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?
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
