Category Archives: Problem Solving

Three problem-solving strategies commonly used in Singapore schools are focused on: Singapore model (or bar) method; Stack method; Sakamoto method.

Make a Ten

June 8, 2023Problem Solving, Singapore Mathalgorithm, arithmetic, Bar Model Method, Common Core Math, drill-and-kill math, four operations of arithmetic, instructional understanding, make a ten, memorizing, methodology, pedagogy, procedure, regurgitation, relational understanding, rote learningKow-Cheong Yan

On June 4, 2023, @PicturesFoIder tweeted the following grade one question:

If you were a dad or mum who’s not familiar with teaching and learning math that focuses on relational understanding, not just on instructional understanding, most teachers and homeschoolers would sympathize with you. You’re not alone!

Make a ten is a simple but not simplistic strategy, commonly used by Singapore math and Common Core math elementary school teachers to teach the operations of addition and subtraction meaningfully rather than procedurally through rote learning.

Angry parents would say, “Why make math more complicated? Wouldn’t that (noble?) way of teaching frighten kids rather than motivate them to do math?” They do have a point, don’t they?

Summary page from CPDD’s “Primary Mathematics Textbook 1A” (2021)

Of course, it’s easier said than done, because given a choice, most of us, teachers, tutors, and parents, would find it more convenient or faster to getting children learn math by rote, by rationalizing that they’d naturally know why the procedure works in later years. For now, just teach them the hows—don’t bother about the whys.

Summary page from CPDD’s “Primary Mathematics Textbook 1A” (2021)

In most parts of the world, teaching math the algorithmic way is the default mode of teaching. A common reply or complaint is “Who’s the time and patience to ensure that 30-odd students in a class have really understood why the procedures for adding and subtracting whole numbers make sense to them?”

The Hows and the Whys

What percentage of grades 1–2 teachers worldwide teach both the hows and whys of addition and subtraction? Do they consciously tell children why they need to learn the algorithms rather than using their fingers to count? Or why is it to their benefit that they learn multiplication and division as a shortcut of addition and division, respectively, not to say, the algorithms to perform these operations?

Just because the majority of us didn’t learn school math relationally or meaningfully in our formative years doesn’t mean we’d also subject schoolchildren to the same boring or uncreative pedagogical ritual due to limited time, or to mimimize conceptual overload or potential confusion.

Teach Not the Way You Learned!

School teachers and parents of yesteryear most likely didn’t know or learn about concepts like “make a ten” and “draw a model,” but our present generation of math educators do know. So there’s no excuse not to introduce them to schoolchildren.

We often underestimate young children thinking that they’d not understand or appreciate the whys, because most are already trying or struggling to make sense of the hows. Valid as this argument may be, patiently (and painfully) providing a good mathematical foundation in the early years would bear much fruit in later years, because understanding trumps rote learning any time.

Relationally and meaningfully yours

The Pseudo-Proportional Problem

May 29, 2023Problem Solving, Recreational Math, Singapore Mathcreative thinking, creativity, critical thinking, elementary school math, grades 1–6 math, lateral thinking, primary school math, problem solving, proportion, pseudo-proportional, rate, ratio, woke mathKow-Cheong Yan

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.

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.

Right Answer, Wrong Method

May 11, 2023Problem Solving, Singapore Matharithmetic, commutative law, concept, grade 3 math, method, method of solution, methodology, multiplication, pedagogy, primary 3 maths, problem solving, process, product, Singapore, Singapore mathKow-Cheong Yan

A grade 3 question with right answer marked wrong.

A grade 3 Singapore math question made some waves among netizens in yesterday’s local paper. https://bit.ly/3VOzpHP

Debatably, the root of the discussion centers around the “right” way to do multiplication.

Process v. Product

In Singapore, it’s not uncommon for elementary school teachers and tutors to witness a student’s incorrect method of solution to a word problem that produces the correct answer. This frustrating situation arises far too often than what many of them would want to admit.

Due to a shortage of time, most school teachers pay lip service to the method of solution, pretending not to see that the students’ workings fall short of what is expected of them. These time-starved civil servants would simply look at the children’s answers and conveniently mark them “correct.”

In some cases or circles, it’d not be surprising too that some teachers or tutors themselves are oblivious of the correct method or procedure to solve a (routine or nonroutine) math question.

Personally, I’d want to give these school teachers the benefit of the doubt that they’re merely “lazy” rather than because they’re conceptually blind to the mathematical stain on their students’ worksheets.

Getting students to master a math concept with understanding requires time and effort (and also patience and pain), and most stressed teachers can’t afford either one in the name of having to “rush to complete the syllabus.”

For example, students’ or parents’ parroting that “multiplication is repeated addition” gives teachers and tutors quasi-zero clues whether they’ve understood the multiplication concept or not.

With regard to this grade three routine question that made the headlines, writing the correct procedure, without the teacher explaining to the student why he or she went wrong, only solves half the problem.

Understandably, some parents would argue that teachers shouldn’t be too rigid or radical about their children’s half-baked solutions to avoid dampening their self-esteem. For mathematically puritan math educators, the process is more important than the product.

Procedural proficiency with little understanding of math concepts would only produce elementary school drill-and-kill math graduates—the whys are as important as the hows.

An early penalty is better than a later one when it comes to a child’s learning of basic mathematical concepts in their formative years, which must be accompanied by a teacher’s or tutor’s explanation of the incorrect solution.

And in this grade three routine multiplication question, order matters.

TikTok Math

April 16, 2023Humor, Problem Solving, Recreational Math, Singapore Math5G, ByteDance, CCP, China, competition, geopolitics, hacking, harvesting, IT war, paranoia, security, spying, technological supremacy, technology, theoretical threat, TikTok, US politicsKow-Cheong Yan

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?

The TikTok 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.

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:

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

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.

√–1 TikTok Math, ∴ √–1 am.

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

Toilet Math

January 23, 2023Humor, Problem Solving, Recreational Math, Singapore Mathdeforestation, ethics, hygiene, math, NEWater, public toilet, recycling, Singapore, toilet, toilet paper, toilet roll, wastage, waterKow-Cheong Yan

I’ve been discreetly and randomly working on the tentative The Little Toilet Math Book in the bathroom, where my best thinking often takes place. I suppose a number of you too get your aha’s or eureka’s there, albeit understandably you wouldn’t admit it.

Yesterday, as I was passing by a community center, I happily saw a toilet rolls collection box. I immediately took a photo shot of its front and side views. And my mind started rolling in some real-world questions that could match the pictures.

Below are a sample of these toilet math (🧻🔢) questions:

If residents in the “fine” city of Singapore were to recycle their toilet rolls, guesstimate how many trees could be saved every year.
How much more space could be used if donors were considerate enough to flatten their toilet rolls before dumping them into the collection or recycle box?
If citizens and residents decided using water rather than toilet rolls to clean themselves up, how many millions of liters of water they would need per day after visiting a public toilet (excluding those hundreds of thousands of men who hardly ever wash their hands after relieving themselves or doing their dirty business)?
For a household, would using a bidet or water at home be dearer or cheaper than relying on toilet rolls in the long run (including medical bills for piles and other related health issues that are directly or indirectly due to paper uncleanliness or poor hygiene)?
Imagine that Singapore could no longer import toilet paper from its neighbors. Wouldn’t switching to NEWater—Singapore’s homemade drinkable water, which comes from polluted sea water and “toilet water” mixed with bacteria-killing agents, and which disputably smacks of or smells like sewage—cost for for the population than using toilet paper for doing their business?

Often times, for a community project to succeed, not only do we need that little extra effort but also an iota of thought to ensure that all stakeholders mindfully (or inconveniently) play their part.

Let’s all do the right thing and the thing right, because success often lies not so much in the doing but rather in the caring.

Remember: There is no Planet B (for Generations 𝛼, 𝛽, and 𝛾).

Environmentally and mindfully yours

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.

Which came first: The chicken or the egg?

Math Word of the Day: Pithon

June 25, 2022Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Mathadder, Florida, humor, math, parody, pie, pizza, problem solving, python, serpent, Singapore, snake, viperKow-Cheong Yan

The day before, we read that a female Burmese python weighting 98 kg and nearly 5 m was caught in Florida. She’s the largest snake ever found in that state before her death, pregnant with an amazing 122 eggs; if stretched vertically, she’d be as tall as a giraffe.

In Florida, where now lives the Viper in Chief after being ousted from the White House, who’s since preoccupied himself with terrorizing those who refuse to propagate his lasagna of lies, pythons have become pests due to irresponsible pet owners of yesteryears releasing or allowing pet pythons to escape in the wild.

With no major predators, Florida’s subtropical climate has provided serpents and snakes a conducive breeding ground for them to multiply, often outcompeting native species. Who knows? Alien vipers might eventually outnumber local pythons, if left on their own to populate the land.

Recently, some human vipers mounted a “mathematical insurrection” against textbook publishers for allegedly promoting “woke math” to K–12 students. And a rising number of foreign pythons are set to keep Florida’s annual “Python Challenge” alive—this year, the event runs from August 5–14 and is expected to lure around 500+ python hunters from 25 different states.

🐍🔢: Math with Pythons & Pithons

Like math questions on vampires and zombies, those on pythons (and pithons) are no less frightening or exciting to problem solvers. Below are two examples:

It is estimated that the female Burmese python, which was caught after Floridian researchers used a male “scout” to find her, was up to 20 years old. In human years, would she be as old as the Viper in Chief?

Python Pies or Pizzas: In 2021, the winner of the “Python Challenge” captured 223 pythons, while the longest snake was 15 feet long. Imagine if this year’s captured foreign pythons were ethically killed and exotically used to make pies or pizzas, how many pieces of either one could be made by the chefs at Mar-a-Lago for the “Florida Python Food Festival”?

Math Word of the Day: Covid-🇸🇬

June 20, 2022Humor, Mathematical Humor, Problem Solving, Recreational Math, Singapore Math, Theomaticsbooster shot, Covid-19, death, Delta, fear, funeral wake, health, humor, infection, lifespan, longevity, math, minister, Omicron, parody, Singapore, vaccination, vaccine, variant, wakeKow-Cheong Yan

On Monday, Singapore’s Health Minister Ong Ye Kung reported that 80,000 seniors aged 60 and above have yet to take their Covid-19 booster shots, urging them to do so as the city-state is expecting a new wave of Omicron infections in the next few months.

The minister added that the first batch of Covid-19 vaccines were engineered more for the “wild-type” virus, and now that the coronavirus has mutated into the Delta and Omicron variants, we need at least three doses of vaccines for “effective” protection—and a fourth jab (or a second booster shot) is recommended for those who’ve so far lived on this planet for at least three scores and two tens (or four scores)—aged 80 and above.

Like thousands of my fellow skeptics, when we read or hear this kind of corona update from a local politician on a Monday, our skepticism index goes up at least twenty points. It sounds more like an indecent number of WHO-approved vaccines are nearing their expiry dates, so they need to come up with some creative eleventh-hour strategies not to waste away those tens of thousands of doses.

These days, even developing countries with low vaccination rates are likely to turn down any donated near-expiry vaccines from those high-GDP hoarders. They’d reply, “Thank you very much for your [“insincere”] donation!” followed by some PC excuses not to offend the donors.

One subtle way to salvage a fraction of these surplus doses is to use some mortality statistics to scare off those who’ve yet to be jabbed or boosted.

For instance, we’re statistically being told that the probability of unvaccinated seniors aged 60 and above ending in the intensive care unit (ICU) or dying from Covid-19 is 1/25, but the figure drops to 1/100 if they’ve been doubly jabbed, or nosedives to a mere 3/1000 if they’ve been boosted.

Minister Ong emphasized that “It makes a difference whether you have taken 0, 1, 2 or 3 shots.” So, the unvaxxed would better pay heed to his life-and-death warning unless they plan to journey to the other side sooner than later.

The sombre message is: Wake up to your minister’s advice if you don’t want to have a minister at your premature wake conducting nightly services to your loved ones and friends and colleagues. The decision is yours to act if you want to prolong your stay on this planet by an extra few years or decades.

Let’s pray that the unvaccinated or unboosted lot would fear Covid-19 more than Covid-🇸🇬, while not letting themselves be paralyzed by either one.

Yan's One Minute Math Blog

News & Views about Singapore Math