afghanistan, to name a few nations they “delivered” against communism, totalitarianism, or terrorism.
You’d easily parrot your list of nations whose peoples’ lives have gotten worse in the name of democracy, political freedom, rule of law, or religion. All these universal human ideals have been traded for poverty and pain.
Even with quality or selective immigration, the US is struggling to maintain its superpower status, much less commanding respect from the world. Its gospel of justice, equality, equity, opportunity, morality, or democracy falls short when we see that the lives of half of its [mostly nonwhite] population have gotten worse in the last three or four decades, when their incomes haven’t kept up with the standard of living.
For those in the Chinese diaspora, communist China or the CCP is arguably autocratic, anticompetitive, and antidemocratic, but these marxists-capitalists aren’t that stupid to ask TikTok or ByteDance to hand over the personal of millions of Americans just because they can.
Hearing the shallow or oft-laughable arguments of some of the technologically challenged US lawmakers or politicians questioning TikTok’s CEO, it’s crystal clear that they’ve quasi-zero idea how the mainland Chinese or Asian or African psyche operates in business settings.
On March 20, 2023, @MathPlus asked the following question:
Yes-states & Yes-nations
A few days earlier, I’d hypothesized that
It looks like President Biden & Co. are a second-rate team that can’t think creatively to contain China, by banning their app and the sale of chips, instead of outsmarting them with better products. https://www.bbc.com/news/technology-64973156 #US #politics #TikTok #ban #China #competition #5G #fear
TikTokers v. Trumpists
Way back in 2020, before the last US presidential election, when Microsoft hinted that they’d be keen to buying TikTok, to poke fun at Trump, I’d posted the following:
Survival Odds: Which group would see their wish come true: TikTokers or Trumpists? Which hashtag would triumph: #SaveTikTok or #SaveTrump? Who would have the last laugh on 11/3: Xi or Trump? #ban #TokTok #Trumpism #US #politics #technology #China #Microsoft #math #odds #Covid-19
On 2/8/20, @Zero_Math tweeted the following:
Political Math: Should President Trump ban TikTok for “security reasons,” guesstimate how many millions of young and old voters he’d lose on 11/3, as he diverts attention on his failure to contain the pandemic crisis. #math #Covid-19 #US #politics #TikTok
Waco: A Tale of Two Faux Messiahs
Comparing David Koresh, 33, a “prophet” of the Branch Davidians cult in 1993 to Donald Trump, 76, Trumpublicans’ “anointed one” and “political messiah” of rural America, before the ex-president’s lies-plagued rally in Waco, under “Political Math,” I’d tweeted:
Guesstimate how many TikTokers would be reserving seats for Trump’s campaign rally in Waco, Texas, without showing up—a prank proposed by his niece, who’s suing him for lying and cheating. cnn.com/2023/03/25/politics/texas-trump-2024-rally/index.html
A cartoon by John McNamee
TikTok & Math
TikTok’s global popularity or notoriety provides math educators a fertile ground for creative mathematical problem posing and problem solving in the midst of polarized politicians’ and puritan parents’ oft-paranoiac security or mental health concerns.
Let not politics, paranoia, or phobia hijack math and math education, because the double-edged TikTok could be a mathematical blessing rather than a curse, thanks to the creativity of tens of thousands of math educators worldwide.
