Those who defend bonus points for Maths and those who claim that all subjects should be valued equally ought to be on the same side of this argument.

In my previous post, I wrote about the standardised nature of the coverage that accompanies the release of Leaving Certificate results each year. One of the rare sparks of novelty in that analysis appeared in 2012, following the reintroduction of bonus points for Maths. Since then, the same question has been frequently asked – are bonus points for Maths are “fair”.

Those who are inclined to think they are unfair typically argue that education should embrace the full range of students’ talents and should place equal value on equivalent achievements across all subjects (for example, see [1]). As a principle for holistic education, this idea has real appeal. But it simply does not follow that, say, a H3 in Maths should get the same number of points as a H3 in any other subject because there is no reason to think that those identical scores represent equivalent levels of achievement.

For example, two athletes may both clear a bar that is 2.5 meters high but if one athlete is competing in the high-jump and the other in the pole-vault, no-one would ever suggest that their achievements were comparable[2]. Two people may race 100 meters in 40 seconds but, if one is swimming and the other is running, no-one would claim that their performances should be valued equally.

It simply is not possible to compare absolute outcomes without considering the differences between the circumstances in which those outcomes took place. Just as it is unreasonable to compare the height cleared by high-jumpers and pole-vaulters it is unreasonable to compare a given grade in Maths to the same grade in another subject without asking what effect the differences in the syllabi and marking schemes might have had.

Athletics has an obvious, simple and elegant solution for this problem. When it comes to giving medals, performances are not measured in absolute terms, they are measured relative to what other people competing in the same discipline were able to achieve. First place gets the gold medal, second the silver and third the bronze. This is the case for the pole-vault and the high-jump and the 100m sprint and the 100m freestyle. Each discipline gets the same number of medals and is valued equally.

In the leaving certificate, an analogous solution would be to ensure that, for all subjects, the top X% of students receive a H1, the next Y% would receive a H2 and so on.

It is probable that many people assume that marking schemes, being arbitrary, have already been adjusted so that this is broadly the case. But if we can agree that this *ought* to be the case then we need only remember that a government department determines the marking schemes to realise that it probably isn’t.

In fact, for Irish and English, the proportions of students getting a H3 or higher are 22% and 24% respectively. For Maths, it is just 10%.

For Irish and English, the proportions of students getting a H6 or higher are 45% and 69% respectively. For Maths, it is just 28%.

The evidence is clear and if we start from the position that each subject should be valued equally then, based on this data, the only conclusion we can draw is that Maths must receive extra points – not as a “bonus” and not as an incentive but as redress or compensation for the fact that, to get any given grade in Maths, you need to outperform more of your peers than you would to get the same grade in Irish or English.

That said, it is also clear from the data that bonus points for Maths were not introduced to balance out the differences in points received for it and other subjects – or, at least, if that was the motivation then their implementation was an abject failure.

To illustrate what I mean, let’s break down the distribution of points for each of the core subjects into quintiles – the 1^{st} quintile being the top 20% of performers in each subject; the 2^{nd} quintile being the next best 20% and so on – and compare the average points obtained by each quintile, in each subject.

Looking at average points received for Maths excluding bonus points, there are clear disparities. Average points received by every quintile in Maths are between 5 and 15 points lower than those received by the corresponding quintiles for Irish. They are between 10 and 24 points lower than those received for English.

When we include bonus points, the first quintile of Maths students now enjoy an average 15-16 point advantage over their counterparts in the first quintiles of Irish and English. However the 3^{rd}, 4^{th} and 5^{th} quintiles in Maths receive absolutely no benefit whatsoever and still remain at a 5-to-24 point disadvantage relative to those quintiles in the other core subjects.

Based on this data, it’s hard to argue that the current bonus points scheme is fairer than not awarding bonus points at all. However it’s also clear that, in effect, Irish and especially English already receive “bonus points” – at all levels of relative achievement – by virtue of being marked less harshly than Maths.

If we are to have a proper conversation about whether bonus points are fair, then it must be one that recognises that for the vast majority of students Maths is, in simple terms, harder than other subjects.

Average points received | Maths (incl. BP) | Maths (excl. BP) | Irish | English |

Quintile | ||||

1^{st} |
99 | 74 | 83 | 84 |

2^{nd} |
56 | 46 | 61 | 68 |

3^{rd} |
33 | 33 | 41 | 57 |

4^{th} |
20 | 20 | 25 | 43 |

5^{th} |
3 | 3 | 8 | 19 |

All | 42 | 35 | 44 | 54 |

All ex 1^{st} quintile |
28 | 25 | 34 | 47 |

*Table 1: Average points by quintile for Leaving Cert. Maths, Irish and English*

[1] “*All students are equal – it’s time to abolish the 25 bonus points rule*”; Irish Independent, 18/05/2016

[2] For some context, the world records for the high-jump and pole-vault are 2.45m and 6.16m respectively

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