Bonus points for maths

The Irish Independent has an interesting article on bonus points & not just because they quote me.

Bonus points for maths: the new policy

It has just been reported that the Irish Universities Association have agreed a policy whereby students taking Higher Maths in the Leaving Certificate and getting at least a D will get an extra 25 points.
Aside from concerns about the possible effects on equality of access raised by Kathleen Lynch , I am curious about what incentives this new scheme provides. So the idea is to get more doing Higher Maths and presumably doing better all round. Often "non-linear pricing" generates perverse incentives.
So at the high end there is no additional incentive: an A is worth more than a B by the same amount. I would have thought there was an argument for increasing the bonus as one gets a higher grade. Say a student wants to get a certain amount of points from maths. In the past he could have got it from say a C-. Now a D will do (I'm not sure of the exact numbers). Might he be tempted to put in less effort, settle for a D instead, and re-allocate effort to other subjects? So one might predict a clumping of the distribution around D for this paper.
Take another student who is thinking of taking Higher Maths but is worried about failing. The relative penalty to failing has increased (the E-D gap in points) so a risk averse student might think "no thanks". There might be an argument for encouraging students to take the chance by giving some additional reward for getting an E (i.e. a smaller bonus).
Finally,lets say the policy is successful in attracting more students to doing higher Maths. Presumably these will be the people who are moderately good at maths. So on the lower paper we get fewer A's and B's and more D's on the higher paper. Why is this something to be so pleased about anyway?
When the distribution of grades is published next year, it will be a nice little project to compare before and after.

Outstanding Issues for the Bonus Points Scheme, and the Points System More Generally

"The manner in which students are admitted for third level education and in particular the points system have become matters of increasing public controversy in recent years." This sentence could have been written in recent months; it was in fact written in the late 1970's, and read before the Statistical and Social Inquiry Society of Ireland on the 24th May 1979. It is an excerpt from "The Leaving Certificate and First Year University Performance" by M.A. Moran and M.J. Crowley (Department of Statistics, University College Cork).

A couple of weeks ago, I outlined all the information that I was able to find on the introduction of bonus points for maths at UCD. Since then, I have developed some thoughts on outstanding issues for the bonus points scheme, and the Irish points system (for college entry) more generally. While the bonus points scheme is somewhat separate to the overall points system, and potential changes to the points system have been discussed before on this blog, the two areas of discussion make for natural bed-fellows. It would also be a shame to lose sight of what is happening in the wider points-system, given the attention currently being given to the topic of bonus points.

In relation to the issue of bonus points, I think that the debate would benefit from more focus on the following:

(i) The overall Project Maths initiative
(ii) The potential introduction of two maths examinations; one testing basic mathematical competency (at the end of Fifth Year), which if passed would secure a pass overall and entry to third level, and another to test advanced mathematics ability
(iii) The availability of higher level maths in schools throughout the country
(iv) The claim that half of second-level maths teachers do not have maths as a major subject in their degree
(v) Whether the bonus points would be awarded only to those who are going on to take a third-level course that requires maths
(vi) Whether there should be bonus points for science subjects in the Leaving Cert.
(vii) Whether maths should be compulsory for CAO points purposes

More broadly in relation to the overall points system, I have the following comments. I know that the points system, despite its flaws, is agreed by many to be the fairest and most transparent way that college places have been allocated to date in Ireland. Thinking about what can actually be changed, my suggestion is that we need more continuous assessment (CA). However, here's the twist --- this CA should be marked anonymously, just as the exams are. This would serve to take away the pressure of the "Big Day", and the CA could even be designed to encourage critical thinking, while at the same time being a fair and transparent assessment method. As things stand, I think that too much importance is given to one exam on one day for each subject.

Finally, I also think that having four (instead of three) compulsory choices might be fairer, in that it would be viewed as a more level playing-field. Looking at Leaving Cert. subject choice between 1997 and 2005 (based on analysis that I conducted before), we know that most students choose Geography, Business Studies, French and Biology for their optional subjects. The following are the most popular subjects, in order. (I should point out that after Accounting, the numbers taking any subject are quite low):

1. Geography
2. Business Studies
3. French
4. Biology
5. Home Econ.
6. History
7. Art
8. Construction
9. Physics
10. Chemistry
11. German
12. Accounting

I should also point out that there is a sizeable fall of about 50% in the numbers taking any subject after Home Economics. We can see that the top four (Geography, Business Studies, French and Biology) include one of Hist/Geog, one "Business" subject, one language and one science subject.

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.