Bad choices for mathematics? (Eugene Gath)

It has been widely agreed for some time that there is a serious problem regarding the teaching of mathematics in Irish schools. In response to a review of maths teaching, a new initiative called Project Maths was launched in 2008 and is being gradually rolled out across post-primary schools. It is often described as the main solution to the mathematics learning issues. Here Dr Eugene Gath, Lecturer in the School of Mathematics and Statistics in the University of Limerick, offers a different view.

It is widely accepted that there is a crisis in Irish school-level maths, from early primary school up, including unqualified teachers, students leaving school innumerate, under-challenged students, low numbers taking Leaving Cert higher level maths, not to mention the low standard of maths among many of those students who actually do get an honour. Many readers may be aware of Project Maths, either through their own children or professionally. It was set up to address this crisis and is essentially the new (new, new) maths for our schools.

What it attempts to do is essentially eliminate all choice from Leaving Cert Maths and to ask exam questions that are ‘unseen’, thereby stopping the cherry-picking of easy questions and reducing the rote learning that is currently rife. That said, it is in my view a retrograde move. The main reason is that the proposed syllabus constitutes a major ‘dumbing down’ of the current syllabus as well as a sea-change in emphasis. There are five strands – one of which is classical geometry (which disappeared 40+ years ago), and another is probability and statistics, the content of which has been at least doubled. The syllabus is a complete distortion of the mathematics required at third level.

What disappears is most material on calculus – a lot of differentiation, almost all integration, as well as all vectors, all matrices, discrete maths and much more. This material is the bread and butter of engineers, scientists, economists, financiers, computer scientists and not least statisticians. Yes, it is difficult, but almost every country exposes their students to the intellectual training and rigour of calculus at second level; soon our students will not know the integral of cosine. The universities assume familiarity with this material in first year maths classes; the impact will be to force the ‘dumbing down’ of first year courses, not just in maths but also physics, applied maths, mechanics etc., thereby, for example, pushing topics such as Laplace Transforms, vector analysis and PDEs much later into the curriculum. Today some of our best students have difficulty sustaining an algebraic calculation over a few lines; the new syllabus would reduce the amount of time spent doing detailed calculations even further. The engineering professional bodies have been supportive of Project Maths, but this was prior to the publication of the full syllabus. Do they realise the extent to which this syllabus runs counter to their goals? I wonder would they rather our Leaving Cert students be well versed in theorems of Euclid and conditional probabilities or in simple integration, vectors and matrices?

Another matter of concern is that Project Maths is very resource intensive.  It is more hands-on and uses lots of ‘laboratory’ equipment that will be needed in every school (e.g. students will be throwing dice to learn about probability). It will also require the retraining of most maths teachers. Even if it results in higher participation rates, at what cost in terms of content and standards? Surely there are better ways to spend any additional funding of mathematics. The government would do well to incentivise maths teaching as a career, as in other countries. The attitudes of students would change with a proper rewards system (such as bonus points, compulsory questions etc.).

Project Maths is not the answer to most of the problems mentioned, it is seriously misguided and it could be very damaging.

 

Advertisement

Introducing bonus points for mathematics

Readers of this blog will know that I have previously addressed the issue of whether students should receive bonus points for higher level mathematics in the Leaving Certificate. A number of universities, including DCU, had previously decided to award bonus points, and this week the same decision was also taken a little later by University College Dublin. A consensus is therefore beginning to emerge that it may be desirable, by way of an experiment, to assess whether such a step can improve the performance of Irish secondary students in mathematics and science and therefore improve the take-up of maths and science programmes at third level.

It would be fair to say that while a consensus is emerging around this, it is not necessarily one that is supported with any great enthusiasm. There is a widespread feeling that a number of issues in secondary education need to be addressed, including the quality of mathematics and science teaching and the adequacy of teacher training in this area. Some academics fear that the introduction of bonus points will take the pressure off the education system to address these matters, which ultimately are much more significant. Nevertheless, it has been accepted that bonus points may make a contribution, and that they are worth a try. These and other issues have ben addressed in a previous discussion on this blog, and also more recently on the blog of UCD’s Geary Institute.

One other thing might be noted in passing. According to the Fine Gael website, the party’s spokesperson on innovation and research, Deirdre Clune TD, has ‘called on Education Minister Mary Coughlan to immediately extend similar schemes in other third level institutions so that all fifth year students can know where they stand’. In making this statement she seems not to be aware of what other universities have already decided, and moreover she seems to be under a misapprehension as to what the role of the Minister is in this regard. Whether bonus points are applied is entirely a matter for the universities, and the Minister has no role in the matter other than to raise it as an issue – which in fairness to her she has done.

Mathematics not adding up

On Wednesday of this week the Tánaiste and Minister for Education and Skills, Mary Coughlan TD, issued a statement congratulating students on the Leaving Certificate results. In this statement she also used the opportunity to address the issue of bonus points for Higher Level Mathematics, as follows:

‘The Tánaiste has made her preference for the introduction of a points bonus for achievement in higher level mathematics clear and has written to the higher education institutions in that regard. The higher education institutions are, as a result, currently considering the question. Some institutions have already confirmed their intention to introduce such a points bonus and the question is under active consideration in others. Further details will emerge over the coming weeks, when institutions have completed their internal considerations.’

However, the ink had hardly dried on her statement (or whatever the equivalent computer age metaphor might be) when the Irish Independent reported that two universities, University College Cork and NUI Galway, had decided not to back the proposal. A decision by UCD is still awaited.

This means that, whatever the universities’ position on bonus points will be, it will not be a united one. For myself, while I remain to be persuaded that bonus points will make a significant practical difference, I am aware that key stakeholders of the universities (including the government, but also industry) are very anxious to see that this change is adopted; and I am not sure how wise it is to reject that.

It remains clear that this country’s ability to attract investment will depend to quite an extent on having a population that is recognised as being highly numerate and science aware. Therefore any steps that could prompt students to pursue higher maths are welcome. The absence of a clear and joint approach by the universities in this matter will not do us any favours.

Edging towards bonus points for mathematics

According to a report in the Irish Independent, all the universities except University College Dublin have now agreed that there should be bonus points in the Leaving Certificate for higher level Mathematics. UCD may also come to the same decision, but it will need to be taken by its Academic Council, which is not due to meet until September.

The issue of bonus points has been covered previously in this blog. While most academics would take the view that this is not the complete solution to low levels of mathematics attainment by secondary students, it is at least potentially part of the answer. What will need to be impressed upon the government, however, is that the situation will not become fully satisfactory until problems at second level have been addressed, including the problem of inadequately trained and motivated mathematics teachers. The risk is that Ministers and officials may think that the universities’ action in applying bonus points at the Leaving Certificate level provides the solution and that no further government action is required. We must not allow that view to gain traction.

Keeping up the correspondence

I gather I have a letter from the Tánaiste (Deputy Prime Minister) and Minister for Education, Ms Mary Coughlan TD. It’s not that I actually have any piece of paper that I took from an envelope signed by the Tánaiste; rather, I read in the Irish Times this morning that she has written to me (and the other university presidents), urging us to admit students to university programmes even where they have failed mathematics in their Leaving Certificate examinations.

Of course the whole question about how we should handle the maths issue is a vital one, and as has already been pointed out in this blog, one of the options we are looking at bonus is the idea of points for students who take higher mathematics. But these are also complex issues, and require careful handling; we don’t just want students to do mathematics, we want them to succeed in it. I guess we’ll need to consider the Tánaiste’s suggestion carefully.

But now my problem is this: by what method do I respond to her? I presume the polite thing to do would be to ask the Irish Times to publish my response in their pages, so maybe I should work on that basis. The alternative would be to suggest that such exchanges are better conducted using the postal services, or by all means email, on a personal basis. In the end I prefer that.

PS. I did the Tánaiste an injustice! The issue was mentioned by her in a letter which was otherwise about bonus points for Higher Level Mathematics a few weeks ago!

The mathematics test

In a previous post on this blog I looked at the issue of whether there should be bonus points for students passing the higher level mathematics examination in the Leaving Certificate. This has been a contentious issue in the university sector, and as I indicated last time, I am myself open to this proposition, as it may compensate for the perceived disadvantage for students who opt for this subject. I might add, however, that many (perhaps most) academics do not share this view.

The idea of bonus points is however getting some traction, with professional bodies giving it strong support – and now the Minister for Education and Skills, Tánaiste Mary Coughlan has also come out in support of the idea. This is how the Irish Independent reported her comments made at the annual conference of the Teachers’ Union of Ireland (TUI):

‘Addressing the Teachers Union of Ireland (TUI) annual conference in Co Clare yesterday, Ms Coughlan jumped the gun on the report and gave her backing to a bonus-point system aimed at encouraging more students to take up higher-level maths. “While I will await and consider the views of the expert group,” she said, “it is my view at this point that we could send a clear signal to our second-level student population with the introduction of a CAO points bonus for achievement in Leaving Certificate maths.’

It needs to be said (as I have mentioned before) that the Minister has no special powers in relation to this issue. Both she and her predecessor have contributed to the discussion in terms suggesting that they can determine or order what points should be awarded to students. In reality this is entirely a matter for the universities, and while the Minister can of course offer a view, she cannot enforce it in any way, at least not directly. That said, clearly the universities should engage with the issue, as indeed they are doing; the Irish Universities Association has been considering it for a while.

Whether we are able to motivate students to take mathematics is one of the key issues of our day, and our educational reputation internationally and our ability to attract global investment to come here both depend on it. It’s time to be seen to be taking this matter seriously.

Bonus points for mathematics?

As many readers of this blog will know, for some time now the issue of how to persuade more Irish students to take Higher Level Mathematics for the Leaving Certificate (Irish final school examinations) has been a topic of heated debate in Ireland. Part of the backdrop is that the number of those taking this option has been declining for some time, and according to an Irish Times report last summer is now below 20 per cent.

The key consequence of this trend is that the 80 per cent who have chosen not to pursue Higher Mathematics will be excluded from most science subjects at university, and this in turn will have a serious impact on our capacity to attract international investment. Some professional bodies have responded by urging the universities to offer bonus points for Leaving Certificate Mathematics, thereby providing an incentive for students. On the other hand, the Minister for Education and Science, Batt O’Keeffe TD – rather misunderstanding his role and powers in this regard – has indicated that he would not authorise such bonus points. Others, including some well-known academic commentators (including TCD’s Sean Barrett) argue that this should be a free market and that politicians and university leaders should not interfere: students should study whatever they want to, without inducements or pressures to do something different.

It may be worth noting that bonus points for mathematics have been applied in an equivalent setting in Australia.

I confess that I am one of those inclined to favour bonus points; but I am open to argument that this is wrong. My chief purpose in raising the issue here is to encourage a response from readers, as I am seeking to consider the arguments right now before contemplating further action.

For what it is worth, however, I do not believe that CAO points represent a ‘free market’, but rather a highly distorted one. I believe that the major cause that makes students turn away from mathematics is its perceived difficult nature, and I tend to think that we may need to compensate for this. I do however also accept that bonus points for mathematics may distort the CAO score if the student uses them to study something unrelated to maths: say, law. But there may be ways of addressing that.

And finally, what we are looking at here is a temporary expedient. The real solution, in my view, is to overhaul and apply radical changes (not excluding complete abolition) to the CAO points system. But that won’t happen overnight.

As I have said, comments on this would be very welcome.

Not adding up

One bit of statistical information that we have just discovered is far more damaging than all the figures on economic slowdown and unemployment. In today’s Irish Times education editor Sean Flynn reports that fewer than 20 per cent of students have opted to take Higher Level Mathematics in the Leaving Certificate examinations beginning this week. He expanded on this subject a little more on broadcaster RTE’s Drivetime programme.

As the response to my last post on innovation indicates, there is some disagreement amongst observers as to the value of an innovation agenda and the elements of innovation that would have the most beneficial effect on our economy. But nobody can seriously doubt that our plans for recovery are in trouble if we have such a large proportion of students who are excluding themselves from any possible education at university level in science and technology. 

What is more, we have known about this problem for a long time, and as a country are not addressing it with the kind of urgency that is now needed. Despite the Minister’s opposition (and it has to be noted again that this actually falls outside his jurisdiction), the universities do need to look again at the possibility of bonus points for Mathematics. And the government in turn needs to address the issues raised in the report of the Task Force on the Physical Sciences, which it commissioned but which it has largely ignored since its publication in 2002. The latter report is somewhat out of date, but many of the recommendations are still good.

The country’s future is at stake here. We need to do more to address this issue.