Wednesday, October 21, 2009

On PSLE math and the child

The Primary School Leaving Examination (“PSLE”) is a major examination taken by all schoolchildren (aged about 12 years) at the end of their sixth year in primary school. It is widely regarded as an important examination because a child’s PSLE grades determine whether he or she would qualify to enter a desired secondary school of choice.

The PSLE comprises 4 subjects (English, mother tongue, math and science), and this year, many schoolchildren experienced difficulty with the math paper. In particular with this question:
“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?”
Now, any good paper should contain at least one or two difficult questions so that we may distinguish the more able candidates. But difficult questions should be fair, and the issue is: is this a fair question that schoolchildren can reasonably solve within their ability? Put in another way, are the schoolchildren sitting for the paper equipped with the skills to solve this math question?

It is this author’s understanding that primary school teachers teach their students to solve such math questions using a model diagram and units method. However, a number of teachers privately admit that the model diagram and units method is difficult to comprehend and cumbersome to utilise, and that most schoolchildren are unable to master it.

Is this the only method to solve the math question? No. The math question is easily, commonly and elegantly solved using algebra and simultaneous equations. These are taught when a child enters secondary school education. They are not taught at the primary school level because algebra is perceived to be of a higher level math and most primary schoolchildren are not ready for it.

But it appears that the schools will generally only allow students to solve such math questions using the model diagram and units method. Any other solution (including algebraic solutions) will be penalised or discouraged.

Nonetheless, a good education system should be flexible, and a good educator should allow students to use any valid method to solve a question, not just one method. Schools ought not insist on a particular method to solve a question (especially if the method is cumbersome, will (in this author’s opinion) have little real world application, and confuses schoolchildren).

The crux is this: if primary schoolchildren are largely confused by the model diagram and units method and hence unable to cope with such math questions, they are evidently not equipped with the necessary skills to solve such questions and it would not be fair to expect them to do so. Why not focus instead on establishing a solid grounding in other more appropriate math topics within their level, and only test them on such math questions at a later stage when they are ready to handle them?

By the way, the answer to the math question (as worked out by this author using algebra and simultaneous equations), is 68. Did you get it right?


  1. Just as our 12yr olds dont understand and utilise algebra the way we do,
    neither do we have their facility with models.
    No correct answer achieved through algebra can be marked down. Unfortunately wrong answers attained through this method will garner no marks for working.
    The difference with the model method is that a wrong answer will still get some points if there was a careless error in the working.
    Yes there are several ways of skinning cat.
    Leave it to the educators to decide which way is best at each stage of development.
    Their decision is not made randomly.

  2. Why restrict the students to only one single method? That's so dead and inflexible, and it might shape the child's mind into such as well. I think so long they can solve the problem and get the answer right, any method should be allowed.

  3. Actually, i think the concept of algebra and higher mathematics should be reserved for A levels or even later. We should move probability and statistics to secondary or even primary school.
    Think about it, if you are not an engineer, you probably never need to use algebra.

    But in almost any profession, you will need to understand statistics and probability. Strange our schools (and not just in Singapore) are so hung up on algebra.

  4. Let the number of chocolate Jim bought be X
    Let the number of sweets ken bought be Y

    After giving each other half, they have 0.5X and 0.5Y

    Jim eat 12 sweet, ratio of sweet to chocolate become 1:7
    0.5x = 7(0.5y-12) ----> (1)

    Ken eat 18 chocolate, ratio of sweet to chocolate become 1:4
    0.5x-18 = 4(0.5y) ----> (2)

    Solving the simulation equations,
    X = 308, Y = 68

    Ken bought 68 sweets.

    Model diagram how to draw?