How to gauge students performance in national exams
The Sunday Nation
Nairobi,
16 January 2011
While launching the 2011 form one selection process this week, the Minister for Education announced that a new method would be used where pupils from public primary schools would be given larger proportion of the available places. This is in addition to the existing regional quota system.
Whereas the old method was criticised as favouring children from richer families that can afford private schools, there is now an outcry against the new public/private quota system: it is said to be punishing hard work. In the circumstances, it becomes necessary to seek for a system that gives equitable weight to both sides.
It is a mistake to assume that all public primary schools are disadvantaged and therefore they need affirmative action. Similarly, it is also not true that all the private ones are well-equipped. Therefore, a blanket public/private quota system is unfair.
In my view, we should focus on the individual pupil’s performance instead of the type of school attended. “Performance” here, does not simply mean the marks scored in the exam; it also includes the rank of a pupil within the school.
Therefore, to gauge performance, we need to incorporate both the actual marks scored and pupils’ rank in their school. This can be done by developing a ranking index. The exam marks are then multiplied by the index to get the “performance” score.
The ranking index may be developed as follows: first, rank the students in order of marks scored in the exam; secondly, for each pupil, subtract their rank from the total number of candidates in the school; thirdly, divide the result from step two by the total number of candidates in the school.
For example, the ranking index of the top student in a school that has 100 candidates would be (100 – 1) divided by 100; that is 0.99. On the other hand, the index for the top candidate in a smaller school of 50 would be (50 – 1)/50 = 0.98.
By the same formula, the ranking index of tenth pupil in the larger school would be (100 – 10)/100 = 0.9, while that smaller one would be (50 – 10)/50 = 0.8.
To get the performance score, we multiply each pupil’s marks with the corresponding ranking index. For example suppose the top pupil in the larger school has 410 marks, the performance score would be 410 x 0.99 = 406. If the top candidate in the small school has 430 marks, the performance score would be 421.
There wouldn’t be much change for the top students, but when we get to the 10th rank, the situation might change. The tenth pupil in the large school may have, say, 400 marks making a performance of 400 x 0.9 = 360.
The tenth pupil in the smaller school may have, say, 420 marks. This works to a performance score of 336. The positions are now reversed!
One curious result from this method is that the last ranked pupil in any school will always get a performance score of zero! Is that good or bad? I will let you be the judge.
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