There is an educational (or psychological or emotional) price a country has to pay if it wants its students to continually rank among the top three in international comparative studies like TIMSS and PISA, or in regional or international math contests and competitions.
An irreverent definition of Singapore’s most dreaded school exam paper
Understandably, parents in Singapore are unhappy about the difficult PSLE (grade 6) math questions that are used to assess their children, before they’d graduate from primary (grades 1–6) school to secondary (middle) school.
And the oft-politically correct or modeled answers from the city-state’s Ministry of Education (MOE) hardly ever pacify or satisfy teachers, parents, and caregivers; in most cases, the canned suggestions or quasi-laughable solutions only make them angrier or more cynical.
PC Slogans for Kiasu Parents
Be it the mantra that “every (local) school is a good school,” or that parents need to help or educate their children believe that “their self-worth or value isn’t dependent on their exam grades” is easier preached than practiced.
When politicians or MOE officials preach to parents that they needn’t be paranoid about their children’s PSLE exam or math score, because it’s not the end of the world, it’s like ex-loansharks-turned-philanthropists or ethically challenged ex-CEOs- or ex-bankers-turned-preachers now telling the financially struggling public that money isn’t everything, or that they’d not make money their god. For the haves to tell the have-nots, it’s utter hypocrisy, to say the least.
Answers and oft-ill-edited half-baked solutions are usually from tutors or teachers-moonlighters.
Tuition: A Necessary Evil for the Nation
Without compulsory tuition or heavy parental involvement, the majority of elementary math students in local schools would likely struggle to score a decent grade in their PSLE math paper.
Singapore’s PSLE math paper with its quota of brain-unfriendly questions looks like a necessary evil that would help define or maintain the “fine” city’s high standard of mathematics regionally and internationally.
FromMid-Year to Mock Exams
This year, Primary 6 students didn’t have to sit for mid-year exams at school, because last year, Education Minister Chan Chun Sing had said that the move would allow them to “focus more on their learning and less on marks.”
In the aftermath of the MOE’s move to do away with all mid-year exams for primary and secondary schools, tuition centers saw a golden opportunity to lure kiasu parents with their mock mid-year exams, whose questions are generally harder (not better) than those set in the PSLE math paper.
Other than parental or peer pressure to excel, most students’ undue stress could be traced to the difficulty of math questions set by neighborhood schools (driven by school rankings) and tuition centers (powered by profits), which are generally harder than those that appear in the PSLE math paper. Yes, they’re the two big culprits that set an unhealthy number of nonroutine questions that often demoralize the kids, by making them feel like they still “aren’t that good in math.”
A Promised Land for Geeks—and Tax Fugitives
Singapore is a “promised land” for those who’re born or blessed with the “mathematical gene” or for those who’d afford a private tutor. However, for the majority of average or math-anxious school children, we can only pray that PSLE math wouldn’t become their bête noire, and that God would keep them motivated and focused as they go through this oft-stressful rite of passage of their schooling years.
I might sound like a mathocrite (short for “mathematical hypocrite”) in giving mathematical or parental advice; nevertheless, let me end with this educational slogan that is worth reiterating, because I believe that the sooner we put it into practice, the less stressful (or peaceful) our life will be: Our math scores or grades don’t define us—in or out of school, and certainly not in life.
It’s an unwritten or unspoken fact that other than local Singapore parents and homeschoolers, both local and foreign math students and teachers are equally kiasu, with the extreme ones being conferred the ignoble title of “Ugly Singaporean.”
In the age of the pandemic, how would you redefine the word “kiasu” in math or math education? Below is one such attempt to relook at this Singaporean “negative trait.”
Singapore’s CPDD’s Primary Math One Textbook
Are we guilty of “mathematical kiasuism” without even being aware of it? Or we think that no one would notice it!
It’s never too late to stop and ask ourselves every now and then whether our actions (or inactions) have made us more or less kiasu.
Are we prone to rationalizing our “selfish” behaviors because after all few folks are really “hurt” or “inconvenienced” by our doings (or “wrongdoings”)? Isn’t it a thousand times easier to spot a “mathematical kiasuist” than reluctantly admitting that we’d be one ourselves, knowingly or unknowingly?
Parents are generally blamed to be super-kiasu. Teachers are über-kiasu. Students are kiasu. What about math editors, writers, or consultants? Are they less so?
Even if math educators are politically apathetic or have near-zero interest in world politics, they can’t discount lightly the irrational thoughts, words, and actions of President Trump and Chairman Kim, because the very presence of these two world “leaders” is two too many—the world is far less secure with these two fellows around, especially when at the push of a nuclear button, millions of innocent civilians would be heading to the other side of eternity sooner than later.
Being neither a mathematician nor a politician, I’d be the most unqualified “math educator” to hypothesize how numerate or “logical” or rational these two disruptive politicians are. However, my educational hypothesis about math education in both North Korea and the US is that North Korea Math is probably less inch-deep-mile-wide than US Math.
On January 2, 2013, I tweeted in tongue-in-cheek the following:
If North Korea were to take part in TIMSS, would it be a surprise if its K–12 #math students outperform their counterparts in the US? #TIMSS
If we factor in the educational budget of each participating country in TIMSS and their local teachers’ limited resources, a politically incorrect ranking would probably look as follows:
There are no ranking errors: Singapore isn’t in the top ten (with or without private tuition).
The Rocket Man and the Mentally Deranged US Dotard
Which “political unthinking” is more dangerous: “Think like Kim” or “Think like Trump”? Who is a more unpredictable or deadly bully? Is “Fatty Kim the Third“—a derogatory term for the well-fed dictator whose own people are starving in the millions—a mere toothless bully vis-à-vis his American counterpart?
Having zero mercy for your political foes, by torturing them and their family members; and poisoning, hanging, or murdering your siblings and relatives, who you suspect are against you.
Or, tweeting and taunting illegal immigrants, radical Islamists, and the LGBT community, which tends to trigger symptoms of insomnia, irrational fear, anxiety, depression, and trauma—the so-called Trump Stress Disorder (TSD)—which unconfirmed reports suggest that they’re more likely to die sooner of heart attack, or to be victims of racial or ethnic persecution.
Kim’s Digital Murder
Below is a quick-and-dirty e-card I tweeted on August 5, 2018 on dictator-murderer Kim, who had his army of hackers or digital terrorists use Photoshop to “digitally murder” his uncle.
If Kim Jong-Un were a radical Muslim-convert, North Korea could become ISIS’s new HQ! #politics #war some.ly/dCh7Y7b
Mathematical Intercourse between Trump and Kim
Another half-baked mathematical e-card I made and tweeted during the Trump-Kim tête-à-tête in Singapore is the following:
On a nonmathematical note,
and the question is: What do you get if you cross a Trump with a Kim? and the answer is: Nothing. You can't cross a dictator with a murderer.
Or, on a mathematical note,
and the question is: What do you get if you cross a mosquito Kim with an overweight Trump? and the answer is: Nothing. You can't cross a vector with a scalar.
A Bromance of Two Dictators
Singapore as the political matchmaker.
Trump claimed that he and Kim “fell in love” after exchanging letters—it sounds like two egomaniacs trying to outwit each other with their insincere sweet words, by stroking each other’s fragile ego.
Trump-Putin, Trump-Xi, Trump-Sisi, Trump-Erdogan, and now Trump-Kim. It appears that dictators do attract each other! A political hypothesis math educators pursuing a PhD in math education might wish to test is: Dictatorship is quadratic!
From Dictator Putin to Emperor Xi to soon-to-be Pharaoh Sisi, Tweeter-in-Chief or Pinocchio-in-Chief Trump, all these power-hungry men have no limits to controlling more yes-men and yes-women, while expecting blind obedience—those who don’t toe the line are likely to be fired prematurely.
In Trump & Kim We Trust
The Symbolic Trump-Kim Meeting in Singapore
Last June, the Singapore government forked out a wallet-unfriendly $20 million to hold the symbolic meeting between President Trump and Chairman Kim.
A Political Math exercise I tweeted then was: Guesstimate how much on average each taxpayer in Singapore “contributed” to footing the $20 million bill for the Trump-Kim meeting. bit.ly/2sVT6jG
Fire and Fury on Kim and His Gang of Killers
@juche_school1
Unlike his dictatorial and murderous grandfather and father who had longed to meeting a US President while they’re still alive, Kim Jong-un is the luckiest of the unholy trinity in finding a “good friend” in Donald Trump.
Political pundits think that North Korea needs more than trade sanctions for its nuclear and missile programs and the threat they pose to the world. A regime change to deliver North Koreans from the tyranny of the Kim dynasty ought to be in the political pipeline.
Unlike Vietnam which tries to threaten Trump and Kim impersonators to stop their “mocking acts,” it’s rather surprising that Singapore didn’t ban these pseudo-tyrants from walking around in town to have some political fun with both locals and tourists.
Abel & Cain 4.0
Thou shalt not kill thy brother.
On the right is an e-card I wrote and tweeted around the time when Kim Jong Un wanted so badly to exterminate his half-brother, Kim Jong Nam.
And below is an approved entry I contributed on “Kim Jong-un and Kim Jong-nam,” which could no longer be publicly accessed online:
Kim Jong-un and Kim Jong-namThe modern-day version of the biblical Abel and Cain, with the chances of the two Kims not meeting their late father and grandfather in hell near to zero.Brothers-rivals Kim Jong-un and Kim Jong-nam serve as ideal plot characters for a Korean spy movie.
Maybe Kim’s hackers felt that the days of its publication should be numbered.
Obama vs. Kim
Unlike a dozen-odd mean tweets on Trump and Kim, any entries on Obama and Kim were in short supply. One I tweeted about them in 2014 in the aftermath of a racist comment on President Obama is the following:
An Unrighteous Deed, IndeedIf Obama is like a "monkey in a tropical forest," then Kim Jong-un must be a "fat pig in Siberia." #North-Korea (@MathPlus on 27/12/14)
Politico-Mathematica à la Singapour
Below are some politically incorrect “political math” questions that teachers could creatively tweak to pitch to their oft-politically challenged students, by conveying the message that math and politics do mix.
1. Parallelism between Two Irrational Personalities
List a dozen parallels between President Trump and Chairman Kim.
For example, Trump and Kim each have been conferred with high-sounding titles for their “contributions” to mankind.
Please call me “Dr. President Trump.”
2. Modeling with Trump and Kim
(a) Trump’s Tweets—Firing by Twitter
Model President Trump’s tweets, which provide a rich source of comedy, into a little juicy formula, which would predict his tweet-before-you-think posts in coming years (assuming that he would still be allowed to tweet behind bars should he be convicted for some political or business collusion with foreign powers).
(b) Kim’s Murders—Murder by Numbers
Formulate a “wicked algorithm” that would guesstimate the number of political critics or foes the Kim dynasty had ordered to be imprisoned, tortured, or killed every year since the Korean War.
3. [Fake] Nobel Prize Winners
What are the odds that the Tweeter-in-Chief and the Murderer-in-Chief might share the coveted the Nobel Peace Prize, if their peaceful actions are perceived to help avert World War III, which could irrationally or maniacally be triggered by pressing their nuclear button?
If someone like Yassir Arafat, who supported terrorism against Israel, could win a Nobel Prize, it’s not far-fetched that both Trump and Kim might be “honored” for fakely bringing world peace to an already-violent world, made insecure by radical Islamists.
4. Political Math
Below are some politico-mathematica questions I posted in recent months.
(a) Political Math: Guesstimate how many false or misleading claims Donald Trump will make by the time he leaves the White House in 2020 (or earlier if he is impeached and imprisoned)—7546 white lies in 700 days. #Singapore #math #politics #estimation #humor (@MathPlus on 30/12/18)
(b) Political Math: Which event has the higher odds of ever happening: Donald Trump winning the Nobel Peace Prize or being canonized as “Saint Trump”? If Arafat can win it, so can Trump! bit.ly/2IwDuP1 #Vatican #peace #sainthood #North-Korea #Singapore #math #miracle #humor (@MathPlus on 18/2/19)
(c) Political Math: What are the odds that if we had had President Hillary Clinton instead of President Donald Trump, she too would have fired the ex-FBI director James Comey, and that her opponents would now be calling for her impeachment and prosecution? #politics #math #hypocrisy (@MathPlus on 3/1/19)
How Trump Does Calculus
(d) Political Math: What are the odds that President Trump would not seek re-election in November 2020 in the aftermath of his impeachment by the House for colluding with Putin and gang? #statistics #SingaporeMath #math #odds #collusion #election #politics #Trump #Putin #humor (@MathPlus on 30/11/18)
5. Murderous Math
Here are some deadly math toughies that may not be apt for politically or religiously immature souls. Caution: Arm yourself, if need be, if you feel that you may be a victim of some form of “mathematical rebellion” from your hostile audience, who may be on a different political or spiritual wavelength as you.
(a) Murderous Singapore Math: What are the odds that there would be a coup in North Korea when Dictator Kim traveled to Hanoi for another symbolic meeting with President Trump? Is China, Iran, Syria, Russia, or Venezuela keen to take him?
Murderous Zeros: If filthy rich Saudis can buy a morally bankrupt fellow like Donald Trump to keep his silence, guesstimate how many “loyal zeros” he is worth to his murderers. #Khashoggi #MBS #murder #guesstimation #math (@Zero_Math on 21/11/18)
Murderous Math: A World Without North Korea—What are the chances that in the aftermath of a North Korean nuclear attack on the US, the Kim dynasty would cease to exist (as the US and allies retaliate to wipe out North Korea from the map)? #war #North-Korea #apocalypse #math (@Zero_Math on 6/12/18)
6. Food & Dog Diplomacy
(a) Singapore Math: What are the chances that North Korea might have a McDonald franchise before having a US embassy? #McKim #humor (@MathPlus on 15/8/17)
McKim was approved on July 13, 2017, and had since been probably “hijacked” by the hackers of the guardian deity of planet Earth.
McKimThe local burger McDonald plans to offer to middle-class North Koreans once Dictator Kim Jong Un and gang give them the green light to operate their first outlet in Pyongyang.The Trump camp thinks that food diplomacy may be a first step to getting the Kim dictatorship to give up its nuclearization program—they've secretly approached McDonald to come up with a North Korean recipe for McKim.
(b) Dog Diplomacy: Chinese Communists give pandas; North Korean Communists give dogs. bbc.co.uk/news/world-asi… #politics #North-Korea #Communism (@MathPlus on 26/11/18)
(c) Faith in god Kim
Kim’s likely promise to Trump: “I want to denuclearize”—as the sanctions hurt and my dynasty must prevail. But like China, Iran, and Russia, where lying and cheating are in their DNA, can the world trust North Korea & the Kim dynasty? #Singapore #politics (@Zero_Math on 10/6/18)
God Has the Final Say in Trump’s Destiny—Not Men or CNN
Let me end on a positive note on how I re-christened or re-defined “President Trump” on 9/11, the date when he’s miraculously elected in 2016.
How God used an ungodly man to effect political change.
Bibliography & References
Monti, R. A. (2018). Donald Trump in 100 facts. UK: Amberley Publishing.
Pater, R. (2016). The politics of design. Amsterdam: BIS Publishers.
A Creative & Disruptive Math Title Coming Your Way*
*Agents keen to represent publishers confident enough to sell an obscene number of If Trump Were Your Math Teachercould contact K C Yan at his e-mail coordinates. A trumpillion thanks!
In recent years, because of the popularity of Singapore math books being promoted and used in many countries, suddenly local publishers seemed to have been hit by an aha! moment. They realized that it’s timely (or simply long overdue?) that they should come up with a general or pop book on the Singapore’s model (or bar) method for the lay public, especially among those green to the problem-solving visualization strategy.
A Monograph à la Singapour
The first official title on the Singapore model method to hit the local shelves was one co-published by the Singapore’s Ministry of Education (MOE) and Panpac Education, which the MOE christened a “monograph” to the surprise of those in academia. Thank God, they didn’t call it Principia Singapura!
A wallet-unfriendly title that focuses on the ABC of the Singapore’s problem-solving visualization strategy
This wallet-unfriendly—over-promise, under-deliver— title did fairly well, considering that it was the first official publication by the MOE to feature the merits of the Singapore’s model method to a lay audience. Half of the book over-praises the achievements of the MOE in reversing the declining math performance of local students in the seventies and eighties, almost indirectly attributing Singapore’s success in TIMMS and PISA to the model method, although there has never been any research whatsoever to suggest that there is a correlation between the use of the model method and students’ performances in international comparison studies.
Busy and stressed local parents and teachers are simply not interested in reading the first part of this “monograph”; they’re looking for some practical teaching strategies that could help them coach their kids, particularly in applying the model method to solving word problems. However, to their utter disappointment, they found out that assessment (or supplementary) math books featuring challenging word problems are a better choice in helping them master the problem-solving strategy, from the numerous graded worked examples and detailed (and often alternative) solutions provided—and most of them cost a fraction of the price of the “monograph.”
A Missed Opportunity for a Better Strategy
Not long after the MOE’s publication, the Singapore public was spoilt with another local title on the bar method. Unfortunately, the editorial team working on Bar Modeling then didn’t take advantage of the lack of breadth and depth of the MOE’s “monograph” to offer a better book in meeting the needs and desires of local parents and overseas math educators, especially those not versed with the bar model method.
Another wallet-unfriendly title that ill-prepares local parents and teachers to mastering the model, or bar, method in solving non-routine word problems
Based on some investigation and feedback why Dr. Yeap Ban Har didn’t seize the opportunity to publish a better book than the one co-published by the MOE, it sounds like Dr. Yap had submitted his manuscript one or two years prior to the MOE’s publication, but by the time his publisher realized that the MOE had released a [better?] book similar to theirs, they had little time to react (or maybe they just over-reacted to the untimely news?); as a result, they seemed to have only made some cosmetic changes to the original manuscript. Sounds like what we call in local educational publishing as an example of “editors sitting on the manuscript” for ages or years only to decide publishing it when a competitor has already beaten them to the finishing line.
This is really a missed opportunity, not to say, a pity that the editorial team failed to leverage on the weaknesses or inadequacies of the MOE title to deliver a better book to a mathematically hungry audience, at an affordable price.
Is Another Bar Model Method Book Needed?
Early this year, we’re blessed with another title on the bar method, and this time round, it’s reasonably affordable, considering that the contents are familiar to most local teachers, tutors, and educated parents. This 96-page publication—no re-hashed Dr. Kho articles and authors’ detailed mathematical achievements—comprises four topics to showcase the use of the model method: Whole Numbers, Fractions, Ratio, and Percentage.
As in Dr. Yeap book, the questions unfortunately offer only one model drawing, which may give novices the impression that no alternative bar or model drawings are possible for a given question. The relatively easy questions would help local students gain confidence in solving routine word problems that lend themselves to the model method; however, self-motivated problem solvers would find themselves ill-equipped to solve non-routine questions that favor the visualization strategy.
In the preface, the authors emphasized some pedagogical or conceptual points about the model method, which are arguably debatable. For example, on page three, they wrote:
“In the teaching of algebra, teachers are encouraged to build on the Bar Model Method to help students and formulate equations when solving algebraic equations.”
Are we not supposed to wean students off the model method, as they start taking algebraic food for their mathematical diet? Of course, we want a smooth transition, or seamless process, that bridges the intuitive visual model method to the abstract algebraic method.
Who Invented the Model method?
Because one of the authors had previously worked with Dr. Kho Tek Hong, they mentioned that he was a “pioneer of the model method.” True, he was heading the team that made up of household names like Hector Chee and Sin Kwai Meng, among others, who helped promote the model method to teachers in the mid-eighties, but to claim that Dr. Kho was the originator or inventor of the bar method sounds like stretching the truth. Understandably, it’s not well-known that the so-called model method was already used by Russian or American math educators, decades before it was first unveiled among local math teachers.
I’ll elaborate more on this “acknowledgement” or “credit” matter in a future post—why the bar model method is “math baked in Singapore,” mixing recipes from China, US, Japan, Russia, and probably from a few others like Israel and UK.
A wallet-friendlier book on the Singapore model method, but it fails to take advantage of the weaknesses of similar local and foreign titles on the bar method
Mr. Aden Gan‘s No-Frills Two-Book Series
Let me end with two local titles which I believe offer a more comprehensive treatment of the Singapore model method to laypersons, who just want to grasp the main concepts, and to start applying the visual strategy to solving word problems. I personally don’t know the author, nor do I have any vested interest in promoting these two books, but I think they’re so far the best value-for-money titles in the local market, which could empower both parents and teachers new to the model method to appreciate how powerful the problem-solving visualization strategy is in solving non-routine word problems.
A number of locals may feel uneasy in purchasing these two math books published by EPH, the publishing arm of Popular outlets, because EPH’s assessment math books are notoriously known to be editorially half-baked, and EPH every now and then churns out reprinted or rehashed titles whose contents are out of syllabus. However, my choice is still on these two wallet-friendly local books if you seriously want to learn some basics or mechanics on the Singapore model (or bar) method—and if editorial and artistic concerns are secondary to your elementary math education.
A no-frills two-assessment-book series that gives you enough basic tools to solve a number of grades 5–6 non-routine questions
References
Curriculum Planning & Development Division Ministry of Education, Singapore (2009). The Singapore model method. Singapore: EPB Pan Pacific.
Gan, A. (2014). More model methods and advanced strategies for P5 and P6. Singapore: Educational Publishing House Pte. Ltd.
Lieu, Y. M. & Soo, V. L. (2014). Mathematical problem solving — The bar model method. Singapore: Scholastic Education International (Singapore) Private Limited.
Composing some Theomatics-related haikus may prove therapeutic for stressful math educators, who are prone to overusing their left part of the brain. Why not let these 17-syllabled verses reactivate some atrophied part of your grey matter? Who knows? This right-brained activity may indirectly help rekindle your mathematical creativity!
The Trinity
The True Living God
Ever Three and ever One
A mystery, indeed!
Christ And Mathematics Education (C.A.M.E)
Come to worship Him
Christ and math education
Join ACMS
Theomatics,Anyone?
Teach math Christianly
As an act of true worship
It sure honors Him
Two Conference Proceedings of the Association of Christians in the Mathematical Sciences (ACMS)
Pi in the Sky
The Biblical pi
Is a rational number
From the Book of Kings
π = 3.14 and John 3:16
So close, yet so far
Rational and eternal
The union is null.
The X-tian Pi
The true Christian life
Is like the contextual pi
Constantly changing
