Bonus Points for Maths at UCD

As reported today in the Irish Times, and on the front-page of the UCD website, the UCD Academic Council have decided to introduce bonus CAO points for Leaving Certificate Higher Level Mathematics for a trial period of four years, commencing in 2012. The idea of a trial period is a welcome addition to the debate surrounding bonus CAO points for Leaving Certificate Higher Level Mathematics (henceforth "bonus points"). Instead of making a decision now in the absence of any (quasi-) experimental evidence, why not experiment with this measure and subsequently make a decison? Of course, the best we can hope for in this case is quasi-experimental evidence; one would imagine that randomising bonus points to different students (or schools) would be potentially very difficult. Not to mention the issue of fairness in the college admissions process. But maybe somebody can come up with a suggestion that would address all of these concerns. In any event, the precise scheme for the awarding of bonus points will be decided in the coming weeks; the objective is to have a single scheme for all institutions that will be awarding bonus points.

The UCD announcement contains a lot of additional content; it states that the introduction of bonus points will "only be successful if it is part of a suite of measures to interest students in mathematics, to ensure the best possible teaching and to support student learning... We will research the impact of bonus points to ensure it is equitable and effective." Specific research questions to be investigated are as follows:

* How much time, compared to other subjects and compared to other students
internationally do students spend on mathematics?

* What is the impact of bonus points on the uptake of higher level mathematics?

* Do bonus points have an effect on equity of access to third level?

The UCD statement recommends the introduction of two examinations; one testing basic mathematical competency, which if passed would secure a pass overall and entry to third level, and another to test advanced mathematics ability. This is as much of a distinct recommendation as introducing bonus points, and arguably a measure that could encourage take-up of Higher Level Maths in the absence of a bonus points scheme. Behavioural economists will recognise the potential role of loss aversion in how Leaving Cert. students decide whether or not to persist with Higher Level Maths. Only 16% of Leaving Certificate students take the higher level paper on the day of the examination but almost 40% of students register with the State Examination Commission to take the paper.

Also, the UCD statement identified three possible dangers:

* That bonus points may contribute to increased competition, or a worsening
points race

* That students who do not require high points might not see bonus points as
much of an incentive to persist with higher maths

* That higher level mathematics would not be available to some students,
particularly in schools in poorer areas, and that this would worsen issues of
access to university. (In 2009, 79 schools had no higher-level candidates
sitting mathematics in the Leaving Certificate. According to UCC Registrar
Professor Paul Giller, about half of second-level maths teachers do not have
maths as a major subject in their degree).

Finally, some outstanding issues in the debate on bonus points are as follows:

(i) Tom Boland, the chief executive of the Higher Education Authority (HEA), has asked whether the bonus points would be awarded only to those who are going on to take a third-level course that requires maths. (According to David Quinn from the Irish Independent: "Those who are good at more literary subjects like History or English will be effectively penalised because they'll find it even harder to compete for university places with those who are good at Maths").

(ii) A HEA report on Career Opportunities in Computing & Technology mentions that Higher level maths and certain science subjects (i.e. physics and chemistry) are seen by many students to be particularly difficult and requiring a level of work that is not conducive to the objective of maximising CAO points. Is bonus points for Maths enough, or should there be bonus points for certain science subjects aswell?

(iii) According to the Irish Independent, the existing courses for which bonus points are available -- including all courses at UL and some courses at DIT -- do not have a higher rate of application from higher-level students, nor do they have a higher number of applicants than courses in the same disciplines where the bonus is not available.

(iv) Also according to the Irish Independent, when bonus points for higher-level maths were removed on foot of curriculum reform in 1993, participation in the subject at higher-level actually increased.

(v) According to David Quinn, journalist at the Irish Independent, "those who are already good at the subject will simply get more points without helping those who are currently failing it".

(vi) Kevin Denny has some comments related to bonus points on Ferdinand von Prondzynski's University Blog: "Is the idea that this initiative will propel more students into technical subjects like science and engineering at third level, thus helping the smart economy etc? This might be a laudable objective but it seems terribly naive to think that having effectively bribed students to do more maths in secondary school that they will just keep going i.e. that this will make them change what they wanted to study at university forgetting that they weren’t that crazy about maths in the first place. Maybe, maybe not but it seems more likely to me that they will take the points and run i.e. study what they wanted to study anyway."

(vii) A separate comment by Kevin Denny on Ferdinand von Prondzynski's University Blog: "There is a good basis for bonus points for maths unrelated to these arguments namely that ability at maths is a better proxy for general cognitive ability. So if we think that more able students should get priority, as the points system does, then a student who does better at Leaving Cert maths than another student is better in general even if they have the same total points (i.e. that student will do significantly better in university)."

(viii) A survey conducted by Engineers Ireland found nearly two-thirds of ordinary-level maths students said they would not opt for higher-level maths even if offered bonus points. The online survey was completed by 122 students who sat higher- or ordinary-level Leaving Cert maths this year.

(ix) On a separate but related point, it has been recommended that Maths should be compulsory for CAO points purposes to ensure students persevere with the subject, according to a report submitted to the Minister for Education Mary Coughlan.

Boys just want to have fun?

RTE today carried the shock news that girls outperform boys in the Leaving Certificate. To be fair the article notes that this is not new and is observed internationally. What I am not aware of is evidence (and no, anecdotes - even from taxi-drivers- do not count) on why this is so.
There is no shortage of theories of course: the feminization of teaching, the feeling of displacement and general uselessness by males due to the evils of feminism etc etc. But this seems an important enough trend to be worth studying and, even, doing something about.

Fairness and efficiency in university admission

My recent paper on the non-effect of fee abolition in Ireland emphasized the socio-economic gradient in secondary school attainment: low SES means low points and therefore a low probability of progressing to university. Fees are a side-issue, at best.
This problem is not unique to Ireland, of course: exactly the same pattern was described in a recent study for the UK. A recent book published by the Brookings Institution suggests ways of dealing with this issue in the US where there is a pronounced SES gradient in the SAT tests. One suggestion is for expanded use of affirmative action programs beyond their traditional emphasis on race. In essence, the idea is that universities take into account the fact that for some people doing well is harder and not because of their innate ability.
Access Programs here, like UCD's New ERA, do this although the scale is necessarily small, see here for an evaluation of its effectiveness we did at the Geary Institute. Some people might take the view that moving away from our simple points-based CAO application system would be messy and expensive. But, on the other hand, the present system is hardly efficient from a national point of view given that it means a huge chunk of our potential labour force is not getting the education that it needs to be at its most productive. Relative to the huge losses arising from not educating our population adequately (for evidence see here), the administrative costs are peanuts.
My own view is that making such adjustments at the point of progression i.e. adjusting the admission criteria to take account of SES, while worth pursuing, is not the best solution. We need to address the causes, not the symptoms of the problem. That is, we need to address the reasons for under-achievement at school level. Access programs do this too as do some government initiatives although their effects are largely unknown.

Grade inflation once again

A recent article in the Irish Times refers to document prepared by the State Examination Commission acknlowledging grade inflation in the Leaving Certificate. This possibility is not new, of course, and has been widely discussed before, sometimes in heated terms. A group of academics at IT Tralee have argued that such inflation exists but many in the education establishment (if I can use that broad term) have taken a different view suggesting a combination of (i) a genuine increase in learning and (ii) an improved facility at taking the tests. By the latter I mean students are better able to "work the system" knowing the various tricks it takes to get high marks. Arguably (ii) should also be regarded as "inflation" to the extent that it does not correspond to an increase in intellectual ability or learning. Distinguishing empirically between these three possibilities ("pure" grade inflation", (i) and (ii)) is a tricky task and I am not sure that we have publicly available data that would allow one to do this reliably. That said, I think the guys at ITT have performed a tremendous public service in their work and are to be commended. Although they probably won't be.
So why should we care? The argument for not having grade inflation is that it corresponds to a lowering of academic standards with the diploma in question proving less useful as a signal of attainment to employers or indeed other educational establishments if they are recruiting the students . If everybody gets an A then its clearly a meaningless achievement. It may have negative effects for international investment if foreign employers are no longer convinced that we have a high quality labour force for them to draw on.
I think its useful to distinguish between different levels of education in this context. If the diploma in question is not an end-point in itself that it surely doesn't matter that much. That is essentially the case for the Junior Certificate now and indeed I believe that exams very future is being questioned. Its clearly not as true for the Leaving Certificate but to a large extent the Leaving has simply become a university entrance exam though this is not exactly what it is designed for. So its unclear to me that grade inflation, per se, at the Leaving level is a big problem. It just pushes up the "price", the points requirements - of course this is largely what economists expect inflation to do.
However it is a matter for concern if this inflation arises from possibility (ii) above. Because then it means we are getting the wrong students i.e. the universities are admitting students who are simply good at the test rather being actually good at the subject. It also imbues bad habits in students where they associate academic success with simply learning various hoops that have to be jumped through. However this is really a much wider question about the curriculum and its assessment.
Where grade inflation, to the extent that it exists, is much more of a concern is at third level. Thats where the concern about employers' perceptions is likely to be an issue. If you believe in efficient markets, rational expectations etc like any house-trained economist you might argue that employers will see through the inflation so its not a problem. They will learn, the argument goes, that an Irish B student is only as good as a German C student (purely hypothetically, I emphasize). I'm not that sanguine about this because of the clumping at the top of the distribution i.e. too many A's. However, there may be ways round this for example by looking at people's rank in the distribution which is inflation proof. Alternatively one can "mark to a curve".
So it seems to me that, in assessing the issue of grade inflation, we need to distinguish between different levels of education with a clear view not only to its extent (if any) but also to why exactly inflation is a problem and to consider assessment strategies that might obviate the problem.

http://www.irishtimes.com/newspaper/frontpage/2010/0607/1224272005470.html

http://www.stopgradeinflation.ie/links_irl.html

http://universitydiary.wordpress.com/?s=grade+inflation

School "league tables"

Ferdinand Von Prondzynski generously invited me to contribute a piece to his University Blog and I write about the arguments for not keeping parents in the dark about their children's school as they are at present in Ireland, a policy that is surprisingly popular amongst educationalists here 'though not with parents (as if their opinion mattered).

http://universitydiary.wordpress.com/2009/12/01/better-by-leagues/

Longer school days

The amount of human capital a person is usually proxied by years of education. But of course one can vary the number of days of education per annum or the number of hours per day. The number of days in school in Ireland is comparatively low it appears. So what would be the effect of lengthening the school day? This paper, for Chile, shows that it keeps adolescent girls out of trouble - literally: an increase in full-day municipal enrollment of 20% reduces the likelihood of teen motherhood by 5%

Delaying the Bell: The Effects of Longer School Days on Adolescent Motherhood in Chile
Diana Kruger & Matias Berthelon

http://ftp.iza.org/dp4553.pdf

Price elasticity of school attendance

This paper uses sibling discounts at Catholic schools to measure the elasticity of demand for private schooling. This has some relevance here as the recession in Ireland is rumoured to be inducing a significant fall in demand for private schools. What the price-responses are I don't know. If supply is inelastic, it should be pretty big.
One of the authors of the paper, Susan Dynarski, will be visiting UCD soon for the launch of the New ERA report.

Cheaper By the Dozen: Using Sibling Discounts at Catholic Schools to Estimate the Price Elasticity of Private School Attendance
Susan Dynarski, Jonathan Gruber, Danielle Li
The effect of vouchers on sorting between private and public schools depends upon the price elasticity of demand for private schooling. Estimating this elasticity is empirically challenging because prices and quantities are jointly determined in the market for private schooling. We exploit a unique and previously undocumented source of variation in private school tuition to estimate this key parameter. A majority of Catholic elementary schools offer discounts to families that enroll more than one child in the school in a given year. Catholic school tuition costs therefore depend upon the interaction of the number and spacing of a family's children with the pricing policies of the local school. This within-neighborhood variation in tuition prices allows us to control for unobserved determinants of demand with a set fine geographic group fixed effects while still identifying the price parameter.
http://d.repec.org/n?u=RePEc:nbr:nberwo:15461&r=edu

The American High School Graduation Rate: Trends and Levels

James J. Heckman and Paul A. LaFontaine: Geary WP/28/2008. The authors establish that:

(a) the true high school graduation rate is substantially lower than widely used measures;
(b) the U.S. graduation rate peaked in the early 1970s;
(c) majority/minority differentials are substantial and have not converged over the past 35 years;
(d) lower post-1970 rates are not solely due to increasing immigrant and minority populations;
(e) their findings explain part of the slowdown in college attendance and the rise in college wage premiums;
(f) growing high school graduation differentials by gender help explain increasing male-female college attendance gaps.

Secondary School Financing Debate

Sean Byrne from the Business Faculty at Dublin Institute of Technology discusses the secondary school financing debate in today's Irish Times.