On the morning that this year’s Leaving Certificate results were published, there was a headline in one of the free Dublin papers proclaiming that more than 20 percent of students had failed mathematics. I was certainly aware that we had problems with mathematics in Ireland, but surely it couldn’t be that bad?
On the morning that this year’s Leaving Certificate results were published, there was a headline in one of the free Dublin papers proclaiming that more than 20 percent of students had failed mathematics. I was certainly aware that we had problems with mathematics in Ireland, but surely it couldn’t be that bad?
A quick read revealed that it wasn’t. The correct failure rate was 10.2 percent, but the error made by the journalist, and presumably approved by the editor, was perhaps more revealing about the true position of mathematics nationally. They reasoned that since 4.5 percent of students had failed the higher level paper, 5.7 percent had failed the foundation level and 12.3 percent had failed the ordinary level paper, it must follow that 4.5 + 5.7 + 12.3 = 22.5 percent of students had failed mathematics. The enormity of such an error and its ability to reach the front page illustrates clearly that many of us are functionally innumerate.
Is there a crisis in mathematics education, or not? A good starting place to examine this might be the OECD Programme for International Student Assessment, or PISA. Mathematics performance of 15 year-old students across the range of OECD countries was measured in a detailed study in 2003 and in a shorter follow-up in 2006. A comparison of our performance at the highest level shows us struggling, with only 1.6 percent of Irish students reaching this level compared to the OECD average of 3.3 percent. PISA may not be foolproof, but such a mediocre performance cannot be easily dismissed, particularly when one looks at our current social and economic aspirations.
Another obvious source of information on the state of our mathematical health is the Leaving Certificate results. Even a casual glance at the statistics will show that something is amiss: along with Irish, mathematics is the only subject that has a Foundation level course. Both also share the dubious distinction of having fewer candidates at higher level than they have at ordinary level.
So, is the Leaving Certificate mathematics programme the root of problem? Recently it seems we have shifted the blame, with many commentators now blaming the inadequacy of preparation at primary level. No doubt the next shift will pass the blame to the parents, who will, in turn, blame the secondary teachers who taught them – and so we will develop an infinite loop with nobody to blame at the end.
Fortunately, there has been some more serious reflection and three primary issues have been identified. Firstly the existence of multiple goals for mathematical education, secondly, the so-called “new” mathematics with its emphasis on abstraction which has dominated secondary teaching since the 1960s and finally, the fact that mathematics is taught with relatively little emphasis on problem solving.
The first point is a serious issue and one that has been, I believe, somewhat neglected. Mathematics as a scientific discipline is built upon a ‘pyramid of knowledge’ and, somewhat akin to music, it needs people to be technically proficient before one can even begin the process of approaching the real core of the subject. Thus, the key skills of numeracy, algebraic manipulation and the other basics need to be learned early and must become second nature.
Fortunately, these too are part of the skills-set needed for most citizens, who interpret the world around them using basic numeracy, data interpretation and problem solving. Advocates of the foundation level programme may argue that this is precisely the purpose of such a course but, unfortunately, this seems not to be true. If it were, everyone would be obliged to take the programme and at a much earlier age.
In the 1980s I tried to argue that the mathematics curriculum should be split right from the beginning of second-level education, with one part focussing on the basic skills and the other on the deeper, more abstract ideas. I wasn’t advocating that students take only one half of the programme, which would be a recipe for disaster, but I was trying to emphasise the importance of both.
Whether we like it or not, the best way to place emphasis on a topic is to examine it rigorously. I still believe that such a splitting of the programme offers a way forward. It is perhaps useful to look at the various reports by the Chief Examiners over the years. A typical comment occurs on the 2005 Leaving Certificate (Higher Paper) Report: “Firstly, foundation skills in mathematics were often not up to the standard required. … Secondly, weaknesses continue to stem from inadequate understanding of mathematical concepts and underdeveloped problem-solving and decision-making skills.” Many such reports are available but little has changed – the new Project Maths initiative may be a worthy one, but how long can we wait to begin tackling the really serious issues on a truly national basis?
Aside from the natural inertia of a bureaucratic system, we also have a problem with the teaching of mathematics. At primary level, many teachers are themselves uncomfortable with mathematics and at secondary level many teachers of the subject have little background in the subject. They are thrown in at the deep-end and struggle. How many honours mathematical graduates enter the teaching profession each year? I don’t have access to official figures, and indeed, the Department of Education & Science may not have such figures, but I would wager the number is very small indeed.
There is, however, another factor that is not so openly discussed. As I mentioned in the opening paragraph, we seem to be rather innumerate as a nation. But worse than this, we seem proud of it. Quite distinguished academics have often told me that they were “useless” at mathematics. It seems that in Ireland it is perfectly acceptable to boast that one was a mathematical failure; contrast this with the likely fate of anyone who dared to even hint that “X is illiterate”! If children’s difficulties in mathematics are met with a collective response “don’t worry, I was useless at mathematics and it never did me any harm”, is it any wonder that we continue to languish behind in mathematical performance?
Professor Brendan Goldsmith is research
director and former President, DIT
