Adding it up

This year's Leaving Cert results are out and the post mortem has brought out all sorts of moaning about the state of mathematics in Ireland. The government reacted with the decisiveness that is to be expected of all politicians; launching an review conveniently handled by a subordinate so the Minister doesn't actually have to deal with the crisis du jour. While there is a high failure rate at Ordinary level, the rates of honours grades on the Honours papers is up presenting the mutually exclusive problems of a huge gulf in education standards or grade inflation.

There have been various causes and solutions proposed. The lack of qualified teachers is certainly a problem. The debate over the value of the Project Maths syllabus continues. The Minister is using the results to emphasise the importance of rolling out the new syllabus (despite results only being "marginally better"), but detractors say that reducing the course content is papering over the cracks and will make things worse in the long term.

I feel some actual analysis backed up with numbers has been missing from the discussion. First of all; let me start with there is no grade inflation. The percentage of students getting over 75 CAO points from mathematics has actually decreased over the past five years from 9% in 2006 to 7.5% this year. Overall the past ten years, the percentage of students getting over 75 points has ranged from 7.2% to 9%, so there isn't exactly a huge amount of difference there.

What is causing the appearance of grade inflation is that the numbers taking honours mathematics is falling. It dipped under 16% for the first time this year. This is down nearly 3% over the past 6 years. It will be very interesting to see how the bonus points for honours maths affect this next year and into the future. I'll go into why I don't think this is the correct solution in a later post. I don't know how it's affected applications for university courses; that data I don't have to hand. The mean amount of CAO points from mathematics is the lowest of the three compulsory subjects at 34.5, compared to 55.1 in English and 41.9 in Irish.

From the the Leaving Cert data it is clear that the rate of failure in mathematics is startling. However, any notion that this is increasing is unfounded, but that doesn't mean it's not an issue. Over the past ten years, an average of 15.88% of all students sitting leaving cert mathematics across all levels receieved a grade that netted them 0 CAO points. I count CAO points as a more meaningful metric as that's what matters for university applications and I didn't want to count pass grades in foundation. There is a weak downward trend over the last ten years, but this year's results left 15.48% without any CAO points from maths.

Interestingly enough, the failure rates, mean CAO points etc. in Irish are quite similar to mathematics. The only big difference is the much higher rate of students taking honours, but it is the statistics for Irish are bolstered by the growing number of students not taking this "compulsory" subject. 14.6% of students sitting the leaving cert didn't sit Irish, up 6% from ten years ago. From the coverage I've read the dire situation Irish finds itself in has been glossed over. In fact the press release from the Dept. of Education praises the increased proportion getting honours in Irish, ignoring the growing problem of students not taking the subject or its effects on the rate of success they're so happy to talk about.

So what does this all mean for mathematics in Ireland. This post is getting a little long, so I'll leave that for later. We need to ask ourselves some hard questions about what outcomes we want for those at the top, middle and bottom of the spectrum and does the current courses cater for all those needs. 

PREVIEW: I think major change is needed. I really mean major. So drastic that I know there is zero chance of either a risk averse government with zero cash to spend or the teaching unions would go for it. 

Debating, Sexual Discrimination & Numbers

There's been a lot of chat recently about how women are under-represented and under or over performing at IVs, Worlds etc. depending on what result you want from it. So I've decided to do what any good number cruncher would do in this scenario; I'm going to put some numbers on it.

For this I'm using the tabs from the recent National Law Debates in Galway and from the Cork IV in December. This is as they are the two most recent tabs I have and I am confident that I was able to identify female names from male names (I wouldn't be so confident with a Worlds or Euros tabs). I also used the total speaks for the competition, not the individual speaks. I could make up some valid reason, but it's 99% because I'm lazy and it's easier to work with.

IV	Male Mean	Male Standard Deviation	Female Mean	Female Standard Deviation
Cork	362.2577	28.45621	361.3617	25.18145
Galway	372.2174	21.89606	370.8286	23.90482

What does this teach us? Apart from the fact that judges at Galway were more generous, it clearly shows that there is no meaningful difference between an average male or female speaker. The boxplot of the cumulative results from both IVs also shows this in a nice visual way. It also shows that the 25% and 75% quartiles lie essentially at the same point, showing that the distributions are essentially the same. A t-test gives the probability of there being no difference in the actual means as 0.772; for there to be a statistically significant difference, that number would have to be less than 0.05.

So one thing is abundantly clear from this; there is no discernible bias towards male speakers from judges.  One thing that has to be remembered here though, is that these were all mostly Irish judges. My own admittedly stereotyped view of the world would suggest that a bias is more likely to exist in not-so-liberal countries and thus would be more prevalent at Worlds (this is the angle I'm selling to try to get a research grant).

Where a difference does appear is in participation numbers. In both IVs the proportion of male to female speakers is approximately 2:1 (32.7% female in Cork, 33.6% male in Galway). Given the small total sample size, the 95% confidence interval (i.e. the range of possible values) for the true proportion of female debaters is between 27.3% and 39.35%. Clearly this is where there is a problem.

As a white, heterosexual, private-schooled male (and thus not part of any oppressed minority), I'm not going to spend too much time discussing the various options available to the debating community to help solve this problem. Just to say that when it comes to participation, I think the onus is much more on the individual societies to up their game in recruitment, training and retention than on changing the rules of the game. There clearly is nothing wrong with the game itself which handicaps women.