Is it fair to ask a 12 year old “How heavy are eight $1 Singapore coins? Six grams, 60g, 600g or 6kg?” for a maths question?

The PSLE question that has parents crying foul – what is the weight of 8 $1 coins? 1) 6g 2) 60g 3) 600g 4) 6000g.

“This is not a Math question!”

Yes it is. Math is more than just arithmetics and pushing numbers around. Our Mathematical syllabus includes Estimation and Tessellation (both taught at Primary 5), as well as patterns and Geometry (taught since Primary 1).

“How many children have an idea how much a coin weigh? This is unfair!”

It is not. Children should have already gone through an activity at either Primary 2 or 3 on Weight, where they have to weigh coins and other objects and got to understand what the various weight is like.

Ultimately, the PSLE is an exam meant to stream out the scholars from the farmers. The ability to answer certain questions would stream out those meant to be at the top. We seriously need to let our children know that it is not the end of the world if their PSLE score is not the most fantastic in the world, and to teach them resilience and ability to accept and move on. Our present bunch of students are too weak emotionally, and will be crushed by the tougher East Asian children who have gone through more stressful educational system than ours do.

In short, yes, it is fair to all such a question. They have enough prep in such questions.

 

The Language of Mathematics

Along the learning curve, some students in Singapore have learnt how to do the various operations of addition, subtraction, multiplication and division, but have no idea what they really mean. Hence, when they come across word problems, they get stuck. Not only that, but it is amazing how many times I have tried to explain concepts to the students, to find out that their understanding of Mathematics concept is seriously weak.

I showed the students 2 apples and 2 oranges. I told them that an apple and an orange had been “taken away”, and asked them what  I must do. Those students weak in concept actually suggested a division, telling me that they should “divide” the 2 apples and 2 oranges by 2. While the end result was the same, the fact that the concept was wrong spells trouble, and I had to throw in the curveball by asking them the result were I to have THREE apples and 2 oranges instead? The stumped look told me a lot.

I had to rephrase, by asking the students what would happen were they to have $50 and I “take away” $20? This time more of them understood, and I took the opportunity to let them know that when we want to “take away” or “remove” something, we use the Mathematical operation of subtraction. So when I “take away” an apple and an orange, we should use subtraction, not division.

Another concept that often got confused is that of multiplication and division. When three boys have a total of 15 apples, how many would each boy have if they shared them equally*? Some students actually did a multiplication operation and gave me 45 apples altogether. I have to actually show them that when we want to do “equal sharing”, we are doing a division operation, by drawing pictures of apples and circling them on the board.

As I reflect on the situation, I can only say that Asian children are trained very well to do the operations quickly and accurately (unlike many of their western counterparts). When it comes to deep thinking, and associating the concepts behind the operations, Asian children appear to be somewhat weaker in general. I believe this could be the result of harried teachers, trying to complete an extremely tight syllabus, before a class of 40+ children, in time to prep and cram the students for their exams.

It can be really difficult for a teacher to really find the time to do all these, and yet have a life beyond the classroom.

————

*I am very insistent on Mathematical questions having this part “shared equally” because it is NOT wrong for a student to indicate that the three boys have 10, 4 and 1 apples respectively if they share them, if the “equally” is missed out.

Interpreting the Correct Preposition in Word Problems

When I first started teaching more than 13 years ago, I remember parents complaining to me that Singapore Mathematics is more a test of the child’s language abilities than his mathematical abilities. I must admit that what he said has more than a grain of truth. The two word problems below illustrate how a single preposition can make a world of a difference in the solution.

Ravi has 20 balloons. He wants to share them with 4 of his friends. How many balloons will each of them get?

Ravi shares the balloons with 4 of his friends, resulting in 5 persons sharing the balloons. The Mathematical statement should be 20 ÷ 5 = 4. Each of them gets 4 balloons.

Ravi has 20 balloons. He wants to share them among 4 of his friends. How many balloons will each of them get?

A simple switch of prepositions has changed the scenario. Ravi is not sharing in the balloons, he is sharing them among his 4 friends. The Mathematical statement should be 20 ÷ 4 = 5. Each of his friends gets 5 balloons.

As a teacher who has brains for both languages and mathematics, however, I am inclined to think that the latter question was poorly set. The word “share” implies that the owner is also a part of the equitable sharing of balloons. Not only that, but in order to ensure no child comes up with a solution where each child has a different number of balloons, all of which add up to 20, I will make sure I add the phrase “share equally”. I believe a question should be set precisely so that the language is clear what the child should do.

Children in Singapore have it tough indeed, with questions like these to tackle under time pressure in our examinations.