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Singapore Math

Thursday, June 27, 2024

Is Age Just a Number?

Cartoon © Anon. (being memeified)

I admit that I’m guilty of ageism, but I make zero apologies for exposing criminality or hypocrisy, especially among (past and present) heads of state.

For the majority of us, oft-reluctant law-abiding citizens of the world, few would admit that the criminal mind is a “creative” mind in disguise—one that we’d learn a thing or two from if we put aside our prejudices.

A Tale of Two Senior Presidential Candidates

What are the odds that the world might soon witness a presidential debate between a patient and a prisoner? If reelected, could either folk serve his full term?

Arguably, we’ve two power-hungry weak “leaders” that America could do without—when both seniors should be grandfathering (or con-sulting) rather than mis-leading or weakening the country for another four years (assuming their Creator doesn’t call them before their term is due).

Cartoon by Rick McKee (@Rick_McKee_Ink)

An Age Limit for Presidency

If the present president and his predecessor are too old to competently serve the challenges or demands of another term, shouldn’t lawmakers pass a constitutional law that no elected president shall be of a certain age on the date of inauguration?

What should that age limit be so that voters feel comfortable that any elected presidential candidate would fulfill his or her responsibilities of office? 65, 70, 75, or some other age?

Bitter Root ≡ Better Fruit?

If a bad tree can’t produce good fruit, it’s preposterous to see millions of voters expect a serial dishonest or corrupt “I-me-myself” candidate to deliver them from their years-old financial, social, and religious ills.

The theological or political argument that voters shouldn’t put too much emphasis on a candidate’s past manifold wrongs (who’s continually denied any wrongdoings) to assess or judge him sounds dangerously frightening. Understandably, the criteria to electing a president must be much lower than those used to choosing a pope. Really?

Cartoon by @DennisGoris (buff.ly/3VlEyaz)

King Saul 2.0

What are the chances that in Biden or Trump, we’d be witnessing a modern-day version of King Saul, whose rule would be cut short? Would those mostly morally bankrupt or corrupt appointees, who condone their lies and falsehoods, expect to operate in a blessed political environment? It looks more likely that political entropy would be the new normal come January 2025.

In politics, irrationality and hypocrisy often prove that a string of wrongs has near-zero bearing on the electability of a corrupt or rogue politician.

When one senior isn’t much younger than the other, the choice isn’t that difficult. You choose the one with (more) character, humility, and honesty. Voting for the alternative is flirting with ineptitude, dishonesty, and chaos—more pain and suffering for the majority of the population, who expect their next president to behave more like a priest or pope.

US Math: An Age Problem

Let’s end with a birthday joke on the two most senior presidential candidates in U.S. politics:

Q: Why even their diehard supporters see both Biden and Trump as old, who should be banned from taking part in a presidential election again?

A: At their last birthday, the candles cost more than the cake.

Electorally yours

© Yan Kow Cheong, June 27, 2024.

Monday, April 22, 2024

Thou Shalt Keep the Mathematical Sabbath!

The Weak Days of the Week

It’s said that working seven days a week makes one weak. Even workaholics who often wished they had an eight-day week couldn’t go on their routine hoping to ever be productive or creative sans experiencing a breakdown sooner than later.

Four-Day Work Week

Recently, there was much talk in the “fine” city about a four-day working week. Sounds like good news for tens of thousands of employees, especially those in the civil service, but bad news for profits-over-people employers or bosses in the private sector, who don’t subscribe to a workplace promoting a less than a 44-hour work week.

A recent poll found that around a third of Singapore workers surveyed expect a four-day work week to be the new normal in the next five years, with about twenty percents of them saying that their employers already offer such a work arrangement as an incentive to promote mental health at work.

Three-Day Weekend

What if schools switched to a four-day week? Would productivity (and creativity) for teachers and students go up? Would parents (and tuition or enrichment centers) support it?

Would the Ministry of Education dare to entertain such an idea in a tiger economy? As Singapore has evolved from a stigma-based streaming to a socially acceptable subject-based banding (a refined version of streaming) education system, it’s not a far-fetched idea of allowing students to come to school for just three or four rather than five days a week.

After all, the aftermath of Covid-19 had given them a foretaste of what schooling or blended learning might be in future, without depriving them of a formal education. A case of “less is more,” just like the politically correct “Teach Less, Learn More” mantra.

The Sabbath Mode

It’s never too late to put yourself in a Sabbath mode. You needn't be religious to see the benefits of the Sabbath—a mind-set that those in demanding jobs appreciate.

Think of those domestic workers in Singapore, whose employers expect them to work seven days a week, even if the Ministry of Manpower has mandated a one-day off for them every week.

A Mathematical Sabbath à la Singapour

Due to lack of understanding or wisdom, for a large part of my student and working life, I was often guilty of paying lip service to keeping the Sabbath, hoping to maximize my studying time, or minimizing my sleeping or resting time. A short-term success formula with long-term costly results.

Below is an attempt to define what a “mathematical sabbath” might entail for math educators around the globe, who long to be at their creative or productive best, week in, week out, without cutting corners on their rest or quiet time.

Your Mathematical Rest Day

Which Weekday Are You In?

On average, we’ve a three-scores-and-ten lifespan, or 70 years. If every day lasts a decade, which day of the week in your life are you in?

Sometimes God gives us an extra Monday, Tuesday, or Wednesday. How many souls do we want to bring along for the remaining days we’ve left with?

On a similar note, recently, I semi-poetically X-ed (or tweeted) the following:

@MathPlus on 3/28/24

Remember the keep the Sabbath day holy—and also the mathematical sabbath wholly.

Restfully & creatively yours

© Yan Kow Cheong, April 22, 2024.

Monday, February 19, 2024

Thou shalt not use an arrow for an equal sign!

Shot from Tiesha Sanders/Facebook

The above grade one math question from Texas is debatably ill-posed. However, the child answer of “7 ones” is “non-mathematically creative” or “irreverently correct.”

The teacher’s reply to the mother that “… this is the new math they have us teaching.” would puzzle many math educators outside TrumpLand. Arguably, the correct answer to this routine question has little or nothing to do with “new math” or “new new math” or whatever politically correct mathematical term we want to christen it.

The child’s “correct” answer that was marked wrong by her teacher defies logic. The use of an equal sign instead of an arrow would have minimized any misunderstanding whatsoever.

In “fine” Singapore, few teachers and parents would disagree that similar grade one place values questions are deemed routine. The chances of any local school teacher or tutor using arrows rather than equals signs for these drill-and-kill questions are quasi-zero.

Even for this ill-posed elementary math question, in the first part, if a child has correctly inserted the digit 7 under the ones column, and to expect them to give the same answer for the fill-in-the-blanks for the number of ones, it doesn’t sound too logical or commonsensical. The problem poser is unlikely to ask (or expect) for “7 ones” twice!

MAGA math: 7 ones ✔️

Insisting that the answer of “7 ones” is equally valid as “27 ones,” or denying that “7 ones” is incorrect, due to the way the question is posed, sounds like the mathematical equivalent of an ex-president insisting that he didn’t lose the election, albeit all the facts or results proved otherwise.

If the child isn’t wrong (because the parent isn’t wrong), and the teacher, too, isn’t wrong, so who’s right then? Could two conceptual negatives give a concrete positive?

Logically & truthfully yours

© Yan Kow Cheong, February 19, 2024.

Monday, December 18, 2023

Did You Commit a Prime Murder?

More than half a dozen years ago, I coined “Prime Murder” as follows:

What proportion of integers are prime? What are the odds that you might commit a prime murder at some point in your mathematical career, be it in teaching, editing, or writing?

Over the centuries, both professional and amateur mathematicians weren’t spared from it. Think of Pierre de Fermat who erroneously thought that 2^(2⁵) + 1, or 2³² + 1, was a prime.

So, for the majority of us, whether we’re born or blessed with the “mathematical gene” or not, the chances of being found guilty of a prime murder might not be limited to a single-digit percent. 

A 2019 graphic novel that explores two most basic mathematical objects: integers and permutations

Below is a simple exercise that might help reduce the odds of someone being a “prime murderer.”

1. Which of the following numbers are prime?

a) 919     b) 1,001     c) 1,763     d) 3,221     e) 8,081     f) 123,321

2. MAGA Math

a) The Pinocchio-in-Chief faces 91 criminal charges across four indictments, all of which he had pleaded not guilty. What are the chances that he is a prime suspect to these charges?

b) A “very stable genius” claimed to have an IQ of 211 (base p). Find the value of p.

c) The “MAGA-in-Chief” wanted a Secretary of State to find 11,780 votes, which would have given him one more than his Democratic opponent. Show that the requested number is not a prime number.

d)  A judge determined that the ex-“Commander in Cheat” had overvalued his Mar-a-Lago property by 2,047% besides claiming that his penthouse in New York was three times its actual size. Is this a “prime percent”?

In Prime Suspects, when Prof. Gauss & team looked at the autopsies of the victims of two seemingly unrelated homicides, they discovered the shocking similarity between the structures of each body.

Let’s end with a prime factoid: The writers of The Simpsons and Futurama have been smuggling complex mathematical ideas into prime-time television for over a quarter of a century.

Primely yours

© Yan Kow Cheong, December 18, 2023.

Monday, October 16, 2023

A Singapore Grade 4 Geometry Question

On Facebook, someone recently posted the above primary 4 (or grade 4) geometry question, asking for help from fellow parents. How would you do it (without calling on ChatGPT)?

If you’re a parent, homeschooler, or tutor, how would you explain it to an eight- or nine-year-old child, who’s struggling with non-drill-and-kill questions on area and perimeter?

Give It a Try First!

Try figuring out the answer on your own first before peeping at two parents’ quick-and-dirty solutions below. Better still, could you present an idiot-proof or peasant-friendly solution that even a smart dog or cat could understand?

 Solution by Belinda Sim


6 width and 6 long = 3units  of the rectangle.

1 rectangle -> 16cm.

3 rectangle 

16x3 = 48cm.

Solution by Jesline Ang

Stretch Your Mind!

Many moons ago, I was commissioned to write Mind Stretchers 2*, a grade 5 problem-solving math book, which was popular in a number of local schools and tuition centers—disturbingly, they’re guiltlessly or blatantly photostating entire chapter questions as part of their worksheets.

And I still recall that on the topic of Perimeter, I’d posed a number of routine and nonroutine questions. What surprised or tickled me then was when the Managing Editor asked me whether or not some of these questions are solvable, because at first glance, they look like there are missing information to solving them.

These geometry questions can give students (and probably their oft-math-anxious parents and teachers) some goose pimples out of fear or panic if they can’t figure out the answers offhand. 

Understandably, without a cool mind and some patience (or perseverance), even perimeter and area questions at the elementary (or olympiad) level can prove to be a challenge to math educators if they’re not trained to tackling them using the right approach.

Frustration and fear usually set in, especially for nonroutine questions that don’t normally appear in drill-and-kill school textbooks and workbooks.

Premature Testing

The danger of setting these types of brain-unfriendly questions too early, or having them prematurely in a class test, especially when most students have yet to fully grasp the concepts of area and perimeter, could be detrimental to the mental health of most average math students.

Parents who freeze at the sight of these questions would often exhibit a knee-jerk reaction, by getting a tutor for their child, if they’d afford it.

Tuition or No Tuition?

Most stressed parents often reason that if they couldn’t even solve these grade 4 questions, things would only get worse in later years, as the higher-grade topics get more complicated and the questions become more challenging. They just don’t want to see their child struggle in math, especially when they themselves had had a negative experience of the world’s most disliked school subject.

Even for math teachers and tutors, there’s nothing to be ashamed of if at first or second reading, they’re clueless how to tackle these nonroutines. Yes, they do appear in mid- or final-year exams arguably as a social filter to separate the nerd from the herd, but once math educators and homeschoolers know how to approach these questions from the right angle, before long, these math problems would become routine to them.

The 4F’s of Mathematical Problem Solving

Few math teachers and writers would admit that (school or olympiad) math involves lots of fears, false starts, frustrations, and failures. The sooner parents and homeschoolers (and their children and grandchildren) are aware of this oft-unspoken problem-solving process or ritual, the pressure or expectation level for all parties ought to go down significantly in reducing any unnecessary mental or mathematical stress.

Pain is (always) part of the joy of creative mathematical problem solving—the no-pain-no-gain mantra is axiomatic in math at all levels.

Geometrically & perseveringly yours

© Yan Kow Cheong, October 16, 2023.

* When the wallet-friendly title was out of print, a senior editorial staff emailed me that he’d pay me a cosmetic S$150 to buy the copyrights. I never bothered to reply to his laughably ridiculous suggestion. I wouldn’t be surprised that they’d since plagiarized the content to be used and reused for other purposes.

Monday, September 25, 2023

How to Celebrate Zero Day

Zero causes so much pain and suffering to tens of millions of students and their parents every day. Indeed, zero is the real troublemaker among the numbers! It's not too late to get even with the Roman Catholic Church’s once-deemed blasphemous infidel number (again).

Below are ten idiot-proof activities you’d do to celebrate Zero Day.

10. Avoid writing the now-redundant zero before a decimal point: .23, .583, .0045, …—move away from dated deception, faux religion, or numerological superstition.

9. Use the letter “o” or “O” when you mean the number or numeral “0”—for example, when giving a bank account or ID number to someone requesting it on the phone for verification purposes.

8. Use “nothing” to half-truthfully convey the idea of zero, even though the number zero is “anything but nothing.”

7. Fight for the Year Zero to be included in the timeline, to avoid confusing billions of people that the year 2023 is conventionally in the 21st century rather than in the 20th century.

6. Canvass for the number zero instead of the number one to be the first number in the set of whole numbers, especially in some puritan or radical circles, where the devil number is excluded.

5. Mobilize semi- or quasi-innumerate folks to use a different numeral when zero is used as a place number and as a number itself—strip zero of its double personality. For instance, use Ø in lieu of 0: 3Ø14Ø to emphasize place-value.

4. Be a zerobreaker, by defying the eleventh commandment, Thou shalt not divide by zero! without life-threatening consequences—that one has the (civil or political or religious) rights to divide by zero, although the answer may prove insensible or unreasonable.

3. Puncture the egos of haughty geeks who think they know it all, by exposing mathematical loopholes in their reasoning, resulting from illegally (or unknowingly) dividing by zero—humble them with fallacies and paradoxes, such as 1 = 0 or π = 3.

2. Have a law that fines companies from offering 0% interest rate as a gimmick to lure gullible customers.

1. Warn people to flee from the free—beware of free gifts, free seminars, and free air tickets, which seldom have zero strings attached.

Now is the time to teach Zero who’s in charge here—zero is your servant, not your master.

Nøtøriøuly yours

© Yan Kow Cheong, September 25, 2023.

Monday, August 21, 2023

A Numbers Puzzle

On X (formerly Twitter), @wiseconnector posed the following question:

How many numbers can you find?

It’s never too late for an eye check-up and also an opportunity to hone your logical and visualization skills.

This logic or math question can serve as an icebreaker at a birthday party even for those who proudly or unashamedly boast of being “hopeless at math or numbers.” 

Try it! The answer is anything but obvious.

Ask a toddler or kindergartener, and also your seniors at home, especially if you’re concerned that they might succumb to dementia or Alzheimer’s in their later years, based on your family health history—a [generational?] curse you can break in the name of Jesus if you don’t want your children and their children to go through this mental illness in their golden years.

Summarize the answers to this puzzle from different age groups in a statistical diagram, say, a pie or bar chart. The information is likely to surprise you, giving you some insights what is going on in people’s minds when they try solving this kind of trick or tricky math question.

This little mathematical quickie has the potential to unite rather than divide people, by bringing them and their loved ones and friends much joy and laughter—never mind if they can’t always agree on the correct answer.

Logically & visually yours

© Yan Kow Cheong, August 21, 2023