Primary 6 maths exam question too tough

From ‘Don’t hurt pupil’s self-esteem with tough questions’, 7 Sept 2011, ST Forum

(Stephen Lin): AS A PARENT, I wonder whether some teachers who set exam papers are really interested in gauging the ability of pupils. Sometimes it seems as though they are simply intent on making life miserable for them.

Take a look at this maths question in a recently concluded Primary 6 preliminary exam:

‘Three halls contained 9,876 chairs altogether. One-fifth of the chairs were transferred from the first hall to the second hall. Then, one-third of the chairs were transferred from the second hall to the third hall and the number of chairs in the third hall doubled. In the end, the number of chairs in the three halls became the same. How many chairs were in the second hall at first?’

I challenge readers to solve this problem in five minutes, which is all the time a Primary 6 pupil has to do it. I challenge school principals to do it, without the help of equations, which Primary 6 pupils aren’t equipped with yet.

Setting such difficult questions serves no educational purpose – it only undermines the pupils’ self-esteem.

The writer didn’t say how long he took to solve this himself, but the ‘chairs in a hall’ problem is a puzzle that can’t be solved by mental sums alone unless you have a precocious maths whiz for a kid.  At first glance you would think this calls for algebra, though I’m not sure what’s the status of algebra as an ‘easy way out’ technique now.  In 2006, algebra was frowned upon as a cheat-sheet to the so-called ‘model method’ (When rules foil creative students, 26 May 2006, Today). In any case, a sturdy grasp of fractions and logic was all that’s needed to uncover the answer.

A sense of incompetence could explain the frustrations of a parent who would think that any question that they can’t solve is equally, if not more challenging for their own children. I suppose such brainteasers were never meant to be relevant to real-world situations; if I had to arrange chairs equally among three halls I’d forget about the fractions and sort them out manually with mere approximation. The real world has no place, nor time, for precision in fractions. Useless maths questions are more a gauge of one’s adeptness in application of heuristics and mental agility, which also trigger certain neural networks in the child’s brain which have become rusty with obsolescence in adult brains like mine. Our utility of primary school maths has been confined to splitting bills (inclusive of GST) with fellow diners, figuring out insurance pay-outs, or computing if mass purchases of discounted items amount to real savings. Other than such everyday puzzles which affect our bank accounts, we’re hardly ever going to make a meal out of sharing candy or distributing water into cylinders, as seen in past papers below. I’m even having trouble reciting the x12 multiplication table now.

More hall chairs in 2007

This was a question posed in a 2009 PSLE paper, using the typical ‘sharing sweets’ scenario which, supposedly, all Primary school kids could relate to:

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4. How many sweets did Ken buy?

Suffice to say I would have flunked this paper even with a calculator, an abacus and physical sweets and chocolates in front of me.   Looking at the modern  solution, not only do you need to know your Excel tables, but bar graphs too. If you take a closer look at these problems, it’s not just technical maths being tested, it’s also the child’s grasp of the  subtleties of the English language and his ability to visualise text to facilitate the crafting of a solution. A well designed question should be coherent in terms of space and time i.e you know where and when the chairs are being moved, or who has the sweets or chocolates at any one time, otherwise all the complex differential equations in the world won’t get you anywhere.

It’s not easy to raise the standards of maths without overly stressing our kids to depression or even suicide, and likewise moderating difficulty levels without letting everyone off too easy. It’s inevitable that in the midst of this juggling act, there will be balls tumbling out of the routine, and even a single, obligatory ‘killer’ question to deter perfect scores will drive a top-student to depression given the ridiculous demands parents impose on their children these days. It’s no wonder we have such a high rate of kids with mental disorders, and parents sending kids to tuition even during holidays.

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21 Responses

  1. As I read this entry, I was reminded of something I’ve read on Greg Mankiw’s (a Harvard professor of economics) blog.

    In response to a student’s question about the extensive use and teaching of mathematics in economics PhD programs, he stated that in some ways, mathematics was used to sort the geniuses from the only smart.

    In my experience as well at the post graduate level, most exams usually includes a really challenging question which wasn’t covered in the syllabus, though the topic matter (but not method of solution) was. The idea was to see who could take what was taught and apply it in a creative way to tackle a novel problem. The examiner usually expects less than a quarter of the class to ‘get it’.

    The point is not to prevent perfect scores. The point is to design the exam in such a way is that the person getting the perfect score deserves it, making attainment meaningful. (And you could then make the rest of the exam sufficiently easy as not to fail half the class 🙂

  2. The 9876 chair question is very easy question. In fact, this is a Primary 4 standard and can be easily solved using 1-dimension models. For P6, models are more complicated. Conclusion, the question is a give-away question

  3. The world is a global village where more knowledge is been coined every day by day, moreso u and i knw that children are doing things that you can’t even imagine that is to say now days children are fast learners. The examers who set this questions can’t even answer almost all the question but they feel they are doing a good job rather causing brain storming to the pupils… EDUCATION IS THE KEY TO SUCCESS

  4. quite easy to me

  5. the chair question has only 1 step how can it be 5marks?

  6. The “sharing sweets” question is so easy, and I’m P6.

  7. is the answer 3292 i solved in like 2 mins

  8. 2ez

  9. 1)4938 chairs
    2)68 sweets

    Am I right?

  10. Jim’s original number of chocolates = 14u
    Ken’s number of chocolates received = 4a
    Formed equation: 7u-18 = 4a (equation 1)

    Ken’s original number of sweets = 2a
    Jim’s number of sweets received = u
    Formed equation: a-12 = u (equation 2)

    Substituting equation 2 into equation 1:
    7u-18 = 4a (equation 1)
    7(a-12)-18 = 4a -substituting-
    7a-84-18 = 4a
    3a = 102
    a = 34
    2a = 68

    Therefore, Ken bought 68 sweets.

  11. I am a primary 6 pupil and i think the answer is 3292

    my steps: 9876 divided by 3 =3292
    3292 divided by 2 x 2

    • Second one is 68

    • oops sorry i put the end for first question

      correct answer should be…3703.5?

    • i try again ah

    • i am very sure it is 4115

      trust me, i got top in level for math

    • working:

      hall1 12u
      hall2 12u } 9876
      hall3 12u

      hall3 at first- 12u/2 = 6u

      hall1 at first- 12u x 5/4 = 15u

      hall2 at first- 12u + (12u – 6u – ( 15u – 12u)) = 15u

      9876/3 = 3292

      3292 x 15/12 = 3292 x 5/4
      =4115

      SAYS WHO THIS UNDERMINES (whatever that means) OUR SELF-ESTEEM?!
      In fact, if all 18 questions are like this, the bell curve would be differenr and the passing score might be 25/30-45 while the A might be 65-70/75 and the A* might be 76-100! Thus the number of fails will be only about 1.something percent!

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