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.

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