Are Parents Right to Be Upset about How PSLE Mathematics is Set and Marked?

We’re sure you’ve heard about the recent saga surrounding the way SEAB marks PSLE mathematics papers after a handful of students who usually score well for their school mathematics papers scored badly in the PSLE. We give our thoughts on this, analyse the PSLE mathematics paper, and offer you tips on helping your child to score all in our latest blogpost.

I. Controversy 1: Unrealistically Challenging Questions

For years, the Sin­ga­pore Exam­i­na­tion and Assess­ment Board (SEAB) has drawn much flak from dis­grun­tled par­ents. Its alleged sin? For set­ting unre­al­is­ti­cal­ly chal­leng­ing ques­tions in the PSLE Math­e­mat­ics paper.

In fact, did you know that a num­ber of Singapore’s PSLE Math­e­mat­ics ques­tions were deemed so inno­v­a­tive­ly mind-bog­gling that they gained inter­na­tion­al noto­ri­ety? These ques­tions have fueled the long-stand­ing debate as to whether the PSLE is too dif­fi­cult or too ear­ly for a twelve-year-old child. Let us revis­it some of these ques­tions that put Sin­ga­pore Math­e­mat­ics on the world map.

2017 ‘Ribbon’ Question
2019 ‘Semi-circles’ and Number Pattern Questions
2020 Shapes Pattern Question
2021 ‘Helen & Ivan’ Question

Undoubt­ed­ly, these ques­tions are chal­leng­ing. And they were delib­er­ate­ly meant to be so. These ques­tions are what we call “AL 1/2 dif­fer­en­tia­tors” because, as the name sug­gests, they were designed to dif­fer­en­ti­ate stu­dents who would score AL 1 and AL 2 from the rest. In the PSLE Math­e­mat­ics paper, a fair per­cent­age of 10% of the paper is reserved for such “AL 1/2 dif­fer­en­tia­tor” ques­tions. Most stu­dents are not expect­ed to get them right.

Time and time again, the Min­istry of Edu­ca­tion has said that it only expects a small minor­i­ty of stu­dents to be able to score an AL 1 or 2. The con­tro­ver­sy – unre­al­is­ti­cal­ly dif­fi­cult Math­e­mat­ics ques­tions – aris­es only because of the pur­suit of aca­d­e­m­ic excel­lence in Sin­ga­pore. Most par­ents and stu­dents cov­et the mouth-water­ing prize that is an AL 1 or 2. Con­se­quent­ly, many par­ents are up in arms when the chal­lenge of ‘AL 1/2 dif­fer­en­tia­tor’ ques­tions are posed to their chil­dren in the PSLE.

Instead of being over­ly crit­i­cal, par­ents should under­stand how the PSLE Math­e­mat­ics paper is usu­al­ly struc­tured. This is so that they can see the log­ic behind the way the paper is set.

PSLE Math questions difficulty table

As seen from this table, the PSLE Math­e­mat­ics paper is intend­ed to be easy to pass but dif­fi­cult to score. What par­ents should realise is that a very respectable score can still be achieved if their chil­dren have their Math­e­mat­ics fun­da­men­tals prop­er­ly ironed out. This is because the remain­ing 90% of ques­tions are not only pre­dictable but also man­age­able with the right amount of prac­tice.

While there is noth­ing wrong with prepar­ing for “AL 1 / 2 dif­fer­en­tia­tor” ques­tions, par­ents and stu­dents should not obsess over them. It is not a wise strat­e­gy to focus too much on them at the expense of the oth­er type of ques­tions which require mas­tery of the main­stream top­ics to be able to solve. Not hon­ing one’s com­pe­ten­cy in main­stream top­ics is a major pit­fall in the PSLE. We would even go so far to say that it is the chief rea­son why stu­dents may under­per­form for PSLE Math­e­mat­ics. Under­per­form­ing for the PSLE Math­e­mat­ics brings us to the lat­est round of con­tro­ver­sy that is plagu­ing the SEAB.

II. Controversy 2: No Transparency of how PSLE Mathematics Papers Are Marked

This year, to the sur­prise of many, the PSLE Math­e­mat­ics paper did not require stu­dents to per­form any men­tal gym­nas­tics. The con­sen­sus is that the ques­tions were fair and with­in the expec­ta­tions of teach­ers, stu­dents and par­ents. As such, you may have thought that the SEAB final­ly steered clear from the spot­light of con­tro­ver­sy.

Unfor­tu­nate­ly, that was not the case. The SEAB just could not catch a break.

Short­ly after the release of the PSLE results, Chan­nel News Asia (CNA) report­ed that 11 par­ents of chil­dren from Nan Hua Pri­ma­ry School wrote in to ques­tion the mark­ing stan­dard of the PSLE Math­e­mat­ics paper as well as the appeal process of the PSLE exam­i­na­tion. Their gripe was two-fold.

First, their chil­dren were all stel­lar stu­dents of Math­e­mat­ics, con­sis­tent­ly scor­ing “95 marks and above for their math exams in school”. How­ev­er, for the PSLE, they under­per­formed and puz­zling­ly only man­aged to obtain “AL3, AL4 or AL5”. Alarm bells were raised as to whether chil­dren were fair­ly giv­en cred­it for the solu­tions they had used to tack­le the prob­lem sum ques­tions. Sec­ond, the appeal process lacks trans­paren­cy as dur­ing the appeal, the SEAB would only reveal whether the marks of every sec­tion were summed up cor­rect­ly. They would not release stu­dents’ answer sheets for par­ents to scru­ti­nise.

While we empathise with the frus­tra­tion of these 11 par­ents, there are good rea­sons why stu­dents’ answer sheets are kept under lock and key. It is like­ly that the SEAB wants to keep the num­ber of appeal cas­es low and man­age­able. Releas­ing answer sheets could open the flood­gates and see an increase in par­ents lodg­ing appeals because they want to scru­ti­nise how their chil­dren had fared for the PSLE and police how the SEAB marks their children’s papers. This is an unde­sir­able out­come for two rea­sons. First, it would be a logis­ti­cal night­mare to respond to hun­dreds if not thou­sands of appeals. Sec­ond, giv­ing par­ents too much infor­ma­tion to the extent that they can scru­ti­nise and chal­lenge how ques­tions are marked would con­ceiv­ably lead to more dis­agree­ments and argu­ments. This would not be an ide­al state of affairs for any­body. Par­ents would be fur­ther away from obtain­ing the clo­sure they seek while the SEAB could risk hav­ing its rep­u­ta­tion sul­lied and its cred­i­bil­i­ty undermined.As cliché as it is, some­times we just need to trust the sys­tem. A pos­i­tive is that when inter­viewed by CNA, SEAB was open about the present saga and did not shy away from address­ing the crit­i­cism head on. The SEAB has assured Sin­ga­pore­ans that it has the best team in place to ensure “PSLE papers are set accord­ing to the syl­labus at appro­pri­ate stan­dards”. More­over, “any solu­tion [includ­ing the use of alge­bra] which demon­strates the cor­rect under­stand­ing and appli­ca­tion of math­e­mat­ics con­cepts and skills as request­ed by the ques­tion will be giv­en full cred­it”. In rela­tion to appeal cas­es, the SEAB deploys “an inde­pen­dent senior mark­er” who would “con­duct a thor­ough review of the mark­ing and check the accu­ra­cy of mark entries”.

These assur­ances are the best the 11 par­ents are going to get from the SEAB. Of course, the mys­tery still remains unsolved: how was it pos­si­ble that so many stel­lar stu­dents fell so far down in one exam­i­na­tion?

As allud­ed to ear­li­er, it could very well be the case that these stu­dents were not rock sol­id in their grasp of the main­stream top­ics. Yes, they might have scored well for their school exam­i­na­tions. But school exam­i­na­tions can nev­er test every­thing. Under each top­ic in the PSLE Math­e­mat­ics syl­labus, there are so many dif­fer­ent ques­tion types. It is entire­ly plau­si­ble that the stu­dents might have been con­fi­dent in the ques­tion types their school had test­ed but not as con­fi­dent in the ques­tion types the PSLE hap­pened to test on that day. To put it in anoth­er way, per­for­mance in school exam­i­na­tions is not always reflec­tive of how a stu­dent would fare for the PSLE.

III. A Little Word of Advice

Alas, all roads lead back to Rome. The con­tro­ver­sies sur­round­ing PSLE Math­e­mat­ics stem from the unde­sir­abil­i­ty of obtain­ing a far-from-ide­al score for the paper. The solu­tion to these con­tro­ver­sies is straight­for­ward and the same. Have your child put the bulk of his or her effort into mas­ter­ing every con­cept cov­ered by the main­stream top­ics, and test your child’s appli­ca­tion of these con­cepts by prac­tis­ing as many dif­fer­ent ques­tions as pos­si­ble. By doing this, your child should find the major­i­ty of the PSLE Math­e­mat­ics paper a breeze and would not need to fret too much over the “AL 1 / 2 dif­fer­en­tia­tor” ques­tions. This is because your child would be in a firm AL 2 / 3 posi­tion, which, as has been men­tioned ear­li­er, is a very respectable score.

Only when your child is supreme­ly con­fi­dent in the main­stream top­ics should he or she attempt to take on the ulti­mate chal­lenge. Con­trary to pop­u­lar belief, “AL 1 / 2 dif­fer­en­tia­tor” ques­tions can be pre­pared for and taught. For exam­ple, chil­dren can be taught heuris­tics to solve chal­leng­ing prob­lem sums. Sim­i­lar­ly, they can also be taught how to iden­ti­fy pat­terns in num­bers and shapes and to visu­alise how dif­fer­ent shapes can be rearranged and formed to solve seem­ing­ly mind-bog­gling ques­tions.

At the risk of sound­ing like a shame­less plug, stu­dents enrolled in our Math­e­mat­ics pro­gramme at Think Teach begin to learn heuris­tics as ear­ly as Pri­ma­ry 3. Our stu­dents are also intro­duced to basic numer­i­cal, geo­met­ri­cal and spa­tial visu­al­i­sa­tion tech­niques which grad­u­al­ly increase in com­plex­i­ty. All these skills are taught in tan­dem with expos­ing our stu­dents to every sin­gle ques­tion type that could be test­ed under the main­stream top­ics. When the years roll by and the PSLE arrives, our stu­dents are primed and ready for what­ev­er the PSLE throws at them.

Since the begin­ning, this is how we have cho­sen to pre­pare for the PSLE and why we have nev­er found the PSLE Math­e­mat­ics paper con­tro­ver­sial. 2022 was a year of reprieve and so too was 2021. The PSLE Math­e­mat­ics exam­i­na­tions have nev­er been so easy for some time now. We believe that the reduced lev­el of dif­fi­cul­ty in the PSLE Math­e­mat­ics exam­i­na­tions of 2021 and 2022 was due to the COVID-caused learn­ing dis­rup­tions stu­dents in those years had faced. How­ev­er, now that we have become used to liv­ing with COVID-19, we pre­dict that the PSLE Math­e­mat­ics exam­i­na­tion will return to its usu­al lev­el of dif­fi­cul­ty.

That said, par­ents need not be afraid. Appre­ci­ate tha the vast major­i­ty (up to 90%) of the PSLE Math­e­mat­ics exam­i­na­tion is filled with man­age­able and pre­dictable ques­tions. Plan your child’s attack strat­e­gy by first secur­ing the low-hang­ing fruit before turn­ing your atten­tion to high­er-lev­el ques­tions. This way you ensure that those “AL 1 / 2 dif­fer­en­tia­tor” ques­tions do what they are sup­posed to do – deter­mine only whether your child scores an AL 1 or 2 and noth­ing low­er than that.

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