math contest | Yan's One Minute Math Blog

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.

From Mid-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.

Grade-consciouslessly yours

Here are some pointers I would share with my students at the start of a secondary math olympiad programme. In Singapore, most mathletes attending these enrichment classes are usually selected by the form or math teacher, who tends to choose the best three math students from each class to form a small group of 15 to 20 participants. They would then graduate to represent the school after attending a six-, eight-, or ten-session training programme, depending on the mathematical needs and wants of the school.

• Take your time! Very few contestants can solve all given problems within the time limit. For instance, in the Singapore Mathematics Olympiad (SMO), both at the junior and senior levels, [unconfirmed] feedback based on different schools’ results hints to the fact that those who can win a medal hover around five percent.

Interestingly but disturbingly, an SMO mathlete who can get six or seven out of 35 questions correct may still win a bronze medal, revealing how unmoderated olympiad math papers had been in recent years, going by the abnormally high rate of failures among the participants. This is primarily due to the fact that few, if any, faculty members who set these competition papers, are familiar with what elementary and middle school teachers are covering in local schools.

• Try the “easier” questions first. The questions aren’t set in ascending order of difficulty. It’s not uncommon to see easier questions in the second half of the paper.

• Olympiad questions don’t “crack” immediately. Be patient. Try various approaches. Experiment with simple cases. Working backwards from the desired result in some cases is helpful.

• If you’re using a contests book, and you’re stuck, glance at the “Hints” section. Sometimes a problem requires an unusual idea or technique.

• Even if you can solve a problem, read the hints and solutions. The hints may contain some ideas or insights that didn’t occur in your solution, and they may discuss intuitive, strategic, or tactical approaches that can be used elsewhere.

Remember that modeled or elegant solutions often conceal the torturous or tedious process of investigation, false starts, inspiration and attention to detail that led to them. Be aware of the behind-the-scenes hours-long dirty mathematical work! When you read the modeled solutions, try to reconstruct the thinking that went into them. Ask yourself, “What were the key ideas?” “How can I apply these ideas further?”

• Go back to the original problem later, and see if you can solve it in a different way, or in a different context. When all else fails, remember the reliable old friend, the guess-and-check strategy (or heuristic, as it’s being arguably called in Singapore)—for instance, substituting the optional answers-numbers given in an MCQ into some given equation or expression may yield the answer sooner than later.

Meaningful or creative problem solving takes practice, with insightful or elegant solutions not being the norm. Don’t get discouraged if you don’t seem to make any headway at first. The key isn’t to give up; come back to the question after a day or a week. Stickability and perseverance are two long-time buddies for full-time problem solvers.

Happy problem solving!

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