Mathematics for All?

Random maths stuff to scare Simon Jenkins.

One of the things I noticed in the news from the UK last week was PM Rishi Sunak’s suggestion that all school students in England should study mathematics to age 18. I’ve emphasized in England because responsibility for education is devolved to the governments of Scotland, Wales and Northern Ireland so what the Prime Minister on this matter says has no bearing outside England.

Anyway, two of the obvious fundamental problems with Sunak’s proposal are:

1. How will making mathematics a compulsory subject at age 16-18 fit within the current system of A-levels, in which most students study only three subjects?
2. Who is going to teach all the extra lessons required when there is already a shortage of STEM teachers?

I’m not sure of the extent to which Sunak has thought through this plan. I suspect it’s nothing more than the usual sort of half-baked idea that his type of politician likes to float in order to distract attention away from serious problems elsewhere (e.g. NHS, the economy, strikes, etc). The suggestion has generated a wide range of responses, including from the Guardian’s resident idiot Simon Jenkins who, as usual, misses the point spectacularly when he writes:

Like many of my generation, I did basic and advanced maths to age 16. This embraced complex algebra, trigonometry, quadratic equations, differential calculus, the use of logarithms and old-fashioned slide rules. I cannot recall ever using one jot of it, all now forgotten. 

I’m tempted to suggest that if Simon Jenkins hadn’t forgotten what he’d learnt at school he might write less garbage, but I won’t. I also studied these things to age 16 and, because I chose a career in science, I have used all of them (except slide rules, which were obsolete, but including logarithms). Of course not everyone will feel the same.

I should however point out that as well as Mathematics and science subjects I also studied Geography, History, French, Latin, and English Literature to O-level (which I took at age 16). I don’t think I have ever “used” any of these since, but I do not for one minute regret having studied them. In my opinion education is not just about the acquisition of things to use, but represents a way of opening the mind up to a range of different ways of thinking. Mathematical reasoning is not the only way of thinking but it is important, as is the process involved in learning another language. As I have written on this blog many times before, education is not just about “skills training”: it’s about expanding the mind.

Putting most of Simon Jenkins’s childish rant to one side, there is a serious point buried in it. What Sunak seems to want to achieve is increased levels of basic numeracy which does not require the fluency in trigonometry or differential calculus. The question then is what has gone wrong with the education of a student who hasn’t acquired that knowledge by the age of sixteen? I’d suggest that indicates as significant failing of the pre-16 education system, which is therefore what needs to be fixed. Remedial action in post-16 education is at best a sticking-plaster solution, when more fundamental reform is required.

I feel obliged to point out, however, that here in Ireland, Mathematics is indeed a compulsory subject up to age 18 at least for those students who take the Leaving Certificate. This plays a role here similar to that of GCE A-levels in the UK, but most students take 7 subjects rather than just three. Mathematics is compulsory (as are English and Irish). All subjects can be taken at Ordinary or Higher level in the Leaving Certificate and Mathematics can also be taken at Foundation level (as can Irish).

Last Semester I was involved in teaching Mathematical Physics to a class of about 130 first-year students at Maynooth University. Most of these students are doing our General Science degree, entry to which requires just Ordinary level mathematics and one science subject at Leaving Cert.

The great strength of the Leaving Certificate, which it shares with the International Baccalaureate, is its breadth. I think having English as a compulsory subject for everyone is just as positive as the Mathematics requirement. The concentration of subjects at A-level can work very well for students who know what they want to do after School – as it did with me – but there are dangers involved in pigeonholing students at age 16. A broader education does not put so much pressure on students to decide so young.

Moving to something more like the Leaving Certificate addresses Item 1. at the start of this piece, but Item 2. remains an issue for England as it does in Ireland. In reality the choice for many students is restricted not by the examination system by the lack of specialist teachers in schools, especially (not not only) in STEM subjects. The problem there is that the pay and working conditions for teachers in state schools are not commensurate with their importance to society. I don’t see Sunak showing any inclination to change that situation.

Another Late Start to the Academic Year

Following on from Monday’s post about uncertainty relating to the start of next academic year, it has now been announced that this summer’s Leaving Certificate results will not be released to students until Friday 2nd September and CAO offers will be made on 8th September.

The timeline for admissions at Ireland’s third level institutions will therefore be roughly the same as last year. Although nothing has been officially announced from Maynooth yet, it seems likely that lectures for first-year students will have to commence a week later than returners just as happened last year.

This is not ideal but at least we have some basis on which to start planning. The start of the current academic year was a bit chaotic to say the least but if this year is a repeat of last at least we have some experience on what worked and what didn’t to guide us. And at least I have something reasonably concrete to say at tomorrow’s Open Day.

From the point of teaching, therefore, things are probably going to be a bit less bad than last year, at least in Maynooth. Some universities were due to start teaching on 5th September so they face a delay of 2-3 weeks.

That doesn’t mean however that things will be better for the students. They will have to wait until September until they know which course they will be on, which will cause considerable stress. On a more practical level it means that that new students will have very little time to find accommodation which is in any case in very short supply.

Now that we know the dates we will make the best plans we can for teaching, but for accommodation there doesn’t seem to be any plan at all. A crisis is looming.

Follow @telescoper

Timeline for Admissions

As the current academic year comes to a close – this week sees the final Exam Board at Maynooth University – thoughts turn with some apprehension to the start of the next.

The Leaving Certificate Examinations are taking place now and will finish on 28th June, more-or-less in line with pre-pandemic times, but the results will come out later. Normally these would be released in mid-August, so the university admissions process run by CAO would start then, giving a whole month before the start of teaching term at third-level institutions.

Last year, however, the results were not released until 3rd September 2021, which made it impossible for new students to start their courses at the scheduled time. At Maynooth, for example, first-years started a week later than returning students and missed the usual orientation week. More importantly for the students, there was a last-minute scramble for accommodation that made it impossible for many students to live anywhere near campus.

Until recently I was assuming that this year would be at least as bad as last. Although the examinations have returned to the traditional format this year, the Leaving Certificate results will be delayed again, for two (connected) reasons. One is that the Minister for Education decided that this year’s results would not be lower than last year so some scaling may be necessary and the other is that it is anticipated that more students will make use of the later alternative sittings provided for those unable to take the regular sitting owing to, e.g. ill health. These are connected because if a large number of students avail of the second setting then the scaling business will have to wait until their marks have been processed.

We know that the results will be late, but we don’t know how late they will be which is a major headache. Autumn Term in Maynooth is scheduled to start on 19th September, for returning students, but at the moment we don’t know when first years will start.

Today however there is an indication that results will probably be released in ‘late August’. If that turns out to be the case then the start of next academic year will probably turn out to be no less chaotic than this year was from at least from the point of view of teaching. I’d be relieved at any outcome that is not worse than last year. It’s even possible that teaching in Maynooth can start on 19th September for all students, though I don’t think I would bet on it. Things will be even be trickier at other institutions whose teaching term starts earlier in September.

That still leaves the problem of student accommodation, though. Here I don’t think the timeline for admissions will help much in averting an entirely predictable crisis. Once we know the dates we will make the best plans we can for teaching, but for accommodation there doesn’t seem to be any plan at all.

Follow @telescoper

A Leaving Certificate Applied Maths Problem

The 2022 cycle of Leaving Certificate examinations is under way and the first Mathematics (Ordinary and Higher) were yesterday there’s been the usual discussion about whether they are easier or harder than in the past. I won’t get involved in this except to point you to this interesting discussion based on an archive of mathematics questions, that this year the papers have more choice for students and that, apparently, the first Higher Mathematics paper had very little calculus on it.

Anyway, I was looking through some old Applied Mathematics Leaving Certificate papers, as these cover some similar ground to our first year Mathematical Physics at Maynooth, and my eye was drawn to this question from 2010 about two balls jammed in a cylinder…

I’d add another: does it matter whether or not the cylinder is smooth (as this is not specified in the question)?

Your answers are welcome through the comments box!

Follow @telescoper

Leaving Certificate Matters

On the last day of a very busy first week of the new term I’ve finally cleared a backlog of things and thought I’d take a break for a quick comment about the arrangements for this year’s Leaving Certificate which has implications for this year’s University admissions (amongst many other things).

It has been decided that this year’s Leaving Certificate will revert to the pre-pandemic style of written examinations, but with the important proviso that the overall distribution of marks will be scaled to be no lower than the results last year (when accredited grades were taken into account). In addition the examinations will offer students more choice, so that they have to answer a smaller subset of the questions than in the good old days before Covid.

Last year’s Leaving Certificate results revealed a big increase in scores and consequent changes in offers for many courses. For example, the points required for our Theoretical Physics and Mathematics course (MH206) at Maynooth University went up by about 50 to around 550. Perhaps surprisingly this resulted in the admissions to this course going up by about a factor three. I won’t speculate on the reasons for this here.

The reason for scaling this year’s results is to ensure that students entering third-level education this year are not disadvantaged relative to those who left school last year and took a year out. Also, there is much less information on which to base accredited grades, because of pandemic interruptions.

My concern about the announcement is not so much about the return to formal examinations but on the matter of choice. Take Mathematics for instance. Instead of answering questions in each of 10 sections, students this year will only have to answer questions from six. That means that students can get very high grades despite knowing nothing about 40% of the syllabus. That matters most for subjects that require students to have certain skills and knowledge for entry into University.

In my own discipline (physics) we already have to get new students rapidly up to speed in, e.g., calculus – a difficulty exacerbated this year by the fact that the first Semester was shortened as a knock-on effect of delays in Leaving Certificate process – this is likely also to be a problem for next year’s entry. I can see we’re going to have to do a lot of thinking over the summer about how to deal with this.

Overall I prefer the Leaving Certificate over the UK system of A-levels, as the former gives the students a broader range of subjects than the latter (as does the International Baccalaureate), but I still have doubts about using a simple points count for determining entry into third-level education. Changing a system so deeply embedded is likely to prove difficult, though, so we for the foreseeable future we just have to make the best of what we’ve got.

Follow @telescoper

Leaving Late Again

Yesterday we were told that, as was the case last year, this year’s Leaving Certificate results will be delayed until September (3rd, to be precise). The first round of CAO offers will be made a few days later, on September 7th. All this is about three weeks later than the usual (pre-Covid) cycle of examinations and results. Last year the announcement of a delay was made in mid-July, but now it’s been done in early June.

I’m actually a bit baffled as to why it is going to take so long this year, given that it’s not a new situation with respect to Covid-19 and there will be fewer examinations to mark than in previous years. Universities are able to turn around marks for thousands of students in just a couple of weeks so why the heck will it take so long to get the Leaving Certificate results out? There will be fewer exams to mark than in pre-Covid era too, as some subject marks will be based on coursework.

Here at Maynooth University the start of the academic year 2021/22 is due to take place on Monday 20th September, with Welcome Week starting on 13th September.   Getting everything ready in time for teaching will be a huge challenge because we will only find out very late in the day how many students we have to accommodate in first-year lectures. It is unlikely that timetable will be possible so we face the prospect of having to scrap the orientation events that usually take place in Welcome Week, delaying the start of term, shortening the teaching semester (again) or scrapping the mid-term Study Break.

We’re not able to make many plans in advance because we don’t have much idea in what form teaching will resume because that depends on public health guidelines. Last year, most lecture rooms had their capacity reduced by more than half. Lecturers need to know how many students they have in order to decide how to use the available lecture slots and how to strike a balance between live and online delivery. It’s an even worse situation for laboratory subjects.

The Minister responsible is saying he expects campuses to be more-or-less fully open in September but I’m not convinced that we’re out of the woods yet. Let’s hope that I’m wrong.

If any prospective student is getting worried reading this, I can promise you that we will be doing the best we can to provide the best education we can in whatever circumstances we find ourselves in this September. So please bear with us. We didn’t want any of this any more than you did, but we just have to make the best of it!

UPDATE: We have now been informed that returning students will start as planned on 20th September, while lectures for new students will start a week later, on 27th September, with the previous week being used for some orientation events.

Follow @telescoper

Leaving Out

This morning students across Ireland have been receiving their Leaving Certificate grades. First of all let me congratulate the 2020 Leaving Certificate Class for their success in what has been a very difficult year!

The release of Leaving Certificate results will trigger even more of a scramble than usual for university places through the CAO process. This year things are likely to be very different from previous years as (a) the process is much shorter in duration (students who get into university will be having their first lectures just three weeks from today) and (b) the distribution of grades is unlike previous years because they are based on “calculated grades” rather than examination results. This has led to an increase in top grades across many subjects. Here is a useful summary from the Irish Times:

(I know it looks small but you can click on it to make it legible…)

Note the number of top grades in Mathematics, Applied Mathematics and Physics has gone up because of the general grade inflation and because the number of students taking them has gone up. This is potentially good news for our recruitment here in Maynooth but it’s probably not so simple. For example, it may be that bigger departments elsewhere try to offset the lack of international students this year by recruiting more home students. We’ll just have to wait and see. By the start of next week the picture will probably be clearer.

At any rate, a certain local celebrity is looking forward to welcoming the new students onto campus shortly…

Follow @telescoper

The Year Ahead

Tomorrow sees the release of the 2020 Leaving Certificate results which this year are based on “calculated grades” rather than examination results. It seems that for about 79% of students these grades will be the same as the teacher’s assessment, about 17% will be lower than the teacher assessment and in about 4% of cases it will be higher. It remains to be seen whether the results will create the sort of stir that this year’s A-level results did.

That seems to imply that CAO points will be a bit higher on average than previous years so more students will make the grade for their first choice of course, which may have a significant impact on recruitment.

We’ll find out all about that next week when the details come in. Teaching term starts on Monday 28th September so there’s very little time to get things organised for the new cohort, especially on the Omnibus Science course on which students have a wide range of alternatives from which to pick their first-year subjects.

Next week at Maynooth University we also have our repeat Examination Board (a week later than usual). After that we will have a good idea of how many students will be returning for Years 2, 3 and 4 and how many will not progress.

So soon we will have enough information to fine-tune our teaching plans. These are challenging this year because of the reduced capacity of the rooms we use for lectures and tutorials due to physical distancing. Some rooms are affected more than others – it’s far worse for large lecture theatres than for tutorial rooms – so we have to look at each module separately.

We had a (virtual) meeting of teaching staff in the Department of Theoretical Physics to coordinate the approaches to different modules. Among other things, that showed how very sensitive everything is to numbers of students taking. If a room can take N students then if the actual number taking the class is less than or equal to N then the class can proceed as usual but if it exceeds N, even by just one, then we have to split the class somehow.

Having detailed numbers is essential to sorting all this out but students can change modules during the first few weeks of teaching, we’re likely to be reorganising as we go along.

All this causes multiple headaches but, despite the extra complications this year, I’m looking forward to seeing the students on campus again. I haven’t given a ‘proper’ lecture since March 12th.

I was so busy last week, grappling with these and other matters, that I missed the fact that I took over as Head of Department on 1st September 2019, a year ago last Tuesday. Little did I know what I was letting myself in for…

Follow @telescoper

The U-turn and After …

One of the many things that Winston Churchill never said (referring to Americans) is that they “…will always do the right thing – after exhausting all the alternatives”. Yesterday the UK Government performed a U-turn on its approach to A-level results but only after extensive protests and after causing immense stress to a great many students. All of this could have been avoided had the Secretary of State for Education bothered to look at the results of the downgrading algorithm. This morning he said that he “wasn’t aware” of what the outcomes would be and tried to put the blame on OfQual. Well, it’s actually his job to be aware of these things and that statement shows he’s not doing his job.

While many students will be mighty relieved that their official A-level grades will go up, that won’t be the end of this fiasco. Many students will find that their places have been already been filled through last week’s clearing process. The Government has lifted the number cap on places in imposed earlier this year, but that won’t help many departments, especially those in the sciences, who have severe constraints on, e.g., laboratory capacity (more so with social distancing in place).

I feel very sorry for friends and former colleagues in UK universities having to deal with this shambles. The Government will be quite happy that it has managed to throw this particularly hot potato into the hands of admissions tutors across the land. Ministers will be hoping that whatever blame now accrues will be attributed to universities being “inflexible” when it is entirely down to incompetence elsewhere. As always it’s the front-line staff who will have to deal with it, as if their job was not stressful enough having to deal with Covid-19.

Meanwhile, here in Ireland, the Government’s plan for “standardisation” of this year’s Leaving Certificate results looks alarmingly similar to the failed approach tried – and subsequently abandoned – in the United Kingdom. Minister for Education Norma Foley has been making statements about the accuracy and reliability of her Department’s plans that sound eerily similar to those issued by officials across the Irish Sea. I hope that I’m wrong about this – and that there’s some frantic activity going on behind the scenes to change the approach ahead of the release of this year’s Leaving Certificate grades (due on September 7th) – but I have a feeling that we’re going to see yet another slow-motion car crash. It wouldn’t be the first time that, having observed something truly shambolic happening in the UK Education system, an Irish Government then proceeds to do exactly the same thing…

Follow @telescoper

Examination Shenanigans

So here I am in my office while the first batch of our repeat examinations gets under way here in Maynooth. They seem to have started correctly so I’ve taken a break to have a cup of coffee and catch up on the news.

I find that examinations seem to be making headlines in the United Kingdom. First there was a to-do and a hoo-ha in Scotland that resulted in school examination results that had been downgraded being upgraded again. The downgrading involved using some sort of statistical model to `correct’ teacher-assigned grades and coursework but this model apparently generated significant anomalies.

Then, not to be outdone by the Scots, the English government has announced that estimated A-level grades, presumably obtained by a similar process to that deployed in Scotland, were to be upgraded too. Or not. It seems they will get the original grades but be able to appeal the results.

Writing in today’s Daily Telegraph, presumably without irony, Gavin Williamson explains the decision not to upgrade A-level results automatically:

Increasing the A Level grades will mean a whole generation could end up promoted beyond their abilities.

Gavin Williamson wrote that. Gavin Williamson.

Universities in the UK receive A-level results a few days before the students in order to make admissions decisions, but this year the results students eventually receive may differ from those the universities got. I can imagine the chaos this is causing behind the scenes.

If I understand correctly the new `Triple Lock’ on A-level results means that a student’s grade will be whichever is the highest of:

• their mock exam result;
• the grade estimated by their teacher;
• an A*.

(OK, I made up that last bit.)

Some people think this approach might lead to grade inflation, but I imagine the authorities are less concerned about that than they are by the prospect of getting sued.

Another issue with the downgrading/upgrading situation is that students who took the International Baccalaureate (IB) and have received algorithmic grades have not had their grades increased, which seems to put them at a disadvantage with respect to students who took A-levels and may cause them to miss out on UK university places.

Meanwhile, here in Ireland, we await the School Leaving Certificate results. These are not due until 7th September but I think the plan is to moderate them as in the United Kingdom. Delaying these results gives Ireland the chance to learn from the UK but whether the process will end up being any fairer here is anyone’s guess!

Follow @telescoper