Wednesday, April 14, 2010

Maths or English?

Sometimes it is not easy to set questions that distinctively test on a single subject, especially when understanding the question that is expressed in some written words.

Here is a primary 2 question:
Natasha plants 6 trees on each side of a square garden. There is a tree at each corner of the garden. How many trees are there altogether?
Depending on different understandings, these may be the solutions given by students:
(a) 6 at each side and a square has 4 sides, 1 at each corner and a square has 4 corners. Thus, there are 6x4 + 1x4 = 24 + 4 = 28 trees.


(b) If those at the corners are considered to be at two sides, then it would be
(b1) 6 at each side, but each tree at corner is counted twice. Thus, there are 6x4 - 1x4 = 24-4 = 20 trees.
(b2) 6 less 1 at one of the corner at each side. Thus, there are (6-1)x4 = 5x4 = 20 trees.
(b3) 6-2=4 at each side but not at corner, and 4 at corners. Thus, there are 4x4 + 1x4 = 16+4 = 20 trees.

The answer from solution (a) is different from solutions (b). However, all solutions are correct based on the interpretation it started with. Getting a wrong answer in the above solutions is not an indication that the student's Maths is poor, but may be the student's English is poor. Thus, it would be good if the maths teacher can mark both as correct, with comments explaining the correct interpretation, or even a note to the English teacher to explain further. Or, if majority of the students get it wrong, then may be need to also consider if it were the teacher's English that is poor.

By the way, in solutions (b1)-(b3), we can appreciate the equality of the expressions 6x4 - 1x4, (6-1)x4 and 4x4 + 1x4. I encourage solving same problem by at least two approaches. It may seem a waste of time but the time spent is worthwhile. First, this is a form of checking as when two different approaches arrive at the same answer, the answer is more likely to be correct. Second, doing so helps one to appreciate mathematics better.

Sadly, are there students so free to work out different approaches on the same question? Actually, there are some lucky ones. Those who are good are likely to be approached for assistance by their classmates and have opportunities to study how others have approached the questions. It is likely that he will not only be exposed to different approaches but also be aware of many mistakes that could be made. Thus, the good [and helpful] ones will become better in the process of helping others.

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