Indeed, it hurts if you’re dubbed one! There is no shortage of negative or unflattering labels to describe those who’re apparently born or blessed with the “math gene.”
Fortunately, these days, with so many math geeks using their talent or gifting to help produce all kinds of technological marvels, or helping the world solve a number of wicked problems, respect or awe for the socially awkward or romantically inept seems to be at an all-time high.
Getting Rich from Math
Think of those tens of thousands of millionaires and billionaires worldwide, who’ve made their fortune thanks to the oft-invisible power or applications of math and science.
Their “square” looks or dating habits might make you avoid them like the plague, but you can be sure that a good percentage of these “bores” or “non-blockheads” are laughing all the way to the bank.
Many of those “squares” or “blocks” are being paid handsomely because of their sought-after mathematical or coding skills.
And many of these (oft-foreign-born) guys Trump & gang think they can do without them because they’re “stealing” white-collar jobs or “spying” on Americans—the MAGA cult want to deport (or even demonize) them to protect local high-tech jobsfrom skilled aliens.
Yes, some of these geeky guys and gals are arguably unhandsome or plain-looking. Who cares when math is their god, which has allowed them to retire prematurely or to attain financial independence, when their non-STEM peers are struggling to pay the bill?
Love + Math = Success
And if you’re a hundredaire or thousandaire, it’s not too late to befriend or even date some of them. There is exponential power or benefit when love meets math. When you discover in no time that the square-looking geek is often an (imperfect) circle inside.
Anecdotally or statistically, an unhealthy number of mathematicians and math educators around the globe are chain-smokers. Out of habit or addiction, they need to puff out before any proof.
Likewise, it wouldn’t be surprising that a (smaller) percentage of them would also need to drink before they derive any mathematical result, or prove or disprove any conjecture, which is worth gracing the pages of a reputable journal or periodical.
Strong Zero
On a visit to a local supermarket two years ago, I spotted Strong Zero, which led me to tweet about it:
Strong Zero: Something to reward yourself with at the end of a long fruitful day indulging in mathematical proof to destress yourself with fellow boozers.
Then, I had in mind to “derive, then drink,” rather than the other way around. The choice is yours! Know your limits!
If you drink, don’t derive! Really?
So, a little boozing and smoking (in moderation) might debatably be an unspoken (inexpensive?) boost or catalyst to experiencing an aha! When the product of two negatives produces a positive!
A Quickie from Russia
Since we’re on the topic of drinking alcoholic beverages or liquor to boost mathematical productivity, let’s end with a mathematical quickie from Putinland, which was pre-Xed (or tweeted) slightly less than a dozen years ago:
A man and his wife drink a keg of kvas in 10 days. He alone can drink it in 14 days. How long will his wife take to drink a keg?
Challenge: Try solving the above proportion problem in a nontraditional way (with or without a drink)! Better still, use a bar model to do it.
Ex-president Trump’s criminal hush-money trial in New York provides much fodder for comedians and political pundits, not to say, math educators and poets, to poke fun at the lasagna of lies exposed by the prosecution and defense teams.
Below is a math meme that was X-ed, when the ex-Commander in Cheat’s defense lawyer was cross-examining his “ex-fixer” in the court case.
Political Math: When two serial liars failed to convince a jury of recreational math educators from the “fine” city of Singapore that they’d be exempted from a mock high school test paper.
@MathPlus on May 20, 2024
5GDishonesty
Thanks to Mr. Pinocchio and his once-most-loyal lawyer, who said he’d take a bullet for his ex-client, even math teachers and writers (and pseudo-poets) around the globe couldn’t resist from indulging in some poetic licence.
A Tale of Two Liars
One lied n times, but repented at the (n+1)th time. The other keeps lying for the nⁿth time.
Another “adult math” meme that was tweeted to irreverently expose the ex-president’s constant denial of his affair with a former porn star is the following:
Political Calculus: The Real Analysis of the Trump-Daniels Affair. Meme posted by Shivam Kr (Jan. 28, 2022) to the “Mathematical Mathematics Memes” page.
@MathPlus on April 17, 2024
More MAGA Haikus
Let’s end with four haikus based on the duo’s decades-long manifold lies.
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.”
Mathin 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?
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.
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.
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.
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.
* 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.
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?
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.
