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

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.

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.