Maths - John C. Kirk
Feb. 12th, 2006
01:44 am - Maths
Here's something that the mathematicians in the audience may be able to help me with, particularly my younger friends (i.e. the people who are more familiar with the current syllabus)...
Basically, I'm thinking about doing an A level in Further Maths, so I was wandering around Blackwells earlier to look at their selection of textbooks, but I was a bit confused about which ones would be useful. That's partly because I kept seeing "Advanced Maths" and thinking "Aha!", then realising "Oh, no, 'Advanced' just means the 'A' in 'A Level'...". I found one book dealing with pure Maths up to the required level, but that was an all-inclusive guide for the normal AS/A levels too. Admittedly, I no longer have my old school textbooks, but I do have my notes, so I don't think I need much of a recap on those concepts.
At this point, a bit of background may be useful.
I was pretty good at Maths when I was at secondary school, so I took my GCSE a year early (and got an A), then went on to do an A/O level in Additional Maths in my 5th year (where I got another A). I carried on with Maths to A level, and I would have liked to do Further Maths as well. Unfortunately, the policy at the time (which may have changed since) said that you could only do that as part of a designated group of four courses: Maths, Further Maths, Physics, and Chemistry. My anosmia meant that I couldn't do Chemistry (or at least, I was advised against it for safety reasons and I didn't have any burning desire to fight that), so that grouping was out, and I wound up doing Maths, Latin, and English Literature instead. The "single Maths" A level had three sections: pure, statistics, and mechanics. Everyone did pure, and then we were automatically assigned to either stats or mechanics for the other half of the course, depending on our other A levels - if you took science subjects then you did mechanics, whereas if you took arts subjects then you did stats (so that's what I did). AS levels were around in those days, but it wasn't like nowadays where everyone does the AS en route to the A level; the attitude was that if you were going to get an A level then you didn't need the AS level too. I'm not even sure if they were available in every subject - the only one I did was in Computing, which was a fourth subject that I took for one year (I failed it with an "N").
When I left school in 1992, my original degree plans had fallen through (I wanted to study Law and become a barrister), so I went through UCCA clearing. (This predates UCAS, i.e. it was UCCA for universities and PCAS for polytechnics.) My A level results were A/C/C, which weren't brilliant, but the A was in Maths, and it had generally been a bad year for Maths results, so I was able to get into the Maths degree at Durham.
The thing is, I didn't start the degree because this was really what I wanted to do with my life, or even because I was particularly interested in the subject. It was simply a case that this got me into university, and I'd always found the subject very easy at school, so I figured that it would do until I sorted out something better. I had a vague idea of doing a Physics A level in my spare time, then doing a one year conversion course to Physics after graduation, and becoming a rocket scientist, but this wasn't based on any kind of carefully researched career plan!
What I actually found was that the first year was a lot harder than I'd expected it to be. I've mentioned "elite syndrome" before, but this was the first time I'd really encountered it. Whereas I'd been at the top of my class at school, I was now in a lecture hall with a hundred other people, all of whom had been at the top of the class in their respective schools. Since we had different backgrounds, the idea was to get us all up to speed within the first term or so. That basically meant that if you'd already done Further Maths at A level then it was probably quite easy, because it was just recapping what you already knew, whereas if you hadn't then it was quite an intensive course. I remember someone telling me that the A/O course was about one quarter of the A level syllabus, which implied that the A level course was moving at twice the speed of the A/O course. (I don't know how the A/O related to GCSE.) Anyway, there was a similar principle here, where a two year course was condensed into one term. At the same time, we all did stats and mechanics, so in my case I was starting mechanics from scratch.
Meanwhile, I was doing Computing as a subsidiary course, to make up my quota of lectures. I mainly chose this on the grounds that I liked computers, even though I wasn't any good at the subject. The surprise was that I suddenly got to grips with it; for whatever reason, I responded a lot better to the teaching at university than I had to the teaching at school. (I'm trying to avoid blaming other people for my failings here.)
Mind you, one thing that has stuck in my mind from the Maths tutorials is one of the homework assignments for probability. I don't have the relevant piece of paper to hand right now (I may dig it out later), but I'd taken a brute force approach to solving a problem, by churning out several pages of permutations (by hand). I eventually got bored, and wrote "etc." or something at the end, rather than doing the whole lot, but my tutor wasn't impressed, so he wrote a note on it saying "You're at university now - don't waste time on stupid things like this." In other words, "Grow up!" That's never a nice thing to hear, but it was a valid criticism, so I'm grateful to him for saying it - that gave me a kick up the arse that I needed. As I say, that's stuck in my mind, so I try to avoid doing comparable things nowadays.
Anyway, it came to the end of the first year, and we had summer exams. I did pretty well in Computer Science, coming out with about 77% overall, i.e. the equivalent of a 1st. By contrast, my Maths results were rather less impressive - in the four different papers I scored 48%, 36%, 24%, and 12% (the pass mark being 40%). I thought it was quite aesthetically pleasing that they were all multiples of 12, but the department didn't share this view; they were particularly miffed about the 12% (in Mechanics). I decided that I'd be better off doing a Computer Science degree (since I'd effectively been doing joint honours for the whole of the first year), and the CompSci department said that they'd be happy to take me, but the Maths department said that I had to pass the course before I could drop it. So, resits ahoy... I didn't have to retake the 48% paper, but I did have to do the other three, and I scraped through on something like 40.5%. After that, I transferred to CompSci, and I've been working with computers ever since.
A few years ago, I decided to do a part-time Physics A level, as part of my masterplan to get onto a postgrad course in computing, so I did that from 2001-2002. This was effectively one day a week (Tuesday mornings and Friday afternoons), and it was an intensive course (one year rather than two), so we did the AS exams in January and the A2 exams in June. I wound up with an A, which I'm quite pleased with, although it was surprisingly easy. I had to work for it, but I do wonder whether I'd have been better off doing this when I was 16. I suspect that either the exams have got easier (the perennial "dumbing down" debate), or it was just that I was used to working at a faster pace at university so it seemed easier by comparison. I do remember one of my classmates saying "Spot the university student" when he saw that I was scribbling away in class, producing at least twice as many notes as the people near me!
Anyway, I'm now interested in boosting my skills a bit. That's partly because I'd like to clear the blot from my record, and prove to myself that I can actually understand this subject, and I'm hoping that mechanics will be easier now that I've done some more Physics. And it's partly because it would be nice to say "I have 3 As at A level", even if that's slightly misleading (by implying that I got them all when I was 18). My A level results aren't entirely relevant nowadays (since I have an MSc), but some people still pay attention to that. For example, my current company's advice to applicants is "Please send your CV (including 'A' level grades and degree class) and a well-presented covering letter". And I'm guessing that universities pay even more attention to this, if I do ever go for a PhD place somewhere.
I'm also slightly concerned about the recent trend of "Ebay results", i.e. A+ and A++; leaving aside the question of whether the exams have been dumbed down, I do think that there's a risk of these new grades devalueing my existing result, since people would look at it and say "Oh, only an A, you weren't good enough for a higher grade then". It would be nice if they could retroactively re-score old exam results to fit the new system, but I suppose that's not really feasible.
At this point, I'm not intending to take time off work again (like I did before), but I'd consider doing some kind of evening/weekend course, if I could fit it around my other commitments. Alternately, I'd be happy to do self-study from books, and then turn up for the exam later, if I could find some suitable guides. I had a look at a mechanics textbook earlier, and the contents page looked very similar to my Physics A level (e.g. equations of motion). For anyone who's done both, how much overlap is there? I still have my first year notes from Durham (although I've sold most of the textbooks), so I'm guessing that they ought to be relevant, although given the trouble I had understanding them before, I'd probably benefit from an introductory guide.
I was also a bit confused by the range of modules out there, e.g. for "Decision Maths", and I haven't found anything useful on the web. There wasn't much info on the MEI site, and the FM Network is a bit more promising, but even that doesn't say much. I'm assuming that Further Maths is split into AS and A2. Are there pre-requisites, e.g. you have to do stats/mechanics in the normal Maths A level before you can do them in Further Maths? Do you do both? I also have no idea about the relative merits of A level vs IB vs GNVQ, although I get the impression that IB may be the best.
As a side note, I did notice an odd discontinuity in the BBC "Have Your Say" topics recently. First they had one about "Are graduates employable?" (employers being unhappy with graduates), so lots of people said "Well yes, that's because of all these useless degrees in golf etc." Then they had one about student skills worsening (universities being unhappy with the intake of students), and the prevailing theme of the comments was "Well yes, that's because universities have maintained high standards, and it's the schools that are dumbing down!" So, best not to pay too much attention to any of those debates, I think.
Anyway, thanks to anyone who's actually read this far, and any comments are welcome.